Systems and methods for compliance mapping of local features for additive manufacturing applications

Abstract

A computer system for implementing finite element analysis is provided. The computer system is programmed to: divide a model of an additive manufacturing (AM) article into sub-models of a region of interest and remaining sections; carrying out gridding on the remaining sections by using a coarse grid; calculating a flexibility matrix of each layer of the remaining section based on the coarse grid; gridding the sub-model using a fine mesh, wherein the fine mesh covers a subset of geometry relative to the coarse mesh; dividing the sub-model into layers on the basis of the fine grids; analyzing each layer of the sub-model based on the fine mesh; determining the influence of the remaining sections on the sub-model based on a plurality of flexibility matrixes; and generating an updated sub-model based on the analysis and the influence of the remaining section on the sub-model.

Description

BACKGROUND

[0001] The present application relates generally to systems and methods for submodel construction, and more particularly to systems and methods for generating a flexibility matrix of a submodel of a model for additive manufacturing applications using finite element analysis.

[0002] Additive manufacturing encompasses various manufacturing and prototyping techniques, such as freeform fabrication, 3D printing, rapid prototyping / machining, etc., in which raw material (such as wire-fed or powder-fed) is applied layer-by-layer onto an underlying substrate to fabricate a freestanding object. The article can be manufactured from a computer-aided design (CAD) model stored in memory that is provided to the additive manufacturing system. The process uses an energy beam to sinter or melt a powder material, or a nozzle to apply a liquid material to produce a solid three-dimensional object, in which the particles of the material bond together.

[0003] The layer-by-layer cycle can include rapid heating and rapid solidification, while melting the top powder layer and re-melting the underlying previously solidified layer, in which the article experiences steep temperature gradients and high cooling rates. Residual stresses caused by the thermal cycle can cause the article to warp or deform, which in turn can cause the article to be out of specification tolerances after solidification.

[0004] Finite element analysis (FEA) systems and methods are commonly used to model physical properties and attributes of an article prior to manufacturing. Computing devices and FEA software implement virtual modeling simulations to determine physical attributes of the article, such as residual stresses, deformations, displacements, etc. Simulations of a coarse mesh model of the article can produce a low resolution FEA simulation of the physical attributes, and simulations of a fine mesh model of the article typically produce a high resolution FEA simulation. However, FEA simulations of fine mesh models require a large amount of computing power and time.

[0005] Accordingly, it is desirable to reduce the computing time required to perform high resolution, fine mesh finite element analysis. SUMMARY

[0006] In one aspect, a computer system for implementing finite element analysis is provided. The computer system includes at least one processor in communication with at least one memory device. The at least one processor is programmed to partition a model of an additive manufacturing (AM) article into a submodel of a region of interest and a remaining section. The at least one processor is further programmed to mesh the remaining section using a coarse mesh. The at least one processor is further programmed to compute a flexibility matrix for each layer of the remaining section based on the coarse mesh. In addition, the at least one processor is programmed to mesh the submodel using a fine mesh, where the fine mesh covers a subset of geometry relative to the coarse mesh. Further, the at least one processor is programmed to partition the submodel into layers based on the fine mesh. In addition, the at least one processor is programmed to analyze each layer of the submodel based on the fine mesh. Further, the at least one processor is further programmed to determine an effect of the remaining section on the submodel based on the plurality of flexibility matrices. Further, the at least one processor is further programmed to generate an updated submodel based on the analysis and the effect of the remaining section on the submodel. The computer system can include additional or alternative functionality, including those discussed elsewhere herein.

[0007] In another aspect, a computer-implemented method for finite element analysis is provided. The method is implemented on a computer system that includes at least one processor in communication with at least one memory device. The method includes partitioning a model of an additive manufacturing (AM) article into a submodel of a region of interest and a remaining section. The method further includes meshing the remaining section using a coarse mesh. The method further includes computing a flexibility matrix for each layer of the remaining section based on the coarse mesh. In addition, the method includes meshing the submodel using a fine mesh, where the fine mesh covers a subset of geometry relative to the coarse mesh. Further, the method includes partitioning the submodel into layers based on the fine mesh. In addition, the method includes analyzing each layer of the submodel based on the fine mesh. Further, the method includes determining an effect of the remaining section on the submodel based on the plurality of flexibility matrices. Further, the method includes generating an updated submodel based on the analysis and the effect of the remaining section on the submodel. BRIEF DESCRIPTION OF DRAWINGS

[0008] The drawings described below depict aspects of the systems and methods disclosed herein. It should be understood that each drawing depicts an implementation of a particular aspect of the disclosed systems and methods, and that every aspect is not limited to the accompanying drawings. Further, in the event of inconsistent usages of terms between this description and the accompanying drawings, the usages in the drawings control.

[0009] The presently discussed arrangement is shown in the drawings, but it is understood that the present embodiments are not limited to the precise arrangement and are the means shown, wherein:

[0010] Figure 1 An exemplary configuration of a finite element analysis (FEA) computer device is depicted in accordance with one embodiment of the present disclosure.

[0011] Figure 2 An area of interest on an article is illustrated where stresses can cause cracks in the manufactured article.

[0012] Figure 3A A perspective view of a model of a matrix that is segmented into coarse elements is illustrated. Figure 1 A perspective view of a model of a matrix that is segmented into coarse elements is illustrated. Figure 2 A perspective view of an exemplary finite element model of an article is illustrated.

[0013] Figure 3B A perspective view of a model of a matrix that is segmented into coarse elements is illustrated.

[0014] Figure 3C A perspective view of a model of a matrix that is segmented into coarse elements is illustrated.

[0015] Figure 3D A perspective view of a model of a matrix that is segmented into coarse elements is illustrated. Figure 3A A submodel of an area of interest of a model is illustrated.

[0016] Figure 4A A model of an area of interest and a remaining section is illustrated.

[0017] Figure 4B A model with only a remaining section (also referred to as a global domain) after an area of interest (also referred to as a subdomain) is removed is illustrated.

[0018] FIG. 4C illustrates an area of interest that is removed.

[0019] Figure 5 A comparison of an exemplary subdomain that is meshed at 0.2 mm and a global domain that is meshed at 0.8 mm is illustrated.

[0020] Figure 6 A process for finite element analysis (FEA) in accordance with at least one embodiment is illustrated.

[0021] Unless otherwise indicated, the drawings provided herein are intended to exemplify features of embodiments of the disclosure. These features are believed to be of universal application to a wide variety of systems, including one or more embodiments of the disclosure. Thus, the drawings are not intended to limit the scope of the disclosure to the precise arrangements shown. DETAILED DESCRIPTION

[0022] Large parts built by additive manufacturing often crack. The elimination of these cracks involves redesign. However, the experimental work is long and can take days and / or weeks. The systems and methods described herein allow for automation of part design such that they can be printed without cracking.

[0023] The present application generally relates to systems and methods for submodel construction, and more particularly to systems and methods for generating a flexibility matrix of a submodel of a model for additive manufacturing applications using finite element analysis. In an exemplary embodiment, a finite element analysis (FEA) computer device is programmed to generate a flexibility matrix of a submodel of a model for additive manufacturing applications using finite element analysis.

[0024] Shape optimization for residual stress minimization in small subdomains of large additive manufacturing parts (DLMLs) automatically provides geometric improvements of local features with reduced residual stress and likelihood of cracking while maintaining design requirements. Through an automated iterative optimization process, candidate geometries for lower residual stress are generated (through changes in cad parameters or parametric deformation of initial geometry). They are then evaluated through fast, accurate residual stress calculations.

[0025] Fast and accurate residual stress calculations are key to shape optimization. The inherent strain method is applied only to the subdomain but needs to account for the influence of surrounding parts. In many cases, a direct force / displacement mapping is possible but not accurate. Reduced order models such as flexibility + loads achieved through substructuring (i.e., super elements, schur complement methods, etc.) are preferred. In this case, layer-wise substructuring (i.e., super elements, schur complement methods, etc.) of all parts except this subdomain is pre-computed and then applied layer-wise for all iterations.

[0026] In many cases, shape optimization for additive manufacturing residual stress minimization requires a large number of finite element simulations to provide residual stresses for each configuration tested. Some current methods such as using finite element simulations with the inherent strain method require a large amount of processing time and resources. Furthermore, the cost of computational resources to provide the number of simulations needed to reach optimization convergence is extremely high. In addition, small details can be missed.

[0027] Accordingly, the systems and methods herein describe creating a fine mesh to isolate and analyze areas where residual stresses need to be minimized. This fine meshing requires a fine resolution of where the stresses are. The fine mesh can also contain features that would only be captured by a small mesh size. In example embodiments, the fine mesh covers a subset of the geometry relative to the coarse mesh. In some additional embodiments, the fine mesh can be significantly smaller than the coarse mesh. In some of these embodiments, for example, consider a shape optimization application where someone wants to try to optimize a subset of the geometry. It can be natural to make the "fine mesh" and the "coarse mesh" have the same voxel / cell size. This would still allow for fast and efficient testing changes to the geometry within the area of interest. In some embodiments, there are cases where one would prefer to use a larger voxel / cell size within the area of interest.

[0028] The systems and methods described herein improve the finite element method for solving residual stresses in a bounded subdomain to provide faster resolution at a fine resolution. In example embodiments, an FEA computer device receives a design of an additive manufacturing (AM) part (also referred to as a domain). The FEA computer device divides the AM part into two sections. The first section is a subdomain of interest where residual stresses need to be reduced in the AM part. Typically, the part fractures at a given location, so this subdomain includes the location of the crack plus an area around the crack that allows for modifications to be made. The second section is the rest of the part. These two sections are divided in any meaningful way to put the location of the residual stresses in the first section and to put as much of the rest of the AM part as possible in the second section.

[0029] Before optimization begins, the FEA computer device meshes the AM part (also referred to as the second section) that does not include the subdomain of interest. The FEA computer device meshes the AM part so that it can be split into layers. In example embodiments, the mesh is a voxel mesh with a coarse mesh size.

[0030] For each layer, the FEA computer device computes the flexibility of the part while leaving the only nodes laying at the "rest of the subdomain / part boundary" as free degrees of freedom. In other words, the linear system provided by the finite element method (including thermal loads, Dirichlet boundary conditions) is not solved completely, but is partially inverted. This provides a linear system of equations of size the number of degrees of freedom at the "rest of the subdomain / part boundary". This is called the flexibility matrix. This is called substructuring. Thus, at the end of this step, the system ends up with as many flexibility matrices as there are layers in the coarse "rest of the part" mesh, each of size the number of degrees of freedom at the "rest of the subdomain / part boundary". The FEA computer device skips the layers below the domain of interest, as they do not contribute to the stresses in the "domain of interest".

[0031] In an example embodiment, the FEA computer device starts the appropriate shape optimization. The FEA computer device draws the configuration of the subdomain of interest (first section), so it can be tested. The FEA computer device meshes the "domain of interest" so that it can be split into layers. The meshing on the domain of interest is performed at a finer scale than the one performed on the second section. The FEA computer device determines the resolution of the mesh based on the domain of interest.

[0032] The FEA computer device applies the layer-by-layer intrinsic strain method to the "region of interest" only finely meshed. The FEA computer device takes into account the influence of the rest of the part on the "region of interest" (stiffness and loads) by applying the stiffness matrix computed above. The FEA computer device derives at each step a mapping between the degrees of freedom of the "rest of the part" at the "rest of the part" / "subdomain of interest" interface and the degrees of freedom of the "domain of interest" at the same interface. In some embodiments, this can be done by establishing constraint equations on these degrees of freedom. Furthermore, this mapping becomes more consistent if the submodel is shifted up (or down) to match the top layer of the current "domain of interest" vertical position with the top layer of the "rest of the part" vertical position. Furthermore, since the height of the domain of interest does not necessarily match the height of the void left in the "rest of the part" after the subtraction of the subdomain, additional mesh layers below the "subdomain of interest" and available to complete the "subdomain of interest" as needed so that there is always a node at the lower boundary.

[0033] At least one of the technical problems addressed by the system may include: (i) improving the speed and accuracy of optimized additive manufacturing; (ii) eliminating cracks in parts used for additive manufacturing; (iii) improving the strength and stability of additively manufactured parts; (iv) improving the strength and stability during the additive manufacturing process; (v) reducing the computer resources required for optimized additive manufacturing; and / or (iv) facilitating the automation of part design so that they can be printed without breaking.

[0034] The methods and systems described herein can be implemented using computer programming or engineering techniques, including computer software, firmware, hardware, or any combination or subset thereof, wherein the technical effects are achieved by performing at least one of the following steps: a) dividing a model of an additively manufactured (AM) article into a sub-model of a region of interest and a remaining segment; b) meshing the remaining segment using a coarse mesh; c) calculating the compliance matrix for each layer of the remaining segment based on the coarse mesh; d) meshing the sub-model using a fine mesh, wherein the fine mesh covers a subset of the geometry relative to the coarse mesh; e) dividing the sub-model into layers based on the fine mesh; f) analyzing each layer of the sub-model based on the fine mesh; g) determining the effect of the remaining segment on the sub-model based on the multiple compliance matrices; h) generating an updated sub-model based on the analysis and the effect of the remaining segment on the sub-model; i) selecting the region of interest for which residual stress needs to be reduced; j) selecting the region of interest based on one or more reports of cracks in the article; k) wherein the region of interest also includes an additional area around the location where the crack is reported. Domain; l) Divide the remaining segment into layers based on the coarse mesh; m) Where the coarse mesh is a voxel mesh; n) Preserve one or more nodes located at one or more boundaries between the submodel and the remaining segment as degrees of freedom; o) Where the compliance matrix is ​​the size of a system of linear equations determined by the number of degrees of freedom at the boundary between the submodel and the remaining segment; p) Determine the mapping between the degrees of freedom of the remaining segment at the interface of the remaining segment submodel and the degrees of freedom of the submodel at the same interface at each step; q) By establishing a or Multiple constraint equations determine the mapping; r) skip one or more layers of the remaining segment below the submodel; s) perform shape optimization on the submodel; t) generate the configuration of the submodel to be tested; u) apply a layer-by-layer intrinsic strain method to the finely meshed submodel; v) wherein the effect includes at least one of stiffness or load; w) shift the submodel up or down so that the top layer of the submodel in vertical position matches the top layer of the remaining segment in vertical position; and / or x) apply the updated subdomain to the remaining segment to generate a build file for the additive manufacturing machine.

[0035] Those skilled in the art will appreciate the advantages more clearly from the following description of preferred embodiments, which have been shown and described by way of example. As will be appreciated, this embodiment can be capable of having other embodiments and different embodiments, and their details can be modified in various ways. Therefore, the drawings and description are to be regarded as illustrative rather than limiting in nature.

[0036] Figure 1 An exemplary configuration of a finite element analysis (FEA) computer device 100 according to one embodiment of this disclosure is depicted. The FEA computer device 100 is operable by a user 102.

[0037] FEA computer device 100 may include a processor 104 for executing instructions. In some embodiments, the executable instructions may be stored in memory area 106. Processor 104 may include one or more processing units (e.g., in a multi-core configuration). Memory area 106 may be any device that allows storage and retrieval of information such as executable instructions and / or transaction data. Memory area 106 may include one or more computer-readable media.

[0038] FEA computer device 100 may also include at least one media output component 108 for presenting information to user 102. Media output component 108 may be any component capable of delivering information to user 102. In some embodiments, media output component 108 may include an output adapter (not shown), such as a video adapter and / or an audio adapter. The output adapter may be operatively coupled to processor 104 and operatively coupled to an output device, such as a display device (e.g., a cathode ray tube (CRT), liquid crystal display (LCD), light-emitting diode (LED) display, or "electronic ink" display) or an audio output device (e.g., a speaker or headphones).

[0039] In some embodiments, the media output component 108 may be configured to present a graphical user interface (e.g., a web browser and / or client application) to the user 102. The graphical user interface may include, for example, an interface for viewing stress information. In some embodiments, the computing device 100 may include an input device 110 for receiving input from the user 102. The user 102 may use the input device 110 to provide information via voice or typing, but is not limited thereto.

[0040] Input device 110 may include, for example, a keyboard, pointing device, mouse, stylus, touch-sensitive control panel (e.g., touchpad or touchscreen), gyroscope, accelerometer, position detector, biometric input device, and / or audio input device. A single component (such as a touchscreen) may serve as both an output device of media output component 108 and an input device 110.

[0041] FEA computer equipment 100 may also include a communication interface 112 communicatively coupled to a remote device, such as a client device (not shown). The communication interface 112 may include, for example, a wired or wireless network adapter and / or a wireless data transceiver used with a mobile telecommunications network.

[0042] Storing in memory area 106 are computer-readable instructions, for example, for providing a user interface to user 102 via media output component 108 and optionally receiving and processing input from input device 110. The user interface may include a web browser and / or client applications, etc. A web browser enables users (such as user 102) to display and interact with media and other information typically embedded in web pages or websites. For example, instructions may be stored by a cloud service, and the output of the execution of those instructions may be sent to media output component 108.

[0043] In an exemplary embodiment, processor 104 receives input parameters such as a 3D virtual model, mesh resolution, and selection of a target region for submodel construction. Processor 104 is further configured to execute the methods described herein as instructions to be executed by processor 104. Processor 104 is also programmed to retrieve finite element analysis (FEA) applications (such as multiphysics modeling module 116) from memory 106 and store the instructions in memory 106. Processor 104 may also output simulations generated by user input to media output component 108 or store the output simulations in memory 106.

[0044] Both the CAD system 114 and the multiphysics modeling module 116 are stored in the memory 106 and are accessible by the processor 104. The CAD system 114 is a three-dimensional virtual environment in which the CAD model is presented. The multiphysics modeling module 116 performs multiphysics mathematical calculations and performs FEA simulations of the CAD model.

[0045] In one embodiment, a computer program is provided, and the program is embodied on a computer-readable medium, such as memory 106. In some embodiments, the system includes multiple components distributed among multiple computing devices. One or more components may take the form of computer-executable instructions contained in a computer-readable medium. As used herein, the terms "software" and "firmware" are interchangeable and include any computer program stored in memory 106 for execution by processor 104, including RAM memory, ROM memory, EPROM memory, EEPROM memory, and non-volatile RAM (NVRAM) memory. The above memory types are merely examples and are therefore not limited to the types of memory that can be used to store computer programs.

[0046] Figure 2 An exemplary article 200 (hereinafter referred to as "article 200") is illustrated. In some embodiments, by means of the memory 106 (in Figure 1 The instructions (shown in the diagram) are input into an additive manufacturing system to manufacture article 200. This additive manufacturing system includes, but is not limited to, laser powder bed melting (LPBF), direct metal laser melting (DMLM), selective laser sintering (SLS), direct metal laser deposition (DMLD), binder jet additive manufacturing (BJAM), powder blow molding additive manufacturing, and / or any other additive manufacturing system. As used herein, the term "additive manufacturing" or "additive manufacturing technology or process" refers to a manufacturing process in which continuous layers of material are deposited on lower layers to build up a three-dimensional component layer by layer. The first layer is deposited and fused to a build plate, and the continuous layers are subsequently partially melted or fused together to form a monolithic or integral component, such as article 200.

[0047] Figure 2 An example is shown of a region of interest 202 on article 200, where stress may cause cracks to appear in the manufactured article 200.

[0048] Due to the repeated melting and fusion of continuous layers, residual stress and warpage can be applied to the article 200. Melting and fusion also cause the lower layer to expand or deform due to the temperature difference between it and the layer above which the melting is being applied. Residual stress, warpage, and temperature difference can be simulated using FEA applications and methods.

[0049] One method for simulating thermal and mechanical properties, as disclosed herein, uses an inherent strain simulation method. This inherent strain simulation method employs a thermomechanical finite element method (FEA) model, which produces approximations of manufacturing-induced residual stresses and warpage (as well as other general mechanical and thermophysical properties). A three-dimensional virtual model of the article is imported into FEA software or created within FEA software. A three-dimensional mesh is applied to the model to divide it into a matrix of cuboid elements. This matrix of cuboid elements is oriented in three-dimensional space such that each layer of cuboid elements is substantially parallel to the building plate, and the sum of the layers defines the total height of the model.

[0050] In some implementations, the first layer (the bottommost layer on the build plate) is constrained to represent the stiffness of the build plate. Negative strain is applied to the nth layer (the topmost layer opposite the bottommost layer), where thermal strain and irreversible deformation associated with metal cooling are combined. For each successive intermediate layer applied to the first layer, a simplified mesh is obtained by discarding all subsequent layers, and finite element mathematical calculations provide the stresses and displacements associated with each successive intermediate layer. The final residual stresses and displacements are calculated by summing the results of each finite element mathematical calculation.

[0051] As used herein, the terms “finite element analysis” or “FEA” should refer to a process, method, or computer-implemented approach in which one or more physical properties of a geometric model are virtually (via software) represented as a finite element model. The model is divided into matrices of elements, which together form the finite element model. The matrix of elements is simulated by calculating mathematical formulas such as partial differential equations to simulate the physical properties of each individual element and the interactions between adjacent elements. The physical properties of the model are illustrated in the simulation, where elements are colored in a color scale, with regions of larger physical property values ​​receiving different shades of color than regions of smaller physical property values.

[0052] As used herein, the term "simulation" refers to the computation of multiphysics mathematical formulas to determine the values ​​of one or more mechanophysical properties of fine and / or coarse elements, and to simulating the interactions between adjacent fine and / or coarse elements. In multiphysics computation, boundary conditions of adjacent fine and / or coarse elements are extracted and applied to the fine and / or coarse elements being simulated. The simulation and computation of multiphysics mathematical formulas are performed by a processor and / or application (such as FEA software). Similarly, as used herein, the terms "applying intrinsic strain simulation" or "performing intrinsic strain simulation" refer to the computation of multiphysics mathematical formulas according to intrinsic strain simulation methods.

[0053] As used herein, the term "coarse element," derived by applying a coarse mesh to a finite element model, refers to a virtual segment of the finite element model having a cuboid shape and volume. Similarly, the term "fine element," derived by applying a fine mesh to a finite element model, refers to a virtual segment of the finite element model having a cuboid shape and volume. The volume of a fine element is smaller than that of a coarse element, and performing a simulation with fine elements yields higher resolution than performing a simulation with coarse elements. In exemplary embodiments, the fine mesh covers a subset of the geometry relative to the coarse mesh. In some additional embodiments, the fine mesh may be significantly smaller than the coarse mesh. In some of these embodiments, consider, for example, a shape optimization application where someone wants to try to optimize a subset of the geometry. It may be natural to have the "fine mesh" and the "coarse mesh" have the same voxel / element size. This would still allow for rapid and efficient testing of changes to the geometry within the region of interest. In some embodiments, there are situations where someone prefers to use a larger voxel / element size within the region of interest.

[0054] In some implementations, these elements are voxel elements used for displacement mapping and simulation, and the FEA systems and methods described herein utilize voxel-based modeling and voxel meshes for displacement mapping.

[0055] Figure 3A An example is given by FEA computer device 100 (in Figure 1 (shown in) Simulated artifact 200 (in) Figure 2 A perspective view of an exemplary finite element model 300 (shown in the figure). Figure 3B A perspective view of model 300, which is an example of a matrix divided into coarse elements 302, is shown. Figure 3C A perspective view of a matrix divided into coarse elements 302 and a region of interest 202 is shown. Figure 3D The region of interest 202 of model 300 is illustrated. Figure 3A Sub-model 320 (shown in the figure). Figures 3A to 3D Each view shown is in at least one media output component 108 (in Figure 1 The virtual representation shown in the image is displayed on the screen and can be accessed by user 102 (in the image). Figure 1 (As shown in the diagram) Rotate or manipulate. As an example, user 102 can rotate and / or selectively zoom in on any view by providing input through input device 110. The region of interest 202 can also be arbitrarily selected by user 102 by providing input through input device 110. In the illustrated embodiment, the region of interest 202 can be selected by user 102 because the region of interest 202 may represent a weak area of ​​model 300, or because user 102 may intend to optimize the shape of the region of interest. Figures 3A to 3DEach view in the diagram is arbitrarily oriented in the XYZ plane.

[0056] In an exemplary implementation, Figure 3D The sub-model 320 shown is divided into fine elements 304, and performing a simulation on sub-model 320 yields a higher resolution compared to model 300, which is divided into coarse elements 302. To achieve even higher resolution, the entire model 300 could be simulated using fine elements 304. However, performing a simulation on fine elements 304 requires significantly more processing resources than simulating coarse elements 302. As an example, in one implementation, performing a FEA simulation on the finite element model 300 with a fine mesh (a matrix of fine elements 304) could require at least fifteen hours of computation time, compared to approximately nine minutes of computation time for performing a FEA simulation on only sub-model 320.

[0057] Embodiments of the present invention generally relate to systems and methods for simulating one or more mechanical-physical properties of a sub-model 320 of a geometric model 300 of a physical article 200 for additive manufacturing applications using FEA systems and methods. These properties may include, but are not limited to, structural, fluid, or thermal behavior, as well as residual stress, deformation, or displacement of the article 200. The method includes using a FEA computer device 100 (in...) Figure 1 A computer device (as shown in the diagram) defines a region of interest 202 of model 300 in at least two dimensions. The FEA computer device 100 subtracts the region of interest 202 from model 300, where the region of interest 202 defines a sub-model 320. The FEA computer device 100 applies a compliance matrix to model 300. The FEA computer device 100 applies intrinsic strain simulation to each of the matrices attributable to at least one physical property of the coarse layer. The FEA computer device 100 applies a compliance sub-matrix to sub-model 320. The FEA computer device 100 applies a mapping matrix between the compliance matrix and the compliance sub-matrices. The FEA computer device 100 solves for the displacements of sub-model 320. The resulting set of equations for sub-model 320 facilitates automatic local redesign to minimize at least one physical property and maintain design specifications.

[0058] Figure 4A Model 400 illustrates the region of interest 202 and the remaining segment 402. The remaining segment 402 has a coarse mesh flexibility map with coarse elements 302. The region of interest 202 is cut out from model 400 to leave the remaining segment 402.

[0059] Figure 4BA model 400 is illustrated after the region of interest 202 (also referred to as the subdomain) has been removed, leaving only the remaining segment 402 (also referred to as the global domain). Figure 4C illustrates the removed region of interest 202. The region of interest 202 has a fine mesh compliance map with fine elements 304. The region of interest 202 also shows a high-stress region 404 and a low-stress region 406. The geometrical split between the region of interest 202 and the remaining segment 402 is the first major step of the FEA method as described herein. In one example, the subdomain 202 has a 0.2 mm mesh applied to it, while the global domain 402 has a 1 mm mesh applied to it.

[0060] During processing, the FEA computer device 100 performs substructuring on the global domain 402. The FEA computer device 100 generalizes the global domain 402 into a substructure encompassing all elements based on compliance and load. This can be generalized to a small linear system and is valid regardless of the subdomain 202. The FEA computer device 100 performs mapping at each layer of the fine mesh. The FEA computer device 100 evaluates stress layer by layer. The FEA computer device 100 is able to map the global substructure to the simulated fine submodel, where the substructure layers match the current layer of subdomain 202. This includes simulating the thermal load in subdomain 202. When the simulated subdomain 202 is applied to the global structure, the FEA computer device 100 calculates stress assumptions and determines the solution for each fine layer. For many geometries, the stress in the geometry of the submodel can be quickly evaluated. The splitting of the geometry means that subdomains can be evaluated and re-evaluated multiple times, while the global structure of the global domain 402 only needs to be evaluated once.

[0061] After geometric decomposition, the FEA computer device 100 evaluates subdomain 202 to optimize its shape, thereby minimizing residual stress. The FEA computer device 100 performs baseline parameterization of subdomain 202 to determine multiple parameters of subdomain 202. For example, the FEA computer device 100 may determine 10 parameters to be evaluated and / or measured for subdomain 202. The FEA computer device 100 performs optimization loops for these parameters. The FEA computer device 100 performs parameter sampling and geometric deformation and meshing on these parameters and subdomain 202. The FEA computer device 100 performs residual stress calculations to maximize stress loss in the simulated subdomain 202. Then, when completion criteria have been met, the FEA computer device 100 selects the best result from the simulation. In an exemplary embodiment, the FEA computer device 100 uses a fast residual stress evaluation criterion. In an exemplary embodiment, the FEA computer device 100 performs multiple optimization loops to determine the optimal parameters for subdomain 202, and thus determine the shape used to construct subdomain 202. The optimal subdomain is then tested against global domain 402. In some implementations, the FEA computer device 100 adjusts one or more of these parameters after evaluating the global domain 402.

[0062] In some implementations, geometric splitting includes voxelization of subdomain 202. Voxelization has an impact on residual stress, improves geographic deformation, and optimizes (i.e., gradient descent).

[0063] Figure 5 A comparison is illustrated between an example subdomain 202 meshed with 0.2 mm and a global domain 402 meshed with 0.8 mm. The FEA computer device 100 is able to process the finely meshed subdomain 202 with a coarsely meshed global domain 402 significantly faster than a finely meshed full model (such as model 300 (shown in Figure 3)). Performing a finite element analysis on model 300 with a fine mesh requires fifteen hours of computation time. Performing a finite element analysis on only submodel 320 requires nine minutes of computation time. This significant saving in computational resources is central to this disclosure.

[0064] Figure 6 An example of a process for finite element analysis (FEA) according to at least one embodiment is illustrated. In an exemplary embodiment, the steps of process 600 are performed by FEA computer equipment 100 (in... Figure 1 (As shown in the image) Execution.

[0065] In an exemplary embodiment, the FEA computer device 100 will display AM parts or articles 200 (in... Figure 2 Model 300 (shown in Figure 3) is divided into regions of interest 202 (shown in Figure 3). Figure 2Sub-model 320 (shown in Figure 3) and global domain or remaining segment 402 (shown in Figure 4) Figure 4B (As shown in the diagram). Sub-model 320 of region of interest 202 is the location where residual stress needs to be reduced. Typically, a part fractures at a given location, so this sub-domain includes the location of the crack plus the area around the crack where modifications are permitted.

[0066] In an exemplary embodiment, the FEA computer device 100 meshes the global domain or remaining segment 402 610. The global domain or remaining segment 402 is meshed 610 such that it can be broken down into layers. In some embodiments, the global domain or remaining segment 402 is meshed 610 as a voxel mesh. The mesh size of the global domain or remaining segment 402 is coarse, which is typically the size required for warp simulation, thereby allowing for reasonable solution time.

[0067] In an exemplary embodiment, the FEA computer device 100 calculates the compliance of the article 200 at each of 615 layers based on a coarse mesh. The FEA computer device 100 preserves the node layout at one or more boundaries between the subdomain 202 and the global domain 402 as degrees of freedom. The FEA computer device 100 generates a system of linear equations, the size of which is determined by the number of degrees of freedom at the boundaries of the subdomain 202 and the global domain 402; this system of linear equations is referred to as the compliance matrix. This is also referred to herein as substructuring. The FEA computer device 100 calculates the compliance matrix for each of the 615 layers of the global domain 402 based on each layer of the coarse mesh. Each compliance matrix is ​​the magnitude of the number of degrees of freedom at the boundaries of the subdomain 202 and the global domain 402. In some embodiments, layers below the region of interest 202 are skipped because they do not contribute to the stress in the region of interest 202.

[0068] In an exemplary implementation, the FEA computer device 100 performs shape optimization on the sub-model 320.

[0069] In an exemplary implementation, the FEA computing device 100 generates a configuration for a sub-model 320 to be tested. The FEA computing device 100 meshes this sub-model 620 using a fine mesh. The FEA computing device 100 bases the mesh on the fine mesh 304 (in...). Figure 3D (As shown in the figure) Sub-model 320 is divided into 625 layers.

[0070] In an exemplary embodiment, the FEA computer device 100 analyzes each layer of the 630 sub-model 320 based on a mesh. In an exemplary embodiment, the FEA computer device 100 applies a layer-by-layer intrinsic strain method to the finely meshed sub-model 320. The FEA computer device 100 determines the influence of the remaining segments 420 of the 635 article 200 on the region of interest 202. In these embodiments, the FEA computer device 100 uses the compliance matrix determined in step 615. In some embodiments, the influence includes at least one of stiffness or load.

[0071] At each step, the FEA computer device 100 determines the mapping between the degrees of freedom of the remaining segment 402 at the interface of the region of interest 202 and the degrees of freedom of the subdomain 202 at the same interface. In some embodiments, the FEA computer device 100 determines this mapping by establishing one or more constraint equations about these degrees of freedom. Furthermore, the FEA computer device 100 improves the consistency of this mapping by shifting the submodel 320 up or down so that the top layer of the current subdomain 202 in its vertical position matches the top layer of the remaining segment 402 in its vertical position. Additionally, since the height of the submodel 320 does not necessarily match the height of the gap left in the remaining segment 402 after subtracting the submodel 320, an additional layer is meshed below the submodel 320 and used to complete the submodel 320 as needed, ensuring that nodes are always present at the lower boundary.

[0072] In an exemplary embodiment, the FEA computer device 100 generates an updated sub-model 320 based on the analysis and the impact of the remaining segment 402 on the sub-model 320. In some embodiments, the FEA computer device 100 applies the updated sub-model 320 to the remaining segment 402 to generate a build file for an additive manufacturing machine.

[0073] Additional Considerations

[0074] The embodiments disclosed herein offer advantages over existing FEA systems and methods that lack the ability to rapidly simulate fine-mesh models. By implementing intrinsic strain simulation on sub-models of the model, only the sub-models need to be simulated. Therefore, the described systems and methods provide modeling of finite-element sub-models of a CAD model at higher resolution with fewer processing resources than simulating the entire model. As an example, in one embodiment, performing an FEA simulation on a fine-mesh finite-element model might require up to approximately fifteen hours of computation, while performing an FEA simulation on only the fine-mesh sub-models might require at most approximately nine minutes of computation.

[0075] The methods, systems, and components disclosed herein are not limited to the specific embodiments described herein, but rather the steps of the methods, the elements of the systems, and / or the components can be used independently and separately from other steps and / or elements described herein. For example, the methods, systems, and components are not limited to being practiced only with rotating machines as described herein. Rather, the methods, systems, and components can be implemented and used in conjunction with many other applications.

[0076] While specific features of various embodiments may be shown in some figures and not in others, this is merely for convenience. Furthermore, the reference to "one embodiment" in the above description is not intended to exclude the existence of additional embodiments that also include the listed features. Based on the principles of this disclosure, any feature of any other figure may be referenced and / or claimed in conjunction with any feature of any other figure.

[0077] As understood based on the foregoing description, the embodiments described above in this disclosure can be implemented using computer programming or engineering techniques, including computer software, firmware, hardware, or any combination or subset thereof. Any such resulting program having computer-readable code components can be embodied or provided in one or more computer-readable media to create a computer program product, i.e., an article of manufacture, according to the embodiments discussed in this disclosure. Computer-readable media can be, for example, but not limited to, fixed (hard disk) drives, magnetic disks, optical disks, magnetic tapes, semiconductor memories (such as read-only memory (ROM)), and / or any transmission / reception medium (such as the Internet or other communication networks or links). An article of manufacture containing the code can be made and / or used by executing the computer code directly from one medium, by copying the computer code from one medium to another, or by transmitting the computer code over a network.

[0078] These computer programs (also referred to as programs, software, software applications, "applications," or code) include machine instructions for a programmable processor and may be implemented in high-level programming languages ​​and / or object-oriented programming languages ​​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., disk, optical disk, memory, programmable logic device (PLD)) used to provide machine instructions and / or data to a programmable processor, including machine-readable media that receive machine instructions as machine-readable signals. However, "machine-readable medium" and "computer-readable medium" do not include transient signals. The term "machine-readable signal" refers to any signal used to provide machine instructions and / or data to a programmable processor.

[0079] As used herein, the term "database" may refer to a data subject, a relational database management system (RDBMS), or both. As used herein, a database may include any collection of data, including hierarchical databases, relational databases, flat file databases, object-relational databases, object-oriented databases, and any other structured collection of records or data stored in a computer system. The examples above are merely illustrative and are therefore not intended to limit the definition and / or meaning of the term "database" in any way. Examples of RDBMS include, but are not limited to, Oracle. ® Database, MySQL, IBM ® DB2, Microsoft ® SQL Server, Sybase ® NoSQL and PostgreSQL. However, any database that implements the systems and methods described in this article can be used. (Oracle is a registered trademark of Oracle Corporation, Inc., Redwood Shores, California; IBM is a registered trademark of International Business Machines Corporation, Inc., Armonk, New York; Microsoft is a registered trademark of Microsoft Corporation, Inc., Redmond, Washington; and Sybase is a registered trademark of Sybase, Inc., Inc., Dublin, California.)

[0080] As used herein, a processor can include any programmable system, including systems that use microcontrollers, reduced instruction set circuitry (RISC), application-specific integrated circuits (ASICs), logic circuits, and any other circuitry or processor capable of performing the functions described herein. The examples above are merely illustrative and are therefore not intended to limit the definition and / or meaning of the term "processor" in any way.

[0081] As used herein, the terms “software” and “firmware” are used interchangeably and include any computer program stored in memory for execution by a processor, including RAM memory, ROM memory, EPROM memory, EEPROM memory, and non-volatile RAM (NVRAM) memory. The memory types described above are merely examples and are therefore not limited to the types of memory that can be used to store computer programs.

[0082] In another example, a computer program is provided, and this program is embodied on a computer-readable medium. In one example, the system executes on a single computer system without requiring a connection to a server computer. In yet another example, the system runs on Windows. ® Running in an environment (Windows is a registered trademark of Microsoft Corporation, Redmond, Washington). In yet another example, the system runs in a mainframe environment and UNIX. ® It runs on a server environment (UNIX is a registered trademark of X / Open Company Limited, located in Reading, Berkshire, United Kingdom). In yet another example, the system runs on iOS. ® It runs on an environment (iOS is a registered trademark of Cisco Systems, Inc., located in San Jose, CA). In another example, the system runs on Mac OS. ® It runs on an environment (Mac OS is a registered trademark of Apple Inc., located in Cupertino, CA). In yet another example, the system runs on Android. ® It runs on an OS (Android is a registered trademark of Google, Inc., located in Mountain View, CA). In another example, the system runs on Linux. ® It runs on an OS (Linux is a registered trademark of Linus Torvalds, Boston, MA). The application is flexible and designed to run in a variety of different environments without affecting any of its main functions.

[0083] In some implementations, the system includes multiple components distributed among multiple computing devices. One or more components may take the form of computer-executable instructions contained in a computer-readable medium. The system and processes are not limited to the specific implementations described herein. Furthermore, each system component and each process may be practiced independently and decoupled from other components and processes described herein. Each component and process may also be used in combination with other assembly packages and processes.

[0084] As used herein, elements or steps listed in the singular and beginning with the words “a” or “an” should be understood to not exclude multiple elements or steps unless such exclusion is explicitly stated. Furthermore, references to “example” or “an example” in this disclosure are not intended to be construed as excluding the existence of other examples that also contain the listed features. Moreover, within the limits used herein, the terms “comprising,” “having,” “containing,” and variations thereof are intended to be included as open transitional terms in a manner similar to the term “including,” without excluding any additional or other elements. The terms “optional” or “optionally” mean that an event or situation subsequently described may or may not occur, and the description includes instances where the event occurs and instances where the event does not occur.

[0085] Unless otherwise indicated, approximate language as used herein, such as “generally,” “substantially,” and “about,” indicates, as will be recognized by one of ordinary skill in the art, that such modified terms may apply only to approximations, not absolute or perfect degrees. Therefore, a value modified by one or more terms (such as “about,” “approximately,” and “substantially”) is not limited to the specified precise value. In at least some instances, approximate language may correspond to the precision of the instrument used to measure the value. Scope limitations can be identified herein and throughout the specification and claims. Unless otherwise indicated by context or language, these scopes may be combined and / or interchanged, and include all subscopes contained herein.

[0086] In addition, unless otherwise indicated, the terms “first,” “second,” etc., are used merely as punctuation and are not intended to impose any order, position, or hierarchy requirements on the items referred to by these terms. Furthermore, for example, a reference to an item “second” does not require or exclude the existence of an item such as “first” or a lower number, or an item such as “third” or a higher number.

[0087] Furthermore, as used herein, the term "real-time" refers to at least one of the following: the time when the associated event occurs, the time when predetermined data is measured and collected, the time when the data is processed, and the time when the system responds to the event and the environment. In the examples described herein, these activities and events occur essentially instantaneously.

[0088] The patent claims at the end of this document are not intended to be used in accordance with 35 USC. 112(f) shall be interpreted unless conventional “component plus function” language, such as “component for…” or “step for…”, is explicitly stated in the claims.

[0089] This written description uses examples to disclose the invention, including the best mode, and also enables any person skilled in the art to practice the invention, including making and using any device or system and performing any combined methods. The patentable scope of the invention is defined by the claims and may include other examples that would occur to a person skilled in the art. Such other examples are intended to be within the scope of the claims if they have structural elements that are not different from the literal language of the claims, or if they include equivalent structural elements that are not substantially different from the literal language of the claims.

[0090] Other aspects of the invention are provided by the subject matter of the following provisions:

[0091] A computer system for performing finite element analysis. The computer system uses at least one processor communicating with at least one memory device. The at least one processor is programmed to: divide a model of an additively manufactured (AM) article into a sub-model of a region of interest and remaining segments; mesh the remaining segments using a coarse mesh; calculate a compliance matrix for each layer of the remaining segments based on the coarse mesh; mesh the sub-model using a fine mesh, wherein the fine mesh covers a subset of geometry relative to the coarse mesh; divide the sub-model into layers based on the fine mesh; analyze each layer of the sub-model based on the fine mesh; determine the influence of the remaining segments on the sub-model based on multiple compliance matrices; and generate an updated sub-model based on the analysis and the influence of the remaining segments on the sub-model.

[0092] In a computer system according to any one of the foregoing clauses, the at least one processor is further programmed to select the region of interest from which residual stress needs to be reduced.

[0093] The computer system according to any one of the foregoing clauses, wherein the at least one processor is further programmed to select the region of interest based on one or more reports of cracks in the article.

[0094] The computer system according to any one of the foregoing clauses, wherein the region of interest further includes an additional region surrounding the location where the crack is reported.

[0095] In a computer system according to any one of the foregoing clauses, wherein the at least one processor is further programmed to divide the remaining segments into layers based on the coarse grid.

[0096] In any of the preceding clauses, the coarse grid in the computer system is a voxel grid.

[0097] The computer system according to any one of the foregoing clauses, wherein the at least one processor is further programmed to retain the laying of one or more nodes at one or more boundaries between the sub-model and the remaining segment as degrees of freedom.

[0098] In any of the preceding clauses, the computer system wherein the compliance matrix is ​​the size of a system of linear equations determined by the number of degrees of freedom at the boundaries of the sub-model and the remaining segments.

[0099] The computer system according to any one of the foregoing clauses, wherein the at least one processor is further programmed to determine at each step a mapping between the degrees of freedom of the remaining segment at the interface of the remaining segment sub-model and the degrees of freedom of the sub-model at the same interface.

[0100] In a computer system according to any one of the foregoing clauses, wherein the at least one processor is further programmed to determine the mapping by establishing one or more constraint equations about the degrees of freedom.

[0101] In a computer system according to any one of the foregoing clauses, wherein the at least one processor is further programmed to skip one or more layers of the remaining segments below the sub-model.

[0102] The computer system according to any one of the foregoing clauses, wherein the at least one processor is further programmed to perform shape optimization on the sub-model.

[0103] The computer system according to any one of the foregoing clauses, wherein the at least one processor is further programmed to generate the sub-model to be tested.

[0104] The computer system according to any one of the foregoing clauses, wherein the at least one processor is further programmed to apply a layer-by-layer intrinsic strain method to a finely meshed sub-model.

[0105] The computer system according to any one of the foregoing clauses, wherein the effect includes at least one of stiffness or load.

[0106] In a computer system according to any one of the foregoing clauses, the at least one processor is further programmed to shift the sub-model up or down so that the top layer of the sub-model in vertical position matches the top layer of the remaining segment in vertical position.

[0107] The computer system according to any one of the foregoing clauses, wherein the at least one processor is further programmed to apply an updated subdomain to the remaining segment to generate a build file for an additive manufacturing machine.

[0108] A computer-implemented method for finite element analysis. The method is implemented on a computer system including at least one processor communicating with at least one memory device. The method includes: dividing a model of an additively manufactured (AM) article into a sub-model of a region of interest and remaining segments; meshing the remaining segments using a coarse mesh; calculating a compliance matrix for each layer of the remaining segments based on the coarse mesh; meshing the sub-model using a fine mesh, wherein the fine mesh covers a subset of geometry relative to the coarse mesh; dividing the sub-model into layers based on the fine mesh; analyzing each layer of the sub-model based on the fine mesh; determining the influence of the remaining segments on the sub-model based on multiple compliance matrices; and generating an updated sub-model based on the analysis and the influence of the remaining segments on the sub-model.

[0109] The method according to any one of the foregoing clauses further includes selecting the region of interest where residual stress needs to be reduced.

[0110] The method according to any one of the foregoing clauses further includes dividing the remaining segments into layers based on the coarse grid.

Claims

1. A computer system for implementing finite element analysis, the computer system comprising at least one processor in communication with at least one memory device, wherein the at least one processor is programmed to: divide a model of an additive manufacturing (AM) article into a submodel of a region of interest and a remaining section; mesh the remaining section using a coarse mesh; compute a flexibility matrix for each layer of the remaining section based on the coarse mesh; mesh the submodel using a fine mesh, wherein the fine mesh covers a subset of geometry relative to the coarse mesh; divide the submodel into layers based on the fine mesh; analyze each layer of the submodel based on the fine mesh; determine an effect of the remaining section on the submodel based on a plurality of flexibility matrices; and generate an updated submodel based on the analysis and the effect of the remaining section on the submodel.

2. The computer system of claim 1, wherein the at least one processor is further programmed to select the region of interest that requires a reduction in residual stress.

3. The computer system of claim 2, wherein the at least one processor is further programmed to select the region of interest based on one or more reports of cracks in the article.

4. The computer system of claim 3, wherein the region of interest further comprises an additional region around a location where the cracks are reported.

5. The computer system of claim 1, wherein the at least one processor is further programmed to divide the remaining section into layers based on the coarse mesh.

6. The computer system of claim 1, wherein the coarse mesh is a voxel mesh.

7. The computer system of claim 1, wherein the at least one processor is further programmed to pave one or more nodes located at one or more boundaries between the submodel and the remaining section as degrees of freedom.

8. The computer system of claim 1, wherein the flexibility matrix is a size of a system of linear equations determined by a number of degrees of freedom at the boundaries of the submodel and the remaining section.

9. The computer system of claim 8, wherein the at least one processor is further programmed to determine, at each step, a mapping between the degrees of freedom of the remaining section at a remaining section submodel interface and the degrees of freedom of the submodel at the same interface.

10. The computer system of claim 9, wherein the at least one processor is further programmed to determine the mapping by establishing one or more constraint equations on the degrees of freedom.

11. The computer system of claim 1, wherein the at least one processor is further programmed to skip one or more layers of the remaining section below the submodel.

12. The computer system of claim 1, wherein the at least one processor is further programmed to perform a shape optimization on the submodel. ​ 13. The computer system of claim 1, wherein the at least one processor is further programmed to generate a configuration of the sub-model to be tested.

14. The computer system of claim 1, wherein the at least one processor is further programmed to apply a layer-by-layer intrinsic strain approach to a finely meshed sub-model.

15. The computer system of claim 1, wherein the influence includes at least one of stiffness or load.

16. The computer system of claim 1, wherein the at least one processor is further programmed to shift the sub-model up or down to match a top layer of a sub-model vertical position to a top layer of a remaining section vertical position.

17. The computer system of claim 1, wherein the at least one processor is further programmed to apply an updated sub-domain to the remaining section to generate a build file for an additive manufacturing machine.

18. A computer-implemented method for finite element analysis, the method implemented on a computer system comprising at least one processor in communication with at least one memory device, wherein the method comprises: dividing a model of an additive manufacturing (AM) article into a sub-model of a region of interest and a remaining section; meshing the remaining section using a coarse mesh; computing a flexibility matrix for each layer of the remaining section based on the coarse mesh; meshing the sub-model using a fine mesh, wherein the fine mesh covers a subset of geometry relative to the coarse mesh; dividing the sub-model into layers based on the fine mesh; analyzing each layer of the sub-model based on the fine mesh; determining an influence of the remaining section on the sub-model based on a plurality of flexibility matrices; and generating an updated sub-model based on the analysis and the influence of the remaining section on the sub-model.

19. The computer-implemented method of claim 18, further comprising selecting the region of interest that requires a reduction in residual stress.

20. The computer-implemented method of claim 18, further comprising dividing the remaining section into layers based on the coarse mesh.

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