Method for calculating dual moduli of fiber reinforced composite sandwich structure

Abstract

The invention discloses a dual-modulus calculation method for a fiber reinforced composite sandwich structure, which comprises the following steps of: establishing a finite element model of the composite sandwich structure, and performing grid division on a three-dimensional entity unit; setting three field variable parameters respectively corresponding to the elasticity moduli of the material in three directions, calculating and extracting the stress component of each grid unit according to the input initial condition of the material attribute applied by each grid unit, endowing the elasticity moduli in different directions according to the positive and negative of the stress components in different directions, and then carrying out iteration to obtain the elastic modulus of the material in different directions. Calculating responses such as stress, strain and displacement of the structure; according to the method, the elastic module and the stress component of each grid unit of the dual-modulus material can be dynamically adjusted in finite element simulation, so that the calculation precision and the convergence speed are improved, and the accurate calculation of the response of the structural stress, strain, displacement and the like of the fiber reinforced composite sandwich structure in the stretching and compression states is realized.

Description

Technical Field

[0001] The present invention specifically relates to a calculation method for the bimodulus of a fiber-reinforced composite sandwich structure. Background Art

[0002] Due to its excellent properties such as light weight, high strength, and corrosion resistance, fiber-reinforced composites have been widely used in non-load-bearing structures and local load-bearing structures such as ships, bridges, and automobiles. In the field of engineering structure calculation, the elastic modulus of a material is an important parameter to describe its mechanical properties. For a single material, its tensile and compressive elastic moduli can usually be regarded as the same, so traditional theoretical calculation and numerical analysis methods can more accurately predict its mechanical response. However, the elastic moduli of fiber-reinforced composites differ significantly in the tensile and compressive states, and this bimodulus characteristic causes large errors in traditional calculations. This characteristic has a significant impact on the mechanical response of engineering structures, making traditional theoretical calculation and numerical analysis methods face challenges when dealing with such materials.

[0003] Currently, the theoretical calculation and numerical calculation methods for bimodulus materials are mainly applicable to single materials and simple geometric structures. When dealing with complex sandwich structures, these methods often lead to calculation difficulties due to slow convergence or even non-convergence. In addition, mainstream finite element analysis software also lacks the function to directly handle bimodulus problems, which further limits the application of bimodulus materials in engineering structure calculations.

[0004] Existing research shows that the bimodulus elastic characteristic has a significant impact on the mechanical response of engineering structures. When the tensile elastic modulus is greater than the compressive elastic modulus, the maximum tensile stress calculated using the same elastic modulus theory will be on the small side; conversely, when the tensile elastic modulus is less than the compressive elastic modulus, the calculated maximum compressive stress will be on the small side. In some cases, the error between the single-modulus and bimodulus calculation results can even reach more than 100%. Therefore, it is of great significance to develop a method that can accurately calculate the bimodulus characteristics of fiber-reinforced composite sandwich structures.

[0005] In summary, although fiber-reinforced composites have broad application prospects in the engineering field, their bimodulus characteristics pose challenges to traditional calculation methods. Existing technologies have deficiencies in dealing with complex sandwich structures and directly handling bimodulus problems, so there is an urgent need for a new method that can accurately calculate the bimodulus characteristics of fiber-reinforced composite sandwich structures.

[0006] The disadvantages of the existing technology include: Low calculation accuracy: Improper handling of bimodulus characteristics: Existing theoretical calculation and numerical analysis methods usually regard the tensile modulus and compressive modulus as equal, ignoring the bimodulus characteristic that the elastic moduli of fiber-reinforced composites are inconsistent in the tensile and compressive states, resulting in low calculation accuracy and large errors.

[0007] Poor convergence: When dealing with complex sandwich structures, due to the slow convergence speed or even non - convergence of the iterative algorithm, it is difficult for existing methods to obtain accurate results.

[0008] Limited scope of application: Single material and simple geometric structure: Existing calculation methods are mainly applicable to single materials and simple geometric structures. For complex sandwich structures, especially fiber - reinforced composite sandwich structures, their applicability is severely limited.

[0009] Affect the safety and reliability of engineering structures: Inaccurate stress calculation: Due to the limitations of the calculation method, it is impossible to accurately calculate the stress distribution of fiber - reinforced composite sandwich structures in the tensile and compressive states, thereby affecting the safety and reliability of engineering structures.

[0010] Design and optimization are restricted: The lack of accurate calculation methods restricts engineering design and optimization, and the performance advantages of materials cannot be fully utilized. Summary of the Invention

[0011] The purpose of the present invention is to provide a calculation method for the double modulus of a fiber - reinforced composite sandwich structure, which dynamically adjusts the elastic modulus and stress components of each grid unit of the double - modulus material in the finite - element simulation, thereby improving the calculation accuracy and convergence speed, and realizing the accurate calculation of the stress of the fiber - reinforced composite sandwich structure in the tensile and compressive states.

[0012] The technical solution adopted by the present invention is as follows: A calculation method for the double modulus of a fiber - reinforced composite sandwich structure, comprising the following steps: Step S1, establish a finite - element model of the composite sandwich structure, and perform mesh division on the structure model using three - dimensional solid elements; Step S2, set three field - variable parameters , and , which respectively correspond to the elastic moduli of the material in three directions. When , it indicates that this direction is the tensile elastic modulus; when ), it indicates that this direction is the compressive elastic modulus; Step S3, according to the input initial conditions of applying material properties to each grid unit, calculate and extract the stress components of each grid unit, and assign different elastic moduli according to the positive and negative of the stress components in different directions, and then perform iterative calculation of the elastic modulus and the corresponding stress components of each grid unit; Step S4, according to the elastic modulus and the corresponding stress components of each grid unit, calculate the stress of the composite sandwich structure through the finite - element model.

[0013] Preferably, the stress components include axial stresses in three directions.

[0014] Preferably, in the step S3, the specific process of iteratively calculating the elastic modulus and the corresponding axial stress components is as follows: Step S31, calculate and extract the axial stresses in three directions of each grid element using the elastic modulus of the material , where represents the grid element number, represents the th iteration, the value of i is (1, 2, 3), which respectively represent the elastic moduli in the directions of three mutually perpendicular coordinate axes. When i = 1, it is the x - direction of the local coordinate system; when i = 2, it is the Y - direction of the local coordinate system; when i = 3, it is the z - direction of the local coordinate system; Step S32, judge the positive and negative of the axial stresses in three directions. If the axial stress is positive, the field variable parameter in the corresponding direction is taken as 1; if the axial stress is negative, the field variable in the corresponding direction is taken as 0. Re - assign the corresponding field variable values to each grid element, and compare the number of elements whose field variables change in the th iteration with that in the th iteration; Step S33, repeat the above steps S31 - 32 for iteration until the number of elements whose field variables change is less than the set percentage value of the total number of grid elements of the overall sandwich structure , and the iteration ends. The calculation result of the last iteration is the final calculation result.

[0015] Preferably, the set percentage value is 0.1%.

[0016] Preferably, in the step S1, a finite - element model of the composite sandwich structure is established in the ABAQUS software.

[0017] Preferably, in the step S1, the three - dimensional solid element is the C3D8R three - dimensional solid element.

[0018] Preferably, in the step S3, the input initial conditions for applying material properties to the grid elements include the tensile or compressive elastic moduli, Poisson's ratios, and shear moduli in different directions of each grid element.

[0019] Preferably, in the step S3, the initial conditions are input through the USDFLD function interface program written.

[0020] Preferably, in the step S33, the specific process of repeated iteration is as follows: After replacing the material properties of each grid element, perform calculations. After the calculations are completed, extract the axial stresses in three directions corresponding to each grid element again, re - assign the corresponding field variable values to each grid element, and compare the The next iteration is equivalent to the number of elements where the field variables change in the next iteration. When the total number of elements where the field variables change is less than the set percentage value of the total number of grid elements of the overall sandwich structure, it can be considered that the calculation converges, the iteration ends, and the above steps are no longer repeated. The calculation result of the next iteration is the calculation result considering the unequal tensile and compressive moduli.

[0021] Preferably, in the step S2, three field variable parameters are set, corresponding to the elastic moduli of the material in three mutually perpendicular directions respectively.

[0022] Preferably, in the step S4, the strain and displacement responses of the composite sandwich structure are also calculated through the finite element model.

[0023] The beneficial effects of the present invention are as follows: In the present invention, a finite element model of the composite sandwich structure is established and meshed; the elastic moduli of each grid are calculated according to the material properties applied to each grid element, the stress components of each grid element are calculated and extracted, and different tensile or compressive elastic moduli in different directions are assigned according to the positive and negative of the stress components in different directions. Then, the elastic moduli and the corresponding stress components of each grid are iteratively calculated, fully considering the bimodulus characteristics of the elastic moduli of each grid element of the fiber-reinforced composite material being inconsistent in the tensile and compressive states. Therefore, the complex stress of each grid of the bimodulus material in the actual situation can be considered, and the dynamic adjustment of the elastic modules and stress components of each grid element of the bimodulus material in the finite element simulation is realized, thereby improving the calculation accuracy and convergence speed, and achieving the accurate calculation of the stress of the fiber-reinforced composite sandwich structure in the tensile and compressive states. Description of the Drawings

[0024] Figure 1 is a flowchart of the bimodulus calculation method for the fiber-reinforced composite sandwich structure in the embodiment of the present invention.

[0025] Figure 2 is a flowchart of the iterative calculation of the elastic modulus and the corresponding axial stress component in the embodiment of the present invention.

[0026] Figure 3 is a schematic diagram of the mechanical model of the bimodulus rectangular cross-section beam in the embodiment of the present invention.

[0027] Figure 4 is a schematic diagram of the cross-sectional property analysis of the bimodulus rectangular cross-section beam in the embodiment of the present invention.

[0028] Figure 5 is the front view of the composite sandwich structure beam in the embodiment of the present invention.

[0029] Figure 6 It is a schematic cross-sectional view of a composite sandwich structure beam in an embodiment of the present invention.

[0030] Figure 7 It is the front view of a simply supported beam in an embodiment of the present invention.

[0031] Figure 8 It is Figure 7 the left view of

[0032] Figure 9 It is the finite element model diagram of a simply supported beam in an embodiment of the present invention.

[0033] Figure 10 It is a schematic cross-sectional view of an equivalent pre-composite sandwich structure beam in an embodiment of the present invention.

[0034] Figure 11 It is a schematic cross-sectional view of an equivalent composite sandwich structure beam after equivalent by the equivalent area method in an embodiment of the present invention. Detailed implementation manners

[0035] In order to make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0036] In the description of the present invention, it should be understood that if there are terms involved such as "center", "longitudinal", "transverse", "length", "width", "thickness", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", "clockwise", "counterclockwise", etc., the orientation or positional relationship indicated is based on the orientation or positional relationship shown in the drawings. It is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation to the present invention. In addition, the terms "first" and "second" are only used for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly indicating the quantity of the indicated technical features. Thus, the features defined with "first" and "second" may explicitly or implicitly include one or more of the described features. In the description of the present invention, "a plurality" means two or more unless otherwise specifically defined.

[0037] In the description of the present invention, it should be noted that unless otherwise clearly specified and defined, the terms "installation", "connection", and "coupling" should be understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or an integral connection. It can be a mechanical connection or an electrical connection. It can be directly connected or indirectly connected through an intermediate medium, and it can be the communication inside two components or the interaction relationship between two components. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0038] Embodiment 1 A method for calculating the bimodulus of a fiber-reinforced composite sandwich structure, as Figure 1 and Figure 2 shown, includes the following steps: Step S1: Establish a finite element model of the composite sandwich structure, and perform mesh division on the structural model using three-dimensional solid elements; Step S2: Set three field variable parameters , and , which respectively correspond to the elastic moduli of the material in three directions. When , it indicates that this direction is the tensile elastic modulus; when ), it indicates that this direction is the compressive elastic modulus; Step S3: According to the input initial conditions of applying material properties to each mesh element, calculate and extract the stress components of each mesh element, and assign different elastic moduli according to the positive and negative of the stress components in different directions, and then perform iterative calculation of the elastic modulus and the corresponding stress components of each mesh element; Step S4: According to the elastic modulus and the corresponding stress components of each mesh element, calculate the stress of the composite sandwich structure through the finite element model.

[0039] Furthermore, the stress components include the axial stresses in three directions.

[0040] The model of the composite sandwich structure is as Figures 5 - 6 shown.

[0041] Embodiment 2 On the basis of Embodiment 1, step S3 is further limited, and the performance of Embodiment 2 after limitation is better.

[0042] In the said step S3, the specific process of performing iterative calculation of the elastic modulus and the corresponding axial stress components is as follows: Step S31: Calculate and extract the axial stresses in three directions of each mesh element using the tensile elastic modulus of the material , where represents the mesh element number, Represents the ith iteration. The value of i is (1, 2, 3), which respectively represent the elastic moduli in three mutually perpendicular coordinate axis directions. When i = 1, it is the x - direction; when i = 2, it is the y - direction; when i = 3, it is the z - direction. The x - direction, y - direction, and z - direction are the three set coordinate axis directions respectively, and the meanings are the same in the following methods; Step S32: Determine the positive and negative of the axial stresses in the three directions. If the axial stress is positive, the field variable parameter in the corresponding direction is taken as 1; if the axial stress is negative, the field variable in the corresponding direction is taken as 0. Re - assign the corresponding field variable values to each grid element, and compare the number of elements whose field variables change in the ith iteration with the number of elements whose field variables change in the iteration; Step S33: Repeat the above steps S31 - 32 for iteration until the number of elements whose field variables change is less than the set percentage value of the total number of grid elements of the overall sandwich structure The iteration ends, and the calculation result of the last iteration is the calculation result considering the unequal tensile and compressive moduli.

[0043] Furthermore, the set percentage value is 0.1%.

[0044] Furthermore, in the above - mentioned step S1, a finite - element model of the composite sandwich structure is established in the ABAQUS software.

[0045] Furthermore, in the above - mentioned step S1, the three - dimensional solid element is the C3D8R three - dimensional solid element.

[0046] Furthermore, in the above - mentioned step S3, the input initial conditions for applying material properties to the grid elements include the tensile or compressive elastic moduli, Poisson's ratios, and shear moduli in different directions of each grid element.

[0047] Furthermore, in the above - mentioned step S3, the initial conditions are input through the USDFLD function interface program written.

[0048] Furthermore, in the above - mentioned step S33, the specific process of repeated iteration is as follows: After replacing the material properties of each grid element, calculations are performed. After the calculations are completed, the axial stresses in the three directions corresponding to each grid element are extracted again, and the corresponding field variable values are re - assigned to each grid element, and compare the number of elements whose field variables change in the ith iteration with the number of elements whose field variables change in the iteration. When the total number of elements whose field variables change is less than the set percentage value of the total number of grid elements of the overall sandwich structure it can be considered that the calculation converges, the iteration ends, and the above steps are stopped. The The calculation result of the current iteration is the calculation result when considering the unequal tensile and compressive moduli.

[0049] Furthermore, in the step S2, three field variable parameters are set, corresponding to the elastic moduli of the material in three mutually perpendicular directions respectively.

[0050] In the step S4, the strain and displacement responses of the composite sandwich structure are also calculated through the finite element model.

[0051] Furthermore, the neutral axis position and axial stress of the material are calculated by other methods: the Ambartsumyan method, the equivalent area method, and the GWFMM method, where the Ambartsumyan method is the method of C.A. Ambartsumyan, and the GWFMM method is the general weighted flexibility matrix material model method.

[0052] 1. When using the Ambartsumyan method, the specific process is as follows: The stress-strain relationship of the two-mode elasticity mechanics is different from that of the classical elasticity mechanics. The Ambartsumyan method proposes an elastic theory for the mechanical analysis of two-mode materials and structures. It is proposed in the principal stress space and is determined by the signs of the three principal stresses in the three-dimensional two-mode elasticity. The constitutive equation of the two-mode material in the principal stress space can be expressed as: (1) (2) (3) (4) In the formula: is the principal strain vector of the grid element; is the principal stress vector of the grid element; is the flexibility matrix, determined by the signs of the principal stresses calculated by the structure, 11 and 11 The subscript 11 of represents the x direction, 22 and 22 The subscript 22 of represents the y direction, 33 and 33 The subscript 33 of represents the z direction.

[0053] (5) (6) In the formula, , are the elastic moduli in the tensile and compressive states, respectively; , are the Poisson's ratios in the tensile and compressive states, respectively. Similar flexibility matrices can be obtained for other stress conditions. Ambartsumyan considered that the material has the same , , and in the three principal stress directions of the material, without considering the anisotropy of the material. At the same time, to ensure the symmetry of the flexibility matrix, it is assumed that the of the material, which greatly reduces the applicable range of the bimodulus theory. Here, when i = 1, it is the x-direction, when i = 2, it is the y-direction, and when i = 3, it is the z-direction.

[0054] On this basis, Ambartsumyan's method gives the calculation methods for the neutral axis and the normal stress of the cross-section of beams, rods, and plates under simple loads. For a bimodulus rectangular cross-section beam structure under pure bending, as Figure 3 and Figure 4 shown, the height of the rectangular beam cross-section is , the width is , the height and elastic modulus of the tensile zone cross-section are and , respectively, and the compressive zone is and . The areas of the tensile and compressive zones are and , respectively, and it bears a bending moment . Under the action of pure bending moment, the heights of the tensile and compressive zones can be expressed as: , (7) The equivalent moment of inertia of the cross-section is: (8) The axial stresses and in the tensile and compressive zones corresponding to pure bending are respectively: , (9) In the formula: is the bending moment of the beam cross-section; is the equivalent bending stiffness of the beam cross-section, , is the distance from the stress calculation point to the x-axis.

[0055] Schematic diagram of a bimodulus rectangular cross-section beam, as Figure 3 and Figure 4 shown.

[0056] Since the equivalent area method only extends the Ambartsumyan method to the composite material cross-section, the calculation results of the Ambartsumyan method are the same as those of the equivalent area method.

[0057] 2. Equivalent area method: The specific calculation process of the equivalent area method includes the following steps: Step 1, cross-section division: Divide the sandwich composite beam cross-section into multiple parts according to different materials, such as the upper and lower skins, core material, stiffened skin, and stiffened core material, etc.; Assume that the tensile and compressive properties of each part of the material are the same, but the elastic moduli may be different; Step 2, equivalent area calculation: Divide the beam cross-section into i parts according to different materials, and assume , where is the elastic modulus of the i-th part of the material, is the reference elastic modulus (such as tensile modulus or compressive modulus); Through cross-section transformation, obtain the equivalent cross-section area under the same modulus , where is the equivalent cross-section area of the i-th part, is the cross-sectional area of the i-th part; Step 3, neutral axis calculation: According to the equivalent area method, calculate the position of the neutral axis of the sandwich composite cross-section , where is the distance from the center of the i-th part to the reference coordinate axis; Step 4, axial stress calculation: According to the position of the neutral axis, further calculate the axial stress of the i-th part of the cross-section , where M is the bending moment, is the moment of inertia of the i-th part relative to the neutral axis.

[0058] Through the equivalent area method, the complex sandwich structure cross-section is simplified to a single material cross-section with an equivalent area, such as Figure 10 and Figure 11 , thus simplifying the calculation process.

[0059] The equivalent area method can also be replaced by: other cross-section simplification methods, such as the equivalent moment of inertia method, which obtains the equivalent moment of inertia of the entire cross-section by calculating the moments of inertia of each part and performing equivalent transformation, so as to calculate the axial stress; among them, the specific method of neutral axis calculation can be adjusted according to the actual situation, such as for composite material stiffened sandwich panels, the neutral axis position control equation can be used to solve the position of the neutral axis.

[0060] 3. When using the GWFMM method, the specific process is as follows: Considering the unequal tensile and compressive moduli and anisotropy of materials, a constitutive model under three-dimensional stress state, namely the Generalized Weighted Flexibility Matrix Material Model (GWFMM), is adopted, and a general analysis module for orthotropic materials with different tensile and compressive elastic moduli is established based on this. The method assigns values to the generalized weighted flexibility matrix according to the signs and magnitudes of the principal stresses of the structure. The constitutive equation of the material is: (10) where: is the principal strain vector in the ij direction, ; is the principal stress vector in the ij direction; is the flexibility matrix, which is determined by the signs of the principal stresses calculated from the structure. According to the distribution of the principal stresses in three directions, there are a total of 8 expressions. Among them, and when the subscript is 11, it represents the x direction; when the subscript is 22, it represents the y direction; when the subscript is 33, it represents the z direction; when the subscript is 12, it represents the shear direction in the xy plane; when the subscript is 13, it represents the shear direction in the xz plane; when the subscript is 23, it represents the shear direction in the yz plane.

[0061] (1) When : (11) (2) When : (12) (3) When : (13)

[0062]

[0063] (4) When : (14)

[0064] Among them, , are the elastic moduli in the tensile and compressive states in the x direction respectively; , are the elastic moduli in the tensile and compressive states in the y direction respectively; , are the elastic moduli in the tensile and compressive states in the z direction respectively; $\nu_{ij}$ ($i = 1, 2, 3$; $j = 1, 2, 3$) is the Poisson's ratio under the load in the $i$-direction in the tensile state (i.e., the ratio of the deformation in the $i$-direction to the deformation in the $j$-direction under the load in the $i$-direction in the tensile state), $\nu_{ij}$ ($i = 1, 2, 3$; $j = 1, 2, 3$) is the Poisson's ratio under the load in the $i$-direction in the compressive state (i.e., the ratio of the deformation in the $i$-direction to the deformation in the $j$-direction under the load in the $i$-direction in the compressive state; when $i$ or $j$ is 1, the 1-direction represents the $x$-direction, when $i$ or $j$ is 2, the 2-direction represents the $y$-direction, and when $i$ or $j$ is 3, the 3-direction represents the $z$-direction); the coefficient 、 、 are parameters related to shear stress and shear strain, and are not affected by the direction and magnitude of the principal stress. For the other 4 stress combinations, the expression of the compliance matrix can be derived similarly. According to the constitutive equation of the material, a finite element iterative analysis algorithm can be written to calculate the bimodulus structure.

[0065] To verify the accuracy of the finite element iterative method proposed in this paper, first, a simply supported beam of a single material under a concentrated load was calculated, and the calculation results of the finite element calculation method in this paper were compared with the calculation results of the GWFMM method. The geometric form of the simply supported beam is as Figures 7 - 9 shown, where the beam length is , the beam width is , the beam height is , the heights of the tensile and compressive zones are and respectively, the magnitude of the concentrated force is , the origin of the coordinate system is located at the mid-span neutral plane, the axis direction along the axis is X axis direction, the normal direction along the neutral plane is Y axis direction, and the direction perpendicular to the XY plane is Z axis direction.

[0066] According to the Figure 1 shown calculation flow chart, in this paper, the C3D8R three-dimensional solid element in the finite element software ABAQUS 2020 was used to model the simply supported beam, and the difference between the tensile modulus and the compressive modulus of the material was realized by calling the written USDFLD subroutine. The performance parameters of the material are shown in Table 1, and the shear modulus of the material is taken as .

[0067] When considering a simply supported beam under a concentrated load, the tensile modulus of the material is 10 times the compressive modulus, and the neutral axis of the cross-section will deviate towards the tensile side. During the iterative process, the material properties of the elements need to be replaced according to the calculation results. Therefore, the element size in the height direction of the beam cross-section should be as small as possible during modeling, while the element sizes in the length and width directions do not have specific requirements. From the calculation results, it can be seen that as the element size in the height direction decreases, the axial stress of the mid-span cross-section gradually increases. When the element size in the height direction is 1 mm, the axial stress will not increase with the further reduction of the element. Therefore, when performing finite element analysis, the element size is taken as 5 mm × 5 mm × 1 mm (length × width × height).

[0068] (a) Geometric model (b) Finite element model Figure 9 Simply supported beam model Table 1 Material properties of the simply supported beam

[0069] Table 2 Calculation results of different methods when the tension and compression models are the same

[0070] First, consider the case where the tension and compression models are the same. Since the equivalent area method only extends the Ambartsumyan method to composite cross-sections, the calculation results of the Ambartsumyan method are the same as those of the equivalent area method. Table 2 presents the calculation results of the height of the tension zone, the height of the compression zone, and the maximum axial tensile stress of various methods when the material parameters are taken as the tensile material parameters. Through calculation, it can be seen that the positions of the neutral planes obtained by the three methods are the same, and the calculated maximum axial tensile stresses are also relatively close. Based on the equivalent area method, the error of the maximum tensile stress obtained by the GWFMM method is -3.0%, and the error of the maximum tensile stress obtained by the finite element calculation method is -5.5%.

[0071] Table 3 presents the calculation results of various methods considering different tensile and compressive moduli. According to the calculation results, it can be seen that the heights of the tension and compression zones of the finite element iterative method proposed in this paper are relatively close to the calculation results of the equivalent area method and the GWFMM method, while the maximum tensile and compressive stresses are relatively small. The main reason is that the influence of the material shear modulus is not considered in the calculation of the reference methods, while the finite element iterative method proposed in this paper can consider the influence of the material shear modulus.

[0072] Since the stress at the stress singularity position caused by loading or constraints is inaccurate, the axial stress in the tensile zone of the bottom surface far from the loading point and the constraint position is selected to analyze the differences between different material properties. According to the calculation results, it can be seen that: (1) When considering the same tensile and compressive properties of the material, the axial stress distributions obtained by using tensile and compressive properties for calculation respectively are the same; (2) When considering different tensile and compressive properties of the material, the calculated tensile stress is about 2.03 times that of the calculation result when considering the same tensile and compressive properties, and the compressive stress is 0.67 times that of the single modulus; (3) The shear modulus of the material has a certain influence on the calculation result. The smaller the shear modulus, the greater the axial stress at the bottom surface of the beam. When the shear modulus is reduced by 9 times, the maximum axial tensile stress increases by 0.7%; (4) When the tensile and compressive properties are not equal, the stress in the compression zone is less than that in the compression zone when the tensile and compressive properties are equal, and the stress in the tension zone is greater than that in the compression zone when the tensile and compressive properties are equal. That is, when the tensile elastic modulus is greater than the compressive elastic modulus, the maximum tensile stress calculated by the same elastic modulus theory is underestimated.

[0073] Table 3 Comparison of calculation results of various methods when the tensile-compression model is unequal

[0074] In the present invention, the accuracy and effectiveness of the method can be proved by comparing different calculation methods.

[0075] It should be noted that in this article, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the term "comprising", "including" or any other variant thereof is intended to cover non-exclusive inclusion, so that a process, method, article or device comprising a series of elements not only includes those elements, but also includes other elements not expressly listed, or also includes elements inherent to such process, method, article or device.

[0076] It should be understood that those of ordinary skill in the art can make improvements or transformations according to the above description, and all such improvements and transformations should fall within the protection scope of the appended claims of the present invention.

Claims

1. A method for calculating the dual modulus of a fiber reinforced composite sandwich structure, characterized in that: The following steps are involved: Step S1, establishing a finite element model of a composite sandwich structure, and meshing the structure model using three-dimensional solid elements; Step S2, setting three field variable parameters , and , which correspond to the elastic modulus of the material in three directions. When , it indicates that the direction is tensile elastic modulus; when ), it indicates that the direction is the compressive elastic modulus; Step S3, according to the input initial conditions of the material properties of each grid unit, the stress components of each grid unit are calculated and extracted, and the elastic modulus in different directions is assigned according to the positive and negative stress components in different directions, and then the elastic modulus and corresponding stress components of each grid unit are iteratively calculated; Step S4, calculating the stress of the composite sandwich structure through a finite element model according to the elastic modulus of each grid unit and the corresponding stress component; In step S3, the input initial conditions for applying material properties to the grid units include the tensile or compressive elastic modulus, Poisson's ratio and shear modulus of each grid unit in different directions.

2. The method for calculating the dual modulus of a fiber reinforced composite sandwich structure according to claim 1, characterized in that: The stress components include axial stress in three directions.

3. The method for calculating the dual modulus of a fiber reinforced composite sandwich structure according to claim 2, characterized in that: In step S3, the specific process of iteratively calculating the elastic modulus and the corresponding axial stress component is: Step S31, using the elastic modulus of the material to calculate and extract the axial stress in three directions of each grid unit ,in represents the grid cell number, Representative The value of i is (1, 2, 3), which represents the elastic modulus in three directions respectively; Step S32, determine the positive and negative of the axial stress in the three directions. If the axial stress is positive, the field variable parameter in the corresponding direction is taken as 1. If the axial stress is negative, the field variable in the corresponding direction is taken as 0. Reassign the field variable value corresponding to each grid unit and compare it with the first The iteration is equivalent to The number of cells in which the iterative field variables change; Step S33, repeat the above steps S31-32 for iteration until the number of cells where the field variables have changed is less than the total number of grid cells of the entire sandwich structure. The iteration ends when the set percentage value is reached, and the calculation result of the last iteration is the calculation result.

4. The method for calculating the dual modulus of a fiber reinforced composite sandwich structure according to claim 3, characterized in that: Set the percentage value to 0.1%.

5. The method for calculating the dual modulus of a fiber reinforced composite sandwich structure according to claim 1, characterized in that: In step S1, a finite element model of the composite sandwich structure is established in ABAQUS software.

6. The method for calculating the dual modulus of a fiber reinforced composite sandwich structure according to claim 1, characterized in that: In the step S1, the three-dimensional solid element is a C3D8R three-dimensional solid element.

7. The method for calculating the dual modulus of a fiber reinforced composite sandwich structure according to claim 1, characterized in that: In the step S3, the initial conditions are input through the written USDFLD function interface program.

8. The method for calculating the dual modulus of a fiber reinforced composite sandwich structure according to claim 1, characterized in that: In step S33, the specific process of repeated iteration is: after replacing the material properties of each grid unit, perform calculations, extract the axial stresses in the three directions corresponding to each grid unit again after the calculations are completed, reassign the field variable values ​​corresponding to each grid unit, and compare the values ​​of the first and second grid units. The iteration is equivalent to Iterate the number of cells whose field variables change, when the total number of cells whose field variables change is less than the total number of mesh cells of the entire sandwich structure When the set percentage value is reached, the calculation is considered to have converged, the iteration ends, and the above steps are stopped. The calculation result of the iteration is the calculation result when the tensile and compressive moduli are not equal.

9. The method for calculating the dual modulus of a fiber reinforced composite sandwich structure according to claim 1, characterized in that: In the step S2, three field variable parameters are set, corresponding to the elastic moduli of the material in three mutually perpendicular directions respectively.

10. The method for calculating the dual modulus of a fiber reinforced composite sandwich structure according to claim 1, characterized in that: In the step S4, the strain and displacement response of the composite sandwich structure are also calculated by the finite element model.

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