Continuous fiber path optimization method and device in additive manufacturing

Abstract

The embodiment of the invention provides a continuous fiber path optimization method and system for additive manufacturing, electronic equipment, a computer readable storage medium and a computer program product. The continuous fiber path optimization method for additive manufacturing comprises the following steps: generating a fiber path based on a stress field of a part comprising continuous fibers, and parameterizing the fiber path based on a B spline; solving the finite element model of the fiber with the B spline parameterization to obtain the mechanical property of the part; and determining a gradient of the mechanical properties relative to the control points of the B-spline parameterized fibers, and optimizing the fiber path based on the gradient.

Description

TECHNICAL FIELD

[0001] Embodiments of the present disclosure relate to the field of composite structure optimization methods. Specifically, to a continuous fiber path optimization method in additive manufacturing, a continuous fiber path optimization method system in additive manufacturing, an electronic device, a computer readable storage medium, and a computer program product. BACKGROUND

[0002] Additive manufacturing of continuous fibers can control local material distribution and mechanical properties. This local control is achieved through fiber path generation and optimization, which is one of the important problems in continuous fiber additive manufacturing. Conventional fiber path generation and optimization methods mostly try to fill the topologically optimized part or align the fiber with the maximum stress direction, which can lead to suboptimal solutions of fiber path generation and optimization or make the computational load of the fiber path generation and optimization process too large. SUMMARY

[0003] Embodiments of the present disclosure provide technical solutions that can at least partially solve the above problems or other problems in the art.

[0004] In a first aspect, embodiments of the present disclosure provide a continuous fiber path optimization method in additive manufacturing, the method comprising: generating a fiber path based on a stress field of a part comprising continuous fibers, and parameterizing the fiber path based on B-splines; solving a finite element model with the fiber parameterized by B-splines to obtain mechanical properties of the part; and determining gradients of the mechanical properties with respect to control points of the fiber parameterized by B-splines, and optimizing the fiber path based on the gradients.

[0005] In some embodiments of the present disclosure, the mechanical properties include at least one of stiffness, mass, stress, strain, compliance, natural frequency, modal shape of the part.

[0006] In some embodiments of the present disclosure, the method further comprises: constructing a potential function, wherein a gradient of the potential function characterizes distances between the continuous fibers and distances between the continuous fibers and boundaries of the part; and using the potential function as a manufacturing constraint in the process of optimizing the fiber path based on the gradients.

[0007] In some embodiments of the present disclosure, solving the finite element model with the fiber parameterized by B-splines comprises: constructing the finite element model; determining fiber reinforced elements in the fiber parameterized by B-splines; and constructing the finite element model with the fiber parameterized by B-splines based on fiber distribution in the fiber reinforced elements and the finite element model.

[0008] In some embodiments of the present disclosure, determining the fiber reinforced unit in the B-spline parameterized fiber comprises: determining candidate units of fiber reinforcement in the B-spline parameterized fiber by a convex hull of the control points; and constructing a semi-analytical intra-cell fiber probability function to identify the fiber reinforced unit from the candidate units, wherein the semi-analytical intra-cell fiber probability function characterizes the intersection relationship between the candidate unit and the B-spline parameterized fiber.

[0009] In some embodiments of the present disclosure, constructing the semi-analytical intra-cell fiber probability function comprises: constructing a semi-analytical relationship of the length of the fiber in the cell, the direction of the fiber in the cell and the control points.

[0010] In some embodiments of the present disclosure, solving the finite element model with the B-spline parameterized fiber to obtain the mechanical performance of the part comprises: establishing a stiffness and mass matrix based on the finite element model; determining the increment of the stiffness and mass matrix of the fiber reinforced unit based on the fiber distribution; and combining the increment with the stiffness and mass matrix into a global matrix, wherein the global matrix characterizes the mechanical performance of the part.

[0011] In some embodiments of the present disclosure, the matrix of the part comprises: at least one of polylactic acid, acrylonitrile-butadiene-styrene copolymer, polyamide, polyether ether ketone and polyvinyl alcohol.

[0012] In some embodiments of the present disclosure, the continuous fiber comprises at least one of carbon fiber, basalt fiber, glass fiber and aramid fiber.

[0013] In a second aspect, embodiments of the present disclosure provide a continuous fiber path optimization system in additive manufacturing, the system comprising: a fiber path generation unit configured to generate a fiber path based on a stress field of a part comprising continuous fibers, and based on a B-spline parameterized fiber path; a finite element unit configured to solve a finite element model with the B-spline parameterized fiber to obtain the mechanical performance of the part; and an optimization unit configured to determine the gradient of the mechanical performance with respect to the control points of the B-spline parameterized fiber, and to optimize the fiber path based on the gradient.

[0014] In a third aspect, embodiments of the present disclosure provide an electronic device, comprising: a processor; a memory communicatively coupled with the processor; wherein the memory stores instructions executable by the processor, and the instructions are executed by the at least one processor to enable the at least one processor to implement the continuous fiber path optimization method in additive manufacturing as described in any implementation manner of the first aspect when executed.

[0015] In a fourth aspect, an embodiment of the present disclosure provides a non-transitory computer-readable storage medium storing computer instructions for enabling a computer to implement the continuous fiber path optimization method in additive manufacturing as described in any implementation of the first aspect when executed.

[0016] In a fifth aspect, an embodiment of the present disclosure provides a computer program product comprising a computer program for enabling a processor to implement the continuous fiber path optimization method in additive manufacturing as described in any implementation of the first aspect when executed.

[0017] The details of one or more implementations of the subject matter of this disclosure are set forth in the accompanying drawings and the description below. Other features, aspects, and advantages of the subject matter will become apparent from the description, the drawings, and the claims. BRIEF DESCRIPTION OF DRAWINGS

[0018] Some example embodiments of the present disclosure will hereinafter be described in conjunction with the accompanying drawings. These drawings are provided for illustrative purposes only and are not intended to limit the claimed technology, in which: Figure 1 A flowchart of a continuous fiber path optimization method in additive manufacturing provided by an embodiment of the present disclosure; Figure 2 A structure and working process diagram of a finite element model with B-spline parameterized fiber according to an example embodiment of the present disclosure; Figure 3 A diagram of discretizing a region using three-node triangular elements according to an example embodiment of the present disclosure; Figure 4 A diagram of identifying fiber paths in an element by an intra-element fiber probability function according to an example embodiment of the present disclosure; Figure 5 A case diagram of a fiber path passing through an element according to an example embodiment of the present disclosure; Figure 6 A diagram of a potential function according to an example embodiment of the present disclosure.

[0019] Figure 7 A diagram of a gradient-based B-spline fiber path optimization working process according to an example embodiment of the present disclosure; Figure 8 A block diagram of a continuous fiber path optimization system in additive manufacturing provided by an embodiment of the present disclosure; and Figure 9 A schematic block diagram of an example electronic device for implementing an embodiment of the present disclosure. DETAILED DESCRIPTION

[0020] For a better understanding of the present disclosure, various aspects of the present disclosure will be described in greater detail below with reference to the accompanying drawings. It is to be understood that the detailed description is merely descriptive in nature and is not intended to limit the scope of the disclosure in any way. Throughout the specification, like reference numerals refer to like elements. The expression "and / or" includes any and all combinations of one or more of the associated listed items.

[0021] It should be noted that the expressions first, second, and so on in the present specification are merely used to distinguish one feature from another feature, and do not indicate any limitation on the features. Thus, the first item discussed below can also be referred to as the second item without departing from the teachings of the present disclosure.

[0022] It should also be understood that expressions such as "include", "including", "have", "has", "contain" and / or "containing" and the like are open-ended terms that are used to mean that there are other items or components that are not listed in the specification, but that are still included in the scope of the present disclosure. In addition, "exemplary" is intended to mean an example or illustration.

[0023] Unless otherwise defined, all terms used in the present disclosure, including technical terms and scientific terms, have the same meaning as commonly understood by one of ordinary skill in the art to which the present disclosure belongs. It should also be understood that terms, such as those defined in a generally used dictionary, should be interpreted as having a meaning that is consistent with their meaning in the context of the relevant art and should not be interpreted in an idealized or overly formal sense unless expressly so defined in the present disclosure.

[0024] It should be noted that the embodiments and features in the present disclosure can be combined with each other as long as there is no conflict. In addition, the specific steps included in the method described in the present disclosure are not necessarily limited to the order described unless explicitly limited or contradicted by the context. The present disclosure will be described in detail below with reference to the accompanying drawings and in conjunction with the embodiments.

[0025] Continuous fiber-reinforced parts are widely adopted in aerospace, automotive, energy, and sports applications due to their light weight, high stiffness, and high strength. Fiber-reinforced parts are generally categorized into standard parts (e.g., laminates and tubes) and parts with complex geometries. For standard parts, traditional manufacturing methods such as pultrusion, fiber winding, and co-weaving can achieve efficient and economical mass production. For parts with complex geometries, methods such as hand layup, resin transfer molding, spray deposition, and vacuum bag molding are commonly used. However, these traditional methods for manufacturing parts with complex geometries often require high-cost molds, which limits their application in small-batch, customized production. In addition, these methods produce consistent fiber directions, which do not fully utilize the anisotropic properties of fibers. Recently, there has been a trend towards customizing the regional and directional mechanical properties of parts. This trend towards optimizing the reliability, strength, weight, and cost of parts requires non-uniform fiber distribution and direction to achieve more complex and interrelated goals, such as enhancing stiffness / strength, reducing fiber usage, customizing frequency response, etc. To meet these goals, local fiber path control can generally be achieved through robot-based fiber tow steering or material extrusion (MEX) of continuous fibers. Fiber tow steering is desirable for high fiber volume fraction, large-scale, and low-curvature structures (e.g., aircraft fuselages), but can encounter problems such as discontinuity, delamination, and wrinkling. On the other hand, MEX of continuous fibers has higher fiber path design freedom and performs better under high-curvature fiber paths. Compared to MEX of short fibers, continuous fibers have been shown to significantly enhance the mechanical properties of fiber-reinforced parts due to their continuity and controllable fiber direction.

[0026] Although the freedom of continuous fiber path is high in MEX processes, the generation of fiber and matrix print paths remains challenging. Unlike the generation of print paths from simple shape and fill ratio information in traditional MEX processes, the generation of fiber paths requires a holistic optimization of the mechanical behavior analysis of inhomogeneous fiber distribution and orientation. Most commercial MEX print path software does not support such fiber path optimization. To fill this gap, many researchers have focused on fiber path generation and optimization methods that consider the mechanical performance of the part. Fernandez et al. developed a bias and equidistant method for filling fiber paths in topologically optimized homogeneous parts without fiber reinforcement. Another mainstream method is to generate fiber paths by maximizing the alignment of fiber paths with the stress field of a homogeneous part without fiber reinforcement. The load-dependent path planning method introduces an optimization problem to align the fiber and local load direction. Liu et al. proposed a wave projection function to design fiber path filling in the stress field. Chen et al. converted the stress vector field into a scalar field to directly calculate the distributed fiber path in the design space. However, these methods are based on the stress field of a homogeneous part without fiber reinforcement and do not consider the contribution of fiber reinforcement to the stress field. Notably, the stress field of a fiber-reinforced part and a homogeneous part can be significantly different. Therefore, to further achieve various fiber path design goals, the stress field of a fiber-reinforced part needs to be considered.

[0027] The challenge with fiber-reinforced parts is that a set of fiber paths needs to be calculated, which is also an optimization variable. Therefore, an iterative optimization method is usually used to solve this problem. Suzuki et al. constructed a finer orientation by iteratively calculating the stress tensor and stiffness decay vector. Kenjiro et al. adopted a similar idea while introducing a regional fiber volume ratio to represent the distance between fiber paths. Hou et al. introduced fiber trajectory points to extract fiber paths from the stress field of each iteration; the closest point on the extracted path determines the orientation and distribution of the fiber inside the element. Papapetrou et al. introduced a finite element model with fiber orientation and density variables in the optimization, and then filled the topologically optimized part with different continuous fiber laying strategies (i.e., bias, equidistant, streamlines). These methods consider the contribution of fibers to the stress field, but there are two main problems. First, fibers are discretized in the mesh, so a large amount of computation is needed to determine the relationship between fibers and mesh elements. This computation can be time-consuming and cause the optimization process to be non-smooth, resulting in a local optimal solution. Second, this type of method usually requires multi-stage optimization (e.g., generation of optimal stress field and fitting of fiber paths); multi-stage optimization can lead to suboptimal solutions.

[0028] To solve these problems, the embodiments of the present disclosure propose a continuous fiber path optimization method in additive manufacturing, which parameterizes the fiber path with B-spline and combines a customized finite element model (FEM) with continuous fiber contribution.

[0029] It should be noted that B-spline, also known as basis spline, is a linear combination of B-spline basis curves and a generalization of Bezier curves. B-spline can be understood as a non-uniform rational B-spline with end-point property, continuity, convex hull property and locality.

[0030] For example, the end points of a B-spline curve are closely related to the control points, and the position of the end points of the curve can be changed by adjusting the control points; the B-spline curve can generate a smooth curve with high-order continuity; the B-spline curve is located in the convex hull of its control points, so the shape of the curve is constrained by the control points; the specific part of the B-spline curve can be adjusted without affecting the entire B-spline curve, where the control points are a set of points that define the B-spline curve, which not only determines the overall shape of the curve, but also flexibly changes the local properties of the curve by adjusting its own position. In the semi-analytical gradient derivation of the finite element model, the control points can be used as variables in the optimization process to optimize the fiber path by adjusting their positions.

[0031] Optionally, the convex hull is a geometric concept that can be understood as the smallest convex polygon or convex polyhedron that contains all the points in a given point set. For B-spline, the convex hull property means that a complex fiber path can be divided into multiple simple, convex segments or regions (hereinafter referred to as segments), which are easier to describe and process.

[0032] Figure 1 A flowchart of a continuous fiber path optimization method 1000 in additive manufacturing is provided for the embodiments of the present disclosure.

[0033] As shown in Figure 1 The continuous fiber path optimization method 1000 can include the following steps: S1: generating a fiber path based on the stress field of a part including continuous fibers, and parameterizing the fiber path based on B-spline.

[0034] S2: solving a finite element model with B-spline parameterized fibers to obtain the mechanical properties of the part.

[0035] S3: determining the gradient of the mechanical properties with respect to the control points of the B-spline parameterized fibers, and optimizing the fiber path based on the gradient.

[0036] The following will be described in conjunction with Figures 1 to 7The detailed description of each step of the continuous fiber path optimization method 1000 is described in the specific process in the embodiments of the present disclosure.

[0037] It should be noted that, for the convenience of understanding, the steps S1 to S3 are described together in the embodiments of the present disclosure. However, those skilled in the art can understand that the execution order of the steps S1, S2 and S3 is not limited by the present disclosure, and the characteristics, implementation principles and technical effects obtained by adopting any order to complete the steps S1, S2 and S3 are similar.

[0038] Figure 2 The structure and working process diagram of the finite element model with B-spline parameterized fibers according to the exemplary embodiments of the present disclosure. Figure 3 The diagram of discretizing the region Ω using three-node triangular elements according to the exemplary embodiments of the present disclosure. Figure 4 The diagram of identifying the fiber path in the element by semi-Analytical Fiber-in-Element Probability (AFEP) function according to the exemplary embodiments of the present disclosure. Figure 5 The case diagram of the fiber path passing through the element according to the exemplary embodiments of the present disclosure. Figure 6 The diagram of the potential function according to the exemplary embodiments of the present disclosure. Figure 7 The diagram of the working process of the gradient-based B-spline fiber path optimization according to the exemplary embodiments of the present disclosure.

[0039] The following will be described in combination with Figures 2 to 7 The steps S1 to S3 of the continuous fiber path optimization method 1000 are described as follows.

[0040] In the following, the finite element model with B-spline parameterization is described in detail, in which the local mass and stiffness matrices using analytical fiber-in-element probability and B-spline convex hull are derived and discussed. This part also covers the assembly of global mass and stiffness matrices to obtain detailed stresses, strains and compliances under specific loading conditions, as well as the natural frequencies and modal shapes of fiber-reinforced parts. In addition, in some embodiments of the present disclosure, semi-analytical gradients of the finite element model with respect to B-spline control points are derived. These gradients enable gradient-based B-spline fiber path optimization with the help of customized fiber distance functions with potential fields. Alternatively, the finite element model with B-spline parameterization and the gradient-based B-spline fiber path optimization method are also verified by simulation and experiment in the embodiments of the present disclosure.

[0041] Thus, according to at least one embodiment of the present disclosure, a computationally efficient semi-analytical finite element model is established, which is compatible with arbitrary fiber paths by analytically determined intra-cell fiber probabilities. Further, a computationally efficient potential function is developed, which is used to control the distance between fibers and the distance between fibers and boundaries in fiber path optimization. Moreover, a gradient-based B-spline fiber path optimization method is developed using the semi-analytical finite element model with gradients, which is compatible with multiple objective functions including compliance, fiber volume fraction, frequency response, etc., and is verified by numerical and experimental case studies.

[0042] The continuous fiber path optimization method 1000 proposed by the embodiments of the present disclosure aims to establish a finite element model considering continuous fiber paths with B-spline parameterization. By changing the mass matrix and stiffness matrix of the local element, the B-spline fiber path passing through the element provides local reinforcement. The method proposed by the embodiments of the present disclosure encourages iteration and optimization of the fiber path, as it does not require re-meshing of the fiber region and the matrix region. Compared with other high-order, high-fidelity models generated by conventional FEM software (e.g., Ansys, Abaqus, etc.), the FEM model proposed by the embodiments of the present disclosure improves computational efficiency and is more compatible with fiber path optimization.

[0043] Specifically, as shown in Figure 2 , the finite element model workflow with B-spline parameterized fibers is shown in the figure, where the workflow of the green part in the figure includes the establishment of the stiffness and mass matrix in the typical FEM, and the analysis of fiber reinforcement by B-spline parameterization; the workflow of the pink part in the figure includes the identification of fiber-reinforced candidate elements by the convex hull of B-spline, and the analytical probability function for positioning the fiber in each candidate element. Based on the distribution of each fiber in the element, the increments of the stiffness matrix and the mass matrix are obtained. Then, the increments are combined with the initial matrix to form the global matrix.

[0044] Optionally, solving the finite element model with B-spline parameterized fibers can include: constructing a finite element model; determining fiber-reinforced elements in the B-spline parameterized fibers; and constructing a finite element model with B-spline parameterized fibers based on the fiber distribution in the fiber-reinforced elements and the finite element model. This will be described in detail below in conjunction with the drawings.

[0045] As shown in Figure 3 , the two-dimensional (2-Dimensional, 2D) region requiring fiber reinforcement can be a region v . The boundary of this region v is defined as . As shown in Figure 3As shown in the (b) diagram in FIG. 1, in some embodiments of the present disclosure, a three-node triangular element can be used to discretize the region Ω without loss of generality. Alternatively, other types of meshes can also be used to discretize the region Ω, which are not limited in the present disclosure.

[0046] The region Ω can include an isotropic matrix region and a fiber-reinforced region In the isotropic matrix region , the physical properties (e.g., elastic modulus, thermal conductivity, etc.) of the continuous fibers are the same in all directions. Such properties make the behavior of the continuous fibers in all directions predictable and not affected by changes in direction. In the fiber-reinforced region , the continuous fibers can exhibit anisotropy, which makes the fiber material have higher physical properties in certain directions, for example, the strength and stiffness of the continuous fibers become higher, thereby significantly improving the load-carrying capacity and stability of the overall structure of the part including the continuous fibers.

[0047] It should be noted that the embodiments of the present disclosure focus on flexibility minimization and fiber usage optimization, so it can be assumed that the fiber-reinforced part works in its elastic region, and the characteristic size of the mesh is significantly smaller than the achievable radius of curvature of the fiber. These assumptions are widely used in the stiffness calculation of the fiber-reinforced part, such as in the Volume Average Stiffness (VAS) model. Therefore, based on this, the fiber slip at the matrix contact area can be ignored in the following modeling process.

[0048] Define displacement field , Within a triangular element, the displacement field is given by the following formula (1):

[0049] wherein, and are the displacements of the node in the x-axis and y-axis, wherein i are equal to 1, 2 and 3, respectively; is the coordinate of the node .

[0050] The shape function is given by the following formula (2):

[0051] wherein, A can be given by formula (3):

[0052] wherein, the coefficient , and in i are equal to 1, 2 and 3, respectively, and the coefficients , and are obtained by cyclically alternating the indices (e.g., 1→2, 2→3, 3→1) according to the same formula in equation (4).

[0053]

[0054] The displacement field relationship in the e th element is expressed in matrix form as equation (5):

[0055] where is the shape function matrix; and is the nodal freedom, given by equation (6):

[0056] As shown in equation (1), the linear displacement relationship, note that in the triangular element, the strain field is assumed to be constant, regardless of whether it is in the fiber region or the matrix region. The strain can be written as equation (7):

[0057] where is the operator matrix, defined by equation (8):

[0058] Substituting equation (5) into equation (7), the element strain is given by equation (9):

[0059] where is the regular geometric matrix of the triangular mesh. Equations (1) to (9) are the conventional finite element model equations. In other words, equations (1) to (9) implement the step of constructing a finite element model of step S2.

[0060] Unlike the constant strain relationship within the matrix region and the fiber region, due to the significant difference in the constitutive relationship of the matrix and the fiber, the stress field is not consistent within the matrix region and the fiber region, for example:

[0061] where is the elastic coefficient matrix in the isotropic matrix region , and is the fiber reinforced region​ The elastic coefficient matrix in the fiber coordinate system is defined as and the material is isotropic with Young's modulus and Poisson's ratio μ, the elastic coefficient matrix is given by the following equation (11):

[0062] Similarly, in the fiber reinforced region the longitudinal Young's modulus and the transverse Young's modulus are defined as and respectively, and the in-plane Poisson's ratio is defined as where = .

[0063] The shear modulus is defined as and the elastic coefficient matrix is given by equation (12):

[0064] where, as shown in (c) of Figure 3 Fig. 2, θ is the angle between the fiber principal coordinate system and the ground coordinate system , and is the transformation matrix given by the following equation (13):

[0065] The finite element model is established by the virtual work principle. Define the vector set of all node degrees of freedom as q, the node displacement e of the i-th element is made up of the subset of q with selection matrix , for example:

[0066] The total potential Π represented by displacement u, strain ε and stress is given by the following equation (15):

[0067] where, U is the strain energy; is the potential volume force work; is the potential concentrated load work; is the potential distributed load work; is the potential inertial force work; b is the body weight density matrix; p is the concentrated external load applied on the node; is the surface load; and is the shape function matrix evaluated along the surface; ρ is the density of the element, is the time-based second derivative of q. Based on the virtual work principle (e.g., δΠ = 0), the dynamic equation of the finite element model can be written as equation (16):

[0068] where M, K, and F are derived from the summation of all elements, e.g.,

[0069] In other words, the increments of the stiffness and mass matrices of the fiber-reinforced region and the finite element model constructed from equations (1) to (9) are combined to form global matrices.

[0070] where the local mass matrix the local stiffness matrix and the local volume and surface force vectors can be expressed as equations (20) to (22):

[0071] where and are the element volume and surface area where external loads exist; t is the element thickness; , and are the areas of the fiber, matrix, and the entire element. From modal analysis, the k th mode satisfies equation (24):

[0072] where and are the corresponding natural frequency and mode shape. For static analysis, the inertia term in equation (16) is zero, and the finite element model can be simplified as follows:

[0073] The static form is mainly used in the following flexibility analysis and fiber path optimization.

[0074] Thus, by solving the finite element model with the B-spline parameterized fiber, the mechanical performance of the part can be obtained. As an option, the mechanical performance of the part can include at least one of the stiffness, mass, stress, strain, flexibility, natural frequency, and mode shape of the part.

[0075] Although the conventional finite element model formula is easy to calculate, the elastic matrix and mass matrix in the fiber-reinforced region require the area and the direction θTo compute these parameters, a mathematical representation of the fiber path is needed, but such a representation is challenging for optimization because it has infinite degrees of freedom.

[0076] To address this issue, in some embodiments of the present disclosure, B-spline parameterization can be utilized to reduce the degrees of freedom of the fiber, thereby reducing the computational complexity. In other words, after generating the fiber path based on the stress field of the part including continuous fibers, the fiber path can be parameterized based on B-spline.

[0077] Optionally, the stress field of the part can be generated by computer aided engineering (CAE) given the boundary conditions.

[0078] After obtaining the B-spline parameterized fiber, a fiber reinforced element in the B-spline parameterized fiber can be determined. For example, a candidate element of fiber reinforcement in the B-spline parameterized fiber is determined by the convex hull of the control points of the B-spline parameterized fiber; and a semi-analytical intra-element fiber probability function is constructed to identify the fiber reinforced element from the above candidate element, wherein the semi-analytical intra-element fiber probability function can characterize the intersection relationship between the candidate element and the B-spline parameterized fiber. Exemplary embodiments will be described in detail below in conjunction with the drawings and formulas.

[0079] The convex hull property of B-spline divides the fiber path into multiple segments and enables parallel computation, which can reduce the computational load of the intra-element fiber probability function. In addition, as an option, the intra-element fiber probability function can calculate the area and direction of the fiber. These parameters are used to calculate the changes in the local stiffness matrix and mass matrix, so that the fiber reinforced element can be obtained based on the homogenized element in a simplified manner.

[0080] B-spline provides a compact and shape-preserving representation method for curves, which effectively reduces the degrees of freedom compared to direct sampling. Thus, the convex hull property of B-spline divides the fiber path into multiple segments and enables parallel computation, which can reduce the computational load of the intra-element fiber probability function.

[0081] In addition, by operating on a limited portion of the curve through the control points, the overall shape of the curve is not affected, thereby increasing the flexibility of the represented path. In addition, the convex hull of the control points encloses and subdivides the B-spline into multiple segments, providing a local geometric interpretation of the fiber path. A standard B-spline is shown by formula (26):

[0082] wherein ξ is the B-spline curve parameter; is the number of control points; is the ξth control point, and is the ξth normalizedm The B-spline basis function of order is defined as formula (27): is a non-decreasing sequence of real numbers The nodes in the sequence are called node vectors. Assume that inside the enhancement region There are continuous fibers, i Continuous fiber has control points m The B-spline representation of order is represented by the control points , , , where each control point These control points are connected into a control point matrix , the matrix is ​​shown by formula (29).

[0083]

[0084] Therefore, the i A continuous fiber can be expressed as:

[0085] in, It is i is a vector combination of the set of basis functions for each B-spline. Without loss of generality, it is assumed that all B-spline parameterizations have the same order and knot spacing. Therefore, for the same number of control points and knot vectors, the basis functions are the same, for example: exist In the case of Without loss of generality, the intersection relation of fiber elements applies to all fiber paths. In the above formula, the superscript ( i ) to reduce the complexity of the formula.

[0086] In the current framework, the fiber path affects the stiffness and mass matrices through its direction and area within the element according to equations (20) and (21). These quantities usually require the calculation of the intersection of the fiber path with each element. Figure 3 As shown in Figure (c), since the characteristic size of the mesh is assumed to be significantly smaller than the achievable curvature radius of the fiber, the direction within the unit can be expressed as the average value. To simplify the calculation. Based on this assumption, the stiffness matrix in formula (21) is simplified to:

[0087] Therefore, when the fiber paths intersect, the change in the local stiffness matrix is ​​given by the following equation (32):

[0088] where ω is the width of the fiber, is the length of the fiber within the element. Similarly, the mass matrix shown in equation (20) can be simplified to equation (33):

[0089] where, and are the densities of the fiber and the matrix material, respectively. and are the mass matrix and the stiffness matrix variation, respectively, which need to establish their semi-analytical relationship with the control points to establish the gradient of the finite element model.

[0090] Precise calculation of intersection points is usually time-consuming and can produce numerical singularity, which hinders efficient optimization. In addition, the actual fiber width and curvature can bring errors to the simplified geometric calculation. Therefore, the above embodiments of the present disclosure establish a semi-analytical fiber probability function within the element, which describes the intersection relationship between the element and the fiber under the probability framework.

[0091] Optionally, constructing the semi-analytical fiber probability function within the element can include constructing a semi-analytical relationship between the length of the fiber within the element, the direction of the fiber within the element, and the control points of the B-spline parameterized fiber. Thus, introducing the probability function instead of precisely calculating the intersection points of the fiber path and the element can efficiently calculate the contribution of the finite fiber width to the finite element model and its gradient with respect to the control points of the fiber path.

[0092] Consider the vertices , a polygon arranged in a clockwise direction . The discriminant condition of any point c inside the polygon is determined by the following cross product condition:

[0093] where, These binary discriminant conditions help to determine the intersection points of the fiber and the element. These binary relationships in equation (35) are combined into a single fiber probability function within the element, which can be defined as:

[0094] where, according to the given vertices , , approximate the probability of any point c inside the polygon. The product of the binary relationship sigmoid function is replaced to represent the probability. The sigmoid function can be defined as:

[0095] It should be noted that when the sigmoid function tends to positive infinity and negative infinity, c are equal to 1 and 0 respectively. This property combined with the side length and fiber width ω, ensuring that the c When the distance from the edge is at least half the fiber width , and when the point c When on the polygon boundary .

[0096] like Figure 4 As shown, this continuous probability is consistent with the intersection area of ​​physical fibers and cells, thereby improving the smoothness of fiber optimization. The continuity of the fiber probability function within the cell can be further illustrated by the following embodiment, which shows the local fiber length when the fiber path passes through the cell. and stiffness increment changes.

[0097] For example, the movement of the fiber path is determined by Figure 5 The displacement percentage shown by the red arrow in Figure (a) The swept triangular elements are numbered, and the corresponding local fiber length and stiffness increments of these elements are plotted in Figure 5 In Figure (b). In addition, Figure 5 Figure (b) also shows the gradients of two variables, local fiber length and stiffness increment, to illustrate the continuity of the fiber probability function within the element.

[0098] With the help of the fiber probability function within the element, the intersection area of ​​the B-spline curve and the triangle element no longer needs to explicitly calculate the intersection point. For a given set of control points, the B-spline curve length function It is given by the following formula (38):

[0099] in, = d is the derivative of the basis function. e Fiber length within a unit It is given by the following formula:

[0100] From the integral form of formula (38) , the derivative of the curve length is given by:

[0101] The vector representing the connection between the entry point and the exit point is given by the following formula (41):

[0102] This vector defines the average direction of the fibers inside the cell, and is thus given by equation (42):

[0103] Thus, the variables and describe the fiber-cell relationship, and they are determined without explicitly calculating intersection points. Substituting these two values into equations (32) and (34) allows the fiber-reinforced cell to be computed.

[0104] Although equations (39) and (42) provide a way to compute the variables and and their gradients, this computation requires the intra-cell fiber probability of all cells, which is computationally inefficient.

[0105] According to some embodiments of the present disclosure, the convex hull property of B-splines can be used to preliminarily screen out cells that are likely to have an impact on fibers, thereby significantly reducing computational complexity. For example, for a B-spline of order with control points, the fiber path can be decomposed into m segments, where the th segment can be defined by the curve parameter j and is only affected by neighboring control points defined by equation (43). m

[0106]

[0107] More specifically, these segments are limited by the convex hull of , which is defined as . Here, the cell set intersecting with can be efficiently identified. This is achieved in two steps: (i) find all the nodes inside and their associated cell set ; (ii) find the cell set containing the vertices of , which is defined as . The cell set with potential intersections can be shown by equation (44):

[0108] This selection is no longer a probabilistic relationship, so the discriminant condition for an arbitrary point c inside the polygon given by equation (35) is modified as:

[0109] ​This modification ensures that the contribution of the fiber width is taken into account when solving Equation (39). Note that the first j paragraph only affects the cells in which leads to the simplification of Equations (39) and (41) as follows:

[0110] With this convex hull assisted computation of the local stiffness and mass matrix, the overall FEM-BFP (Finite Element Model with B-spline Fiber Parameterization) is summarized in the pseudo-algorithm shown in Table 1.

[0111]

[0112] Table 1

[0113] Gradients can improve the efficiency and speed of optimization in optimization algorithms. In the current FEM-BFP framework with semi-analytical expressions, the gradients of the stiffness matrix and the mass matrix with respect to the B-spline control points can also be conveniently constructed in the implementation described below. In addition, in the implementation described below, to achieve the ideal distance between fibers and between fibers, a semi-analytical potential function with gradients can also be constructed.

[0114] Optionally, the continuous fiber path optimization method in additive manufacturing further comprises: constructing a potential function, wherein the gradient of the potential function represents the distance between the continuous fibers and the distance between the continuous fibers and the boundary of the part; and in the process of optimizing the fiber path based on the gradient, the potential function is taken as a manufacturing constraint condition. Specifically, this will be described below in conjunction with the drawings and formulas.

[0115] The control points of the j convex hull are part of ; their relationship is specified by a selection matrix , for example:

[0116] The gradient of the stiffness matrix increment (as defined in Equation (32)) with respect to the local control points is given by the following Equation (49):

[0117] and the gradient to all control points is specified by the following Equation (50):

[0118] Similarly, the gradient of the mass matrix is given by equation (51):

[0119] Without loss of generality, the gradients apply to all convex hulls. Therefore, to simplify the equations, the superscript j may be omitted from the above equations. From equations (39) and (46), the two partial derivatives and are given by equation (52).

[0120]

[0121] The introduction of the fiber probability function within a continuous element makes possible the convenient calculation of this characteristic With equation (40), equation (53) shows the first term in equation (52):

[0122] While the first term in equation (52) is given by equation (54):

[0123] In addition to the partial derivative , the partial derivative can be calculated by the Chain Rule.

[0124]

[0125] Based on the definition of from equation (31) and from equation (12), the first and second terms in equation (55) can be determined conveniently:

[0126] The directional gradient can be shown by equation (58):

[0127] where

[0128] Using these semi-analytical gradients defined in equations (49) to (60), the gradients of the mass and stiffness matrix increments can be established in relation to the local control points.

[0129] ​In addition to the contribution of fiber paths to the stiffness matrix, manufacturing constraints need to be considered in the optimization process. These constraints include the distance between fibers and the distance between fibers and the part boundary, which need to be reserved enough space to avoid manufacturing defects such as fiber overlap and crossing. On the other hand, the distance between fibers needs to be reduced to enhance the local fiber density and achieve the best reinforcement effect. Therefore, a potential field can be introduced to the fibers, which provides an attractive force at a long distance and a repulsive force at a short distance.

[0130] As shown in Figure 6 , the potential function can be defined as:

[0131] where, is the reference width, is the repulsive force strength, is the attractive force strength, r is the distance between two points, is the dimensionless length parameter of the attractive region. Without loss of generality, the potential function between two fiber paths with control points and can be expressed as:

[0132] These relationships apply to the evaluation of the distance between any two fibers. As shown in equation (65), the control points are connected for ease of calculation of the semi-analytical gradient.

[0133]

[0134] Then, the gradient of equation (62) is given by the following equation:

[0135] According to equation (61), the first term of equation (66) is given by the following expression:

[0136] The second term of equation (66) can be easily calculated according to the norm of the vector, and the third term is given by the following equation (68):

[0137] Similarly, a potential function that only provides a repulsive force can also be introduced between the fiber and the boundary, which is defined as:

[0138] where, is the reference width for the boundary spacing. For fiber paths, the potential function in the direction of the boundary can be expressed as:

[0139] where, is the point of the boundary of the part. Accordingly, the gradient can be expressed as:

[0140] where the first term can be expressed as:

[0141] for the expression of the term shown in equation (62) can be the same, and = N. In embodiments of the present disclosure, by means of these potential functions, a fiber spacing control mechanism for fiber path optimization can be established.

[0142] The optimization of the fiber path aims to enhance the mechanical performance of the part by adjusting the control points of the fibers. Since the optimization problem can encounter non-convex problems, resulting in falling into local minimum, the influence of the initial position of the control points on the gradient-based optimization method needs to be considered. Considering the control points located in the low stress region, the gradient of the stiffness matrix will have a gentle slope, and the trend of fiber movement can be negligible. Therefore, the initial position of the control points should be close to the high stress region. There are many methods to generate the initial fiber path. Some embodiments of the present disclosure adopt a stress-based method, such as the Principal Stress Direction (PSD) method, because it can directly align the fibers with the load transfer region, thereby improving the computational efficiency. The overall optimization is defined as:

[0143] where the main objectives are the total compliance , the fiber length , and the natural frequency k of the th mode; , and are the optimization weights of each individual term. The function refers to a user-defined penalty function for the structural natural frequency. Although the equations for and are given, the natural frequency is calculated through eigenvalue analysis and cannot provide a gradient formula. For these cases, the numerical gradient related to this frequency term can be used.

[0144] In addition to these objectives, it is noted that the number of fibers in this optimization problem can be freely chosen. This can be done by adding a term to the objective function that penalizes the number of fibers An additional integer optimization variable is set to be implemented, resulting in a mixed integer optimization problem. In a practical setting, the number of fibers can be determined by a trade-off study using computationally efficient fiber path generation methods (e.g., principal stress direction method, etc.). The inter-fiber potential and the fiber-to-boundary potential are constraint conditions in the manufacturing process to control the distance of the print tool path. Based on the FEM-BFP discussed in Section 2 and the gradient evaluation in Section 3, the optimization problem in Equation (74) can be conveniently solved by various optimization algorithms, which can include the truncated Newton algorithm, the conjugate gradient algorithm, the quasi-Newton algorithm, etc. Since these algorithms are used for unconstrained optimization, and are added as soft constraints to the objective to control the inter-fiber spacing. The overall process of the Gradient-based B-spline Fiber path Optimization (GBFO) is shown in Figure 7 The process iteratively evaluates the objective function by implementing the FEM-BFP. The contribution of each fiber path is solved and will be added to solve the mass and stiffness matrices and their gradients. The objective function adds the constraint of the solution and the inter-fiber spacing potential. Once converged, the optimized control points and the optimized part FEM are output for manufacturing.

[0145] In addition, both the FEM-BFP and the GBFO proposed by the embodiments of the present disclosure can be run on a desktop computer. Alternatively, the matrix material and the continuous fiber can be selected as Polylactic Acid (PLA) and carbon fiber, respectively, which can be, for example, Continuous carbon fiber reinforced thermoset polymer, where Table 2 shows the mechanical properties of the above-mentioned materials.

[0146] In addition, the continuous fiber reinforced part can be manufactured by a printer, where the printer can form the continuous fiber reinforced part based on the MEX manufacturing process of the continuous fiber.

[0147] After the fiber path optimization of the continuous fiber reinforced composite material part by the embodiments of the present disclosure, tensile and bending tests can be performed by a universal testing machine. In addition, an impact hammer modal test can also be performed by an impact hammer and a vibration analyzer.

[0148]

[0149] Table 2

[0150] Further, in some embodiments of the present disclosure, to validate the FEM-BFP method, two representative samples, for example, a dumbbell-shaped sample with four fiber paths and a ring-shaped sample with four fiber paths, were designed and fabricated, where the dumbbell-shaped sample with four fiber paths can be used for tensile testing and the ring-shaped sample can be used to validate the modal response prediction of the FEM-BFP.

[0151] Table 3 shows the comparison of the test data of the samples manufactured by the FEM-BFP method provided according to the embodiments of the present disclosure and the test data of the Abaqus simulation.

[0152] As shown in Table 3, in this embodiment, the FEM-BFP method provided according to the embodiments of the present disclosure and the Abaqus simulation reached a similar level of accuracy, and the FEM-BFP method used significantly fewer elements. The number of elements in Abaqus has been adjusted to the convergence point. In addition, the calculation time of the FEM-BFP method is also less than Abaqus, and additional gradient information about the fiber control points is provided.

[0153]

[0154] Table 3

[0155] Further, in some embodiments of the present disclosure, a plurality of ring-shaped samples were printed using the PSD method and the GBFO method. As shown in Table 4, the parts using the GBFO method have higher stiffness and strength than the PSD method, and the amount of fiber used also becomes less.

[0156] In addition, the FEM-BFP method is relatively accurate in estimating the stiffness of the part, with a prediction error of 6.8% and 0.9% for the PSD and GBFO fiber paths, respectively. The initial fiber path is generated by the PSD method, which can be considered close to the optimal solution. Therefore, the enhancement effect from the initial fiber path is not as significant as the optimization result of the unoptimized path. In the tensile test, the GBFO method increased the stiffness by 17.3% and the strength by 8.1%, highlighting the effectiveness of the proposed method.

[0157]

[0158] Table 4

[0159] Thus, the accuracy and effectiveness of the semi-analytical finite element model method with B-spline parameterized fibers are verified by comparing with the simulated cases using finite element analysis software Abaqus, and the comparison experiments include tensile tests and impact hammer modal tests. With the semi-analytical finite element model with B-spline parameterized fibers and its probabilistic framework, the gradients of the stiffness matrix and the mass matrix with respect to the control points of the B-spline fibers are conveniently established, so as to realize the gradient-based fiber path optimization method with the objective of minimizing the compliance and the fiber usage. In addition, the additional constraints on the distances of the fibers to the fibers and the distances of the fibers to the boundary are introduced into the optimization through the continuous potential function with explicit gradients. The results of the gradient-based fiber path optimization method provided by the embodiments of the present disclosure are compared with the principal stress direction method, and the fiber path generated by the method provided by the embodiments of the present disclosure is aligned with the maximum stress direction. In the simulation and the experiment, the fiber parts generated by the gradient-based fiber path optimization method show the characteristics of the stiffness enhancement and the less fiber usage.

[0160] The embodiments of the present disclosure solve the continuous fiber path optimization problem in additive manufacturing by establishing the semi-analytical finite element model with B-spline parameterized fibers and the gradient-based fiber path optimization method. The semi-analytical finite element model with B-spline parameterized fibers defines the probabilistic distribution of the fibers in the element, thereby bypassing the computationally intensive determination of the intersection points of the fibers and the element. The probabilistic distribution and the convex hull of the B-spline make it easy to evaluate the increments of the local stiffness and mass matrices. These increments are combined to obtain the global stiffness and mass matrices, so as to be able to effectively predict the load response, the stiffness, the natural frequency and the like.

[0161] Figure 8 A block diagram of a continuous fiber path optimization system 100 in additive manufacturing is provided by the embodiments of the present disclosure.

[0162] As shown in Figure 8 Another aspect of the embodiments of the present disclosure provides a continuous fiber path optimization system 100 in additive manufacturing. The continuous fiber path optimization system 100 in additive manufacturing can include a fiber path generation unit 110, a finite element unit 120 and an optimization unit 130, wherein the fiber path generation unit 110 is configured to generate a fiber path based on a stress field of a part including continuous fibers, and parameterize the fiber path based on B-spline; the finite element unit 120 is configured to solve a finite element model with B-spline parameterized fibers to obtain mechanical properties of the part; and the optimization unit 130 is configured to determine gradients of the mechanical properties with respect to control points of the B-spline parameterized fibers, and optimize the fiber path based on the gradients.

[0163] Thus, according to at least one embodiment of the present disclosure, a computationally efficient semi-analytical finite element model is established, which is compatible with arbitrary fiber path by analytically determined intra-cell fiber probability; a computationally efficient potential function is developed, which is used to control the distance between fibers and the distance between fibers and boundaries in fiber path optimization; and a gradient-based B-spline fiber path optimization method is developed based on the semi-analytical finite element model with gradient, which is compatible with multiple objective functions including compliance, fiber usage, frequency response, etc., and is verified by numerical and experimental case studies.

[0164] In particular, in some embodiments of the present disclosure, the mechanical performance of the part can include at least one of stiffness, mass, stress, strain, compliance, natural frequency, modal shape of the part.

[0165] In addition, the continuous fiber path optimization system 100 in additive manufacturing further includes a potential function unit (not shown), which is configured to construct a potential function, wherein the gradient of the potential function represents the distance between the continuous fibers and the distance between the continuous fibers and the boundaries of the part; and the potential function is used as a manufacturing constraint condition in the process of optimizing the fiber path based on the gradient.

[0166] In addition to the contribution of the fiber path to the stiffness matrix, manufacturing constraints need to be considered in the optimization process. These constraints include the distance between fibers and the distance between fibers and part boundaries, which need to reserve enough space to avoid manufacturing defects such as fiber overlap and crossing. On the other hand, the distance between fibers needs to be reduced to enhance local fiber density and achieve optimal reinforcement effect. Therefore, a potential field is introduced to the fibers, which provides an attractive force at a long distance and a repulsive force at a short distance.

[0167] Optionally, the finite element unit 120 is further configured to: construct a finite element model; determine a fiber reinforced element in the B-spline parameterized fiber; and construct a finite element model with B-spline parameterized fiber based on the fiber distribution in the fiber reinforced element and the finite element model.

[0168] As an option, the finite element unit 120 is further configured to: determine the candidate units for fiber reinforcement in the B-spline parameterized fiber by the convex hull of the control points; and construct a semi-analytical unit intra-fiber probability function to identify the fiber-reinforced unit from the candidate units, wherein the semi-analytical unit intra-fiber probability function characterizes the intersection relationship between the candidate unit and the B-spline parameterized fiber. In other words, the area and direction of the fiber are calculated by introducing the probability function of the fiber within the unit. These parameters are used to calculate the changes in the local stiffness matrix and the mass matrix, so that the fiber-reinforced unit can be simplified based on the homogeneous unit. Therefore, the convex hull property of the B-spline control point divides the fiber path into multiple segments and realizes parallel calculation, thereby reducing the computational complexity of the probability function.

[0169] In addition, the finite element unit 120 is further configured to construct a semi-analytical relationship between the length of the fiber in the unit, the direction of the fiber in the unit, and the control points.

[0170] In some embodiments of the present disclosure, the finite element unit 120 is further configured to: establish a stiffness and mass matrix based on the finite element model; determine the increments of the stiffness and mass matrices of the fiber reinforced unit based on the fiber distribution; and combine the increments with the stiffness and mass matrices into a global matrix, wherein the global matrix characterizes the mechanical properties of the part.

[0171] Thus, embodiments of the present disclosure address the problem of continuous fiber path optimization in additive manufacturing by establishing a semi-analytical finite element model of fibers with B-spline parameterization and a gradient-based fiber path optimization method. The semi-analytical finite element model of fibers with B-spline parameterization defines a probability distribution of fibers within a cell, thereby bypassing the computationally intensive process of determining the intersection points of fibers with cells. This probability distribution, along with the convex hull of the B-spline, facilitates the evaluation of increments in the local stiffness and mass matrices. These increments are combined to obtain the global stiffness and mass matrices, enabling efficient prediction of load response, stiffness, natural frequencies, and the like.

[0172] In some embodiments of the present disclosure, the matrix of the part includes at least one of polylactic acid, acrylonitrile-butadiene-styrene copolymer, polyamide, polyetheretherketone, and polyvinyl alcohol.

[0173] In some embodiments of the present disclosure, the continuous fiber includes at least one of carbon fiber, basalt fiber, glass fiber, and aramid fiber.

[0174] Figure 9 FIG. 2 is a schematic block diagram of an exemplary electronic device 200 for implementing an embodiment of the present disclosure.

[0175] like Figure 9As shown, the electronic device 200 includes one or more processors 201, a memory 202, and an interface that connects the various components, including high-speed interfaces and low-speed interfaces. The various components communicate via one or more buses that are used to transmit information. The processor(s) can process instructions for execution within the electronic device, including instructions stored in the memory or on storage to display graphical information for a GUI on an external input / output device, such as a display device coupled to the interface. In other implementations, multiple processors and / or buses can be employed as desired to implement various instructions communicating hardware and software elements. Figure 9 The processor 201 is used as an example in the present disclosure.

[0176] The memory 202 is a non-transitory computer-readable storage medium provided by the present disclosure. The memory stores instructions executable by at least one processor to cause the at least one processor to perform the continuous fiber path optimization method in additive manufacturing provided by the present disclosure. The non-transitory computer-readable storage medium of the present disclosure stores computer instructions for causing a computer to perform the continuous fiber path optimization method in additive manufacturing provided by the present disclosure.

[0177] The memory 202 is a non-transitory computer-readable storage medium that can be used to store non-transitory software programs, non-transitory computer-executable programs and modules. The processor 201 performs various functional applications and data processing of the server by running the non-transitory software programs, instructions and modules stored in the memory 202, that is, implements the continuous fiber path optimization method in additive manufacturing in the above method embodiments.

[0178] The memory 202 can include a program storage area and a data storage area, wherein the program storage area can store an operating system, at least one application required by a function; the data storage area can store data created according to the use of the electronic device for quality control, etc. In addition, the memory 202 can include a high-speed random access memory, and can also include a non-transitory memory, such as at least one magnetic disk storage device, a flash memory device, or other non-transitory solid-state memory device. In some embodiments, the memory 202 can include a memory disposed remotely with respect to the processor 201, which can be connected to the electronic device through a network. Examples of the above network include but are not limited to the Internet, an intranet, a local area network, a mobile communication network, and a combination thereof.

[0179] The electronic device 200 can further include an input device 203 and an output device 204. The processor 201, the memory 202, the input device 203, and the output device 204 can be connected through a bus or other means, Figure 9 The connection through the bus is taken as an example.

[0180] The input device 203 can receive inputted digital or character information, and generate key signal input related to user settings and function control for controlling the quality of the electronic device, such as a touch screen, a keypad, a mouse, a trackpad, a touchpad, a pointing stick, one or more mouse buttons, a trackball, a joystick, etc. The output device 204 can include a display device, an auxiliary lighting device (e.g., an LED), and a tactile feedback device (e.g., a vibration motor), etc. The display device can include, but is not limited to, a liquid crystal display (LCD), a light emitting diode (LED) display, and a plasma display. In some embodiments, the display device can be a touch screen.

[0181] Various embodiments of the systems and techniques described here can be realized in digital electronic circuitry, integrated circuitry, specially designed ASICs (application specific integrated circuits), computer hardware, firmware, software, and / or combinations thereof. These various embodiments can include implementation in one or more computer programs that are executable and / or interpretable on a programmable system including at least one programmable processor, which can be special or general purpose, coupled to receive data and instructions from, and to transmit data and instructions to, a storage system, at least one input device, and at least one output device.

[0182] These computer programs (also known as programs, software, software applications or code) include machine instructions for a programmable processor, and can be implemented in a high-level procedural and / or object-oriented programming language, and / or in assembly / machine language. As used herein, the terms "machine-readable medium" and "computer-readable medium" refer to any computer program product, apparatus and / or device (e.g., magnetic discs, optical disks, memory, Programmable Logic Devices (PLDs)) used to provide machine instructions and / or data to a programmable processor, including a machine-readable medium that receives machine instructions as a machine-readable signal. The term "machine-readable signal" refers to any signal used to provide machine instructions and / or data to a programmable processor.

[0183] To provide interaction with a user, the systems and techniques described herein can be implemented on a computer having: a display device (e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor) for displaying information to the user; and a keyboard and pointing device (e.g., a mouse or trackball) through which the user can provide input to the computer. Other types of devices can also be used to provide interaction with the user; for example, the feedback provided to the user can be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback); and input from the user can be received in any form (including acoustic input, voice input, or tactile input).

[0184] The systems and techniques described herein can be implemented in a computing system that includes back-end components (e.g., as a data server), or a computing system that includes middleware components (e.g., an application server), or a computing system that includes front-end components (e.g., a user computer with a graphical user interface or a web browser through which a user can interact with implementations of the systems and techniques described herein), or a computing system that includes any combination of such back-end components, middleware components, or front-end components. The components of the system can be interconnected by any form or medium of digital data communication (e.g., a communication network). Examples of communication networks include a local area network (LAN), a wide area network (WAN), and the Internet.

[0185] A computer system may include a client and a server. The client and server are generally remote from each other and typically interact via a communication network. The client-server relationship arises through computer programs running on the respective computers and having a client-server relationship with each other. The server may be a server in a distributed system or a server integrated with blockchain. The server may also be a cloud server, or an intelligent cloud computing server or intelligent cloud host with artificial intelligence technology. The server may be a server in a distributed system or a server integrated with blockchain. The server may also be a cloud server, or an intelligent cloud computing server or intelligent cloud host with artificial intelligence technology.

[0186] Yet another aspect of the present disclosure provides a computer program product, comprising a computer program, wherein when the computer program is executed by a processor, the computer program implements the continuous fiber path optimization method in additive manufacturing.

Claims

1. A continuous fiber path optimization method in additive manufacturing, comprising: generating a fiber path based on a stress field of a part comprising the continuous fiber, and parameterizing the fiber path based on B-splines; solving a finite element model with the fiber parameterized by B-splines to obtain mechanical properties of the part; and determining gradients of the mechanical properties with respect to control points of the fiber parameterized by B-splines, and optimizing the fiber path based on the gradients.

2. The method of claim 1, wherein, The mechanical properties comprise at least one of stiffness, mass, stress, strain, compliance, natural frequency, modal shape of the part.

3. The method of claim 1, wherein, Further comprising: constructing a potential function, wherein gradients of the potential function characterize distances between the continuous fibers and distances between the continuous fibers and boundaries of the part; and incorporating the potential function as a manufacturing constraint in optimizing the fiber path based on the gradients.

4. The method of claim 1, wherein, Solving the finite element model with the fiber parameterized by B-splines comprises: constructing a finite element model; determining fiber reinforced elements in the fiber parameterized by B-splines; and constructing the finite element model with the fiber parameterized by B-splines based on fiber distribution in the fiber reinforced elements and the finite element model.

5. The method of claim 4, wherein, Determining fiber reinforced elements in the fiber parameterized by B-splines comprises: determining candidate elements of fiber reinforcement in the fiber parameterized by B-splines by a convex hull of the control points; and constructing a semi-analytical intra-element fiber probability function to identify fiber reinforced elements from the candidate elements, wherein the semi-analytical intra-element fiber probability function characterizes intersection relationships between the candidate elements and the fiber parameterized by B-splines.

6. The method of claim 5, wherein, Constructing a semi-analytical intra-element fiber probability function comprises: constructing semi-analytical relationships of fiber length in an element, fiber orientation in an element, and the control points.

7. The method of claim 4, wherein, Solving the finite element model with the fiber parameterized by B-splines to obtain mechanical properties of the part comprises: establishing stiffness and mass matrices based on the finite element model; determining increments of the stiffness and mass matrices of the fiber reinforced elements based on the fiber distribution; and combining the increments with the stiffness and mass matrices into global matrices, wherein the global matrices characterize the mechanical properties of the part.

8. The method of claim 1, wherein, The matrix of the part comprises at least one of polylactic acid, acrylonitrile butadiene styrene, polyamide, polyether ether ketone, and polyvinyl alcohol.

9. The method of claim 1, wherein, The continuous fiber comprises at least one of carbon fiber, basalt fiber, glass fiber, and aramid fiber.

10. A continuous fiber path optimization system in additive manufacturing, comprising: a fiber path generation unit configured to generate a fiber path based on a stress field of a part comprising the continuous fiber, and parameterize the fiber path based on B-splines; a finite element unit configured to solve a finite element model with the fiber parameterized by B-splines to obtain mechanical properties of the part; and an optimization unit configured to determine gradients of the mechanical properties with respect to control points of the fiber parameterized by B-splines, and optimize the fiber path based on the gradients.

11. An electronic device, comprising: a processor; and a memory coupled with the processor; wherein, The memory stores instructions executable by the processor, the instructions being executed by the processor to cause the processor to perform the continuous fiber path optimization method in additive manufacturing of any one of claims 1 to 9.

12. A computer readable storage medium storing a computer program, the computer program being executed by a processor to implement the continuous fiber path optimization method in additive manufacturing of any one of claims 1 to 9.

13. A computer program product comprising a computer program, the computer program being executed by a processor to implement the continuous fiber path optimization method in additive manufacturing of any one of claims 1 to 9.

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