CN113946994A - A Numerical Calculation Method of Smooth Finite Element Based on Digital Twin - Google Patents

Abstract

The invention belongs to the technical field of computers, and discloses a smooth finite element numerical calculation method based on a digital twin body, which comprises the following steps: acquiring solid material data and polygonal unit data of a solid material; dividing each polygon unit in a target range into a plurality of smooth units respectively; calculating a stiffness matrix of each smooth unit, and obtaining a stiffness matrix of the polygonal unit; obtaining a solid material rigidity matrix and a load matrix based on the rigidity matrix of the polygonal unit; and performing matrix operation according to the rigidity matrix and the load matrix of the solid material to obtain a displacement approximate solution matrix U of the static elasticity problem of the solid material. On the premise of not increasing the calculation cost, the method greatly improves the solving precision and the energy convergence speed of the finite element, can eliminate the limitation on the shapes of the bilinear isoparametric elements, more flexibly disperses the problem domain and solves the problem of the limitation on the shapes of the mapping units by the traditional finite element method.

Description

A Numerical Calculation Method of Smooth Finite Element Based on Digital Twin

technical field

The invention relates to the field of computer technology, in particular to a smooth finite element numerical calculation method based on a digital twin.

Background technique

After more than half a century of development, the finite element method has become a powerful and versatile numerical simulation technique in the fields of engineering and science. Mapping elements (such as isoparametric elements) play a very important role in finite element analysis. Currently, the basic requirement for using mapping cells is that the cells must be convex and not allowed to distort sharply to guarantee a one-to-one coordinate correspondence between the physical and natural coordinates associated with the cells. Specifically, for four-node elements using mapped bilinear shape functions, a requirement is that any interior angle should theoretically be no greater than 180°. In numerical implementations, the positivity of the determinant of the Jacobian should be checked frequently to avoid severe distortion of the cells. In addition to the complexity of implementation, the quadrature rules required for higher-order approximate function problems will greatly increase the amount of computation.

Therefore, how to overcome the limitation of the shape of the mapping element by the traditional finite element method, so as to make the discrete problem domain more flexible, has become an urgent problem to be solved by those skilled in the art.

SUMMARY OF THE INVENTION

The embodiment of the present invention provides a smooth finite element numerical calculation method based on a digital twin, so as to solve the problem that the shape of the mapping element is limited by the traditional finite element method. In order to provide a basic understanding of some aspects of the disclosed embodiments, a brief summary is given below. This summary is not intended to be an extensive review, nor is it intended to identify key/critical elements or delineate the scope of protection of these embodiments. Its sole purpose is to present some concepts in a simplified form as a prelude to the detailed description that follows.

According to a first aspect of the embodiments of the present invention, a smooth finite element numerical calculation method based on a digital twin is provided.

In one embodiment, a smoothed finite element numerical algorithm for digital twins, comprising:

A smooth finite element numerical calculation method based on a digital twin, characterized in that the method comprises:

Obtain solid material data and polygon element data for solid materials;

Dividing each of the polygonal units within the target range into a plurality of smooth units;

Calculate the stiffness matrix of each smooth element, and obtain the stiffness matrix of the polygonal element;

obtaining a solid material stiffness matrix and a load matrix based on the stiffness matrix of the polygon element;

According to the solid material stiffness matrix and the load matrix, the matrix operation is carried out, and the displacement approximate solution matrix U of the static elastic problem of the solid material is obtained.

Further, obtaining the solid material data of the solid material specifically includes:

Obtain Young's modulus and Poisson's ratio for solid materials.

Further, acquiring the polygon unit data of the solid material specifically includes:

Get the element number, element node number, and node coordinates of a polygonal element.

Further, the polygon unit is a quadrilateral unit.

Further, each of the polygon units within the target range is divided into a plurality of smooth units, specifically:

Divide each quadrilateral element in the target range into four smooth elements.

Further, the stiffness matrix of each smooth element is calculated, and the stiffness matrix of the polygonal element is obtained, which specifically includes:

Each of the smooth elements is looped to determine the element area and normal of each smooth element, and a smooth operation is performed based on the element area and normal to obtain the smooth element stiffness matrix.

Further, a smoothing operation is performed based on the element area and normal, including:

Determine the definition domain of the static elasticity problem of the solid material, and obtain the outer boundary normal and boundary displacement of the defined domain based on the preset boundary conditions;

obtaining a displacement gradient of the definition domain based on the boundary outer normal and the boundary displacement;

A smoothing operation is performed on the displacement gradient of each smoothing element in the domain.

Further, the definition domain of the static elasticity problem of the solid material is determined, and the outer boundary normal and boundary displacement of the definition domain are obtained based on the preset boundary conditions, which specifically includes:

Assuming a two-dimensional static elastic problem domain Ω, the boundary of the domain is calculated based on the following formula:

σ _ij +b _j =0 in Ω

Γ = Γ _u + Γ _t

为空集；where σ _ij is the stress tensor, b _j is the body force, Γ is the boundary of the definition domain Ω, Γ _u is the forced displacement boundary, Γ _t is the traction force boundary,

is the empty set;

At this point, the boundary conditions are:

σ _ij n _j =t _i onΓ _t

为强制位移，u_i为边界Γ_u的位移。where t _i is the traction force, n _j is the normal outside the boundary,

is the forced displacement, and _ui is the displacement of the boundary Γ _u .

Further, the obtaining the displacement gradient of the definition domain based on the boundary outer normal and the boundary displacement specifically includes:

Variational weak processing is performed using the following formula:

为位移梯度的对称部分，D_ijkl为材料矩阵，δ为δ函数，k、l均为节点序号。in,

is the symmetrical part of the displacement gradient, D _ijkl is the material matrix, δ is the δ function, and k and l are the node numbers.

The smoothing operation is performed on the displacement gradient of each smoothing element within each element using the following formula:

Among them, Φ is the smooth function, u ^h (x _C ) is the displacement after the smooth operation, and x _C is the coordinate of the smooth element;

According to the distribution integral, the right-hand side of the above formula is transformed into:

Among them, n(x) is the normal vector outside the boundary;

The simultaneous formula can be obtained:

为光滑操作后的位移梯度。where Γ _C is the smooth element boundary,

is the displacement gradient after smooth operation.

Further, the variational weak formula satisfies the following conditions:

Among them, B _I is the standard gradient matrix, and N _I is the shape function matrix.

Further, the specific form of the smooth function Φ is as follows:

Among them, Ω _C is the smooth element, AC is the area of the smooth element Ω _C , u ^h (x _{C ) is the displacement after the smoothing operation, and x C is} the coordinate of the smooth element.

Further, the following formula is used to calculate the smooth strain:

为光滑应变矩阵，

为光滑应变，d_I为弹性模量。in,

is a smooth strain matrix,

is the smoothing strain, and _dI is the elastic modulus.

Further, the smooth strain matrix is calculated by the following formula:

where n _k (x) is the normal vector outside the boundary.

Further, the obtained solid material stiffness matrix and load matrix based on the stiffness matrix of the polygonal element specifically include:

The stiffness matrix of the smooth element is combined to obtain the stiffness matrix of the polygonal element, and the boundary conditions of the static elastic problem of the solid material are loaded to obtain the final stiffness matrix K and load matrix F of the solid material.

According to a second aspect of the embodiments of the present invention, a computer device is provided.

In some embodiments, the computer device includes a memory and a processor, the memory having a computer program stored thereon, the processor implementing the steps of the algorithm described above when the computer program is executed.

According to a third aspect of the embodiments of the present invention, a computer-readable storage medium is provided.

In some embodiments, the computer storage medium contains one or more program instructions for performing the method as described above.

The technical solutions provided by the embodiments of the present invention may include the following beneficial effects:

The digital twin-based smooth finite element numerical calculation method provided by the present invention obtains solid material data and polygon element data of the solid material, and divides each polygon element within the target range into a plurality of smooth elements respectively; Then, the stiffness matrix of each smooth element is calculated, and the stiffness matrix of the polygonal element is obtained. Based on the stiffness matrix of the polygonal element, the solid material stiffness matrix and the load matrix are obtained; and the matrix is obtained according to the solid material stiffness matrix and the load matrix. Operation is performed to obtain the displacement approximate solution matrix U of the static elastic problem of solid materials. Therefore, without increasing the computational cost, the solution accuracy and energy convergence speed of the finite element are greatly improved, and the restriction on the shape of the bilinear isoparametric element can be eliminated, and the problem domain can be discretized more flexibly, solving the traditional finite element. The problem of the limitation of the method on the shape of the mapping unit.

It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the invention.

Description of drawings

The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the invention and together with the description serve to explain the principles of the invention.

1 is a flow chart of a method for numerically calculating smooth finite element based on a digital twin according to an exemplary embodiment;

2 is a schematic structural diagram of a cantilever beam according to an exemplary embodiment;

Fig. 3a is a schematic diagram showing the comparison of the norm shift of the algorithm of the present invention and the traditional finite element method according to an exemplary embodiment;

Fig. 3b is a schematic diagram showing the energy norm comparison between the method of the present invention and the traditional finite element method according to an exemplary embodiment;

3c is a schematic diagram showing the comparison of the calculation time between the algorithm of the present invention and the traditional finite element method according to an exemplary embodiment;

4a is a schematic diagram of regular polygon meshing according to an exemplary embodiment;

Fig. 4b is a schematic diagram of irregular polygon meshing according to an exemplary embodiment;

Fig. 4c is a schematic diagram showing the comparison between the calculation result of the algorithm of the present invention under different grids and the analytical solution according to an exemplary embodiment;

FIG. 5 is a schematic structural diagram of a computer device according to an exemplary embodiment.

Detailed ways

The following description and drawings sufficiently illustrate the specific embodiments herein to enable those skilled in the art to practice them. Portions and features of some embodiments may be included in or substituted for those of other embodiments. The scope of the embodiments herein includes the full scope of the claims, along with all available equivalents of the claims. Herein, the terms "first," "second," etc. are only used to distinguish one element from another, and do not require or imply any actual relationship or order between the elements. In fact the first element can also be called the second element and vice versa. Furthermore, the terms "comprising", "comprising" or any other variation thereof are intended to encompass a non-exclusive inclusion such that a structure, device or device comprising a list of elements includes not only those elements, but also others not expressly listed elements, or elements inherent to such structures, devices, or equipment. Without further limitation, an element qualified by the phrase "comprising a..." does not preclude the presence of additional identical elements in the structure, apparatus or device that includes the element. The various embodiments herein are described in a progressive manner, and each embodiment focuses on the differences from other embodiments, and it is sufficient to refer to each other for the same and similar parts between the various embodiments.

The terms "portrait", "landscape", "top", "bottom", "front", "rear", "left", "right", "vertical", "horizontal", "top", " The orientation or positional relationship indicated by "bottom", "inner", "outer", etc. is based on the orientation or positional relationship shown in the drawings, and is only for the convenience of describing the text and simplifying the description, rather than indicating or implying that the indicated device or element must be It has a specific orientation, is constructed and operates in a specific orientation, and therefore should not be construed as a limitation of the present invention. In the description herein, unless otherwise specified and limited, the terms "installed", "connected" and "connected" should be understood in a broad sense, for example, it may be a mechanical connection or an electrical connection, or it may be the internal communication between two elements, It can be directly connected or indirectly connected through an intermediate medium. For those of ordinary skill in the art, the specific meanings of the above terms can be understood according to specific situations.

As used herein, unless stated otherwise, the term "plurality" means two or more.

In this article, the character "/" indicates that the preceding and following objects are in an "or" relationship. For example, A/B means: A or B.

Herein, the term "and/or" is an associative relationship describing objects, indicating that three relationships can exist. For example, A and/or B, means: A or B, or, A and B three relationships.

In a specific embodiment, the digital twin-based smooth finite element numerical calculation method provided by the present invention projects the strain field onto one or a group of constant fields based on the smooth element in the mapping element. As shown in Figure 1, the method includes the following steps:

S1: Obtain the solid material data and polygon element data of the solid material.

For the convenience of operation, the polygon unit data is specifically and quadrilateral unit data. Specifically, the solid material data and the quadrilateral element data belong to the static elastic problem data of the solid material, which are input numerical data. The solid material data includes Young's modulus and Poisson's ratio, and the quadrilateral element data includes element number, element node number, and node coordinates.

S2: Divide each of the polygonal units in the target range into a plurality of smooth units respectively. Based on the foregoing, step S2 specifically includes dividing each quadrilateral element within the target range into four smooth elements.

S3: Calculate the stiffness matrix of each smooth element, and obtain the stiffness matrix of the polygonal element.

Specifically, step S3 is to cycle through each smooth element to determine the element area and normal of each smooth element, and perform a smoothing operation based on the element area and normal to obtain a smooth element stiffness matrix.

In step S3, the following steps are included when performing the smooth operation:

S31: Determine the domain of definition of the static elastic problem of solid materials;

S32: and obtain the outer boundary normal and boundary displacement of the definition domain based on the preset boundary conditions;

S33: Obtain the displacement gradient of the definition domain based on the outer normal of the boundary and the boundary displacement;

S34: Perform a smoothing operation on the displacement gradient of each smoothing element in the definition domain.

Specifically, in a specific scenario, in order to illustrate the principle of the method, assume that the two-dimensional static elastic problem has a domain of definition Ω, and consider the elastic-static problem on the domain of definition Ω, and its governing equation is as follows:

σ _ij +b _j =0inΩ (1)

Γ = Γ _u + Γ _t (2)

为空集。where σ _ij is the stress tensor, b _j is the body force, Γ is the boundary of the definition domain Ω, Γ _u is the forced displacement boundary, Γ _t is the traction force boundary,

is the empty set.

At this point, the boundary conditions are as follows:

σ _ij n _j =t _i onΓ _t (4)

为强制位移，u_i为边界Γ_u的位移。where t _i is the traction force, n _j is the normal outside the boundary,

is the forced displacement, and _ui is the displacement of the boundary Γ _u .

Further, the variational weak form of the above formula (1) is as follows:

为位移梯度的对称部分，D_ijkl为材料矩阵，δ为δ函数，k、l均为节点序号。in,

is the symmetrical part of the displacement gradient, D _ijkl is the material matrix, δ is the δ function, and k and l are the node numbers.

In order to ensure the convergence of the numerical solution, the linear accuracy of the weak-form solution should be ensured, so the following conditions must be satisfied:

Among them, B _I is the standard gradient matrix, and N _I is the shape function matrix.

Perform a smooth operation on the displacement gradient of each smooth element within each element as follows:

Among them, Φ is a smooth function, and the specific form is as follows:

Among them, Ω _C is the smooth element, AC is the area of the smooth element Ω _C , u ^h (x _{C ) is the displacement after the smoothing operation, and x C is} the coordinate of the smooth element.

According to the distribution integral, the right-hand side of formula (9) can be transformed into:

Among them, n(x) is the normal vector outside the boundary.

Simultaneous formulas (9) and (10) can be obtained:

为光滑操作后的位移梯度。where Γ _C is the smooth element boundary,

is the displacement gradient after smooth operation.

The smooth function converts the element area integral to the element boundary line integral, and similarly, the smoothed strain can be obtained by:

为光滑应变矩阵，

为光滑应变，d_I为弹性模量。in,

is a smooth strain matrix,

is the smoothing strain, and _dI is the elastic modulus.

的定义如下：For two-dimensional problems,

is defined as follows:

where n _k (x) is the normal vector outside the boundary.

可由下式进行计算：If a line integral is performed along each segment boundary with a Gaussian point, then

It can be calculated by the following formula:

上的高斯积分点，

和

分别为边界线段

的长度与外法线，

为边界线段

上的高斯积分点。Among them, x _i is the boundary line segment

The Gaussian integration point on ,

and

boundary line segments

The length of and the outer normal,

for the boundary line segment

Gaussian integration points on .

S4: Obtain a solid material stiffness matrix and a load matrix based on the stiffness matrix of the polygonal element.

The step S4 is specifically combining the stiffness matrices of the smooth elements to obtain the stiffness matrix of the quadrilateral element, loading the boundary conditions of the static elasticity problem of the solid material, and obtaining the final stiffness matrix K and load matrix F of the solid material.

S5: Perform matrix operations according to the stiffness matrix K and the load matrix F of the solid material to obtain the approximate displacement matrix U of the static elastic problem of the solid material.

Specifically, the element stiffness matrix after smoothing can be composed of the stiffness matrices of all smooth elements of the element, that is, the matrix operation is performed according to the solid material stiffness matrix K and the load matrix F to obtain the displacement approximate solution matrix U of the static elastic problem of the solid material. .

Among them, the solid material stiffness matrix is calculated according to formula (16), as:

为光滑应变矩阵，D为固体材料的材料矩阵。where _Ke is the stiffness matrix,

is the smooth strain matrix, and D is the material matrix of the solid material.

Taking the cantilever beam as an example below, a specific embodiment of the digital twin-based smooth finite element numerical calculation method provided by the present invention is given.

As shown in Figure 2, a cantilever beam with a length of L and a height of D, the cantilever beam is subjected to a parabolic traction force at the free end, and the relevant parameters are: E=3.0×10 ⁷ kPa, v=0.3, D=12m, L=48m , P=1000N. Assuming that the cantilever has unit thickness, the exact solution for its displacement is as follows:

The corresponding exact stress solution is as follows:

σ ₂₂ (x,y)=0 (21)

In order to verify the convergence speed of the algorithm of the present invention, two paradigms are used, namely the displacement paradigm _ed and the energy paradigm _ee :

As shown in Fig. 3a and Fig. 3b, the smoothing finite element numerical algorithm (SFEM) of the present invention is compared with the convergence speed of the traditional finite element method (FEM), and both methods achieve equivalent convergence in displacement and energy. velocity, and the displacement of the method of the present invention is more accurate than the traditional finite element method. Compared to using S1, the SFEM energy convergence with S2 is approximately twice as fast. In scheme 1 (S1), SC/GP=4 is used to calculate stiffness matrix (displacement) and stress (energy), while in scheme 2 (S2), SC/GP=4 is used to calculate stiffness matrix (displacement) only , SC/GP=1 is used for post-processing of stress and energy, in scheme 3 (S3), SC/GP=1 is always used).

The calculation time of the smooth finite element numerical algorithm (SFEM) of the present invention and the traditional finite element method is shown in Fig. 3c. When the number of discrete elements is not very large, both methods require almost the same time. However, with the increase of elements, the calculation time of the smooth finite element numerical algorithm of the present invention is less than that of the traditional finite element method.

In order to demonstrate the function of the smooth finite element numerical algorithm of the present invention with complex shape elements, the beams are divided into regular elements and irregular polygon elements, as shown in Fig. 4a and Fig. 4b. The settlement results are then plotted together with the exact solution in Fig. 4c, and the calculated results agree with the exact solution results. Irregular polygon elements cannot be used in the traditional finite element method.

The smooth finite element numerical algorithm of the present invention greatly improves the solution accuracy and energy convergence speed of the finite element without increasing the calculation cost, and can eliminate the restriction on the shape of the bilinear isoparametric element, and discretize the problem more flexibly. area.

In one embodiment, a computer device is provided, and the computer device may be a server, and its internal structure diagram may be as shown in FIG. 5 . The computer device includes a processor, memory, and a network interface connected by a system bus. Among them, the processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium, an internal memory. The nonvolatile storage medium stores an operating system, a computer program, and a database. The internal memory provides an environment for the execution of the operating system and computer programs in the non-volatile storage medium. The database of the computer equipment is used to store static information and dynamic information data. The network interface of the computer device is used to communicate with an external terminal through a network connection. The computer program, when executed by the processor, implements the steps in the above algorithm embodiments.

Those skilled in the art can understand that the structure shown in FIG. 5 is only a block diagram of a partial structure related to the solution of the present invention, and does not constitute a limitation on the computer equipment to which the solution of the present invention is applied. Include more or fewer components than shown in the figures, or combine certain components, or have a different arrangement of components.

In one embodiment, a computer device is also provided, including a memory and a processor, where a computer program is stored in the memory, and the processor implements the steps in the above algorithm embodiments when the processor executes the computer program.

In one embodiment, a computer-readable storage medium is provided, on which a computer program is stored, and when the computer program is executed by a processor, implements the steps in the above algorithm embodiments.

Those of ordinary skill in the art can understand that all or part of the algorithm in the above-mentioned embodiments can be implemented by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage In the medium, when the computer program is executed, it may include the flow of the above-mentioned algorithm embodiments. Wherein, any reference to memory, storage, database or other media used in the various embodiments provided by the present invention may include at least one of non-volatile and volatile memory. The non-volatile memory may include Read-Only Memory (ROM), magnetic tape, floppy disk, flash memory or optical memory, and the like. Volatile memory may include random access memory (RAM) or external cache memory. By way of illustration and not limitation, the RAM may be in various forms, such as static random access memory (Static Random Access Memory, SRAM) or dynamic random access memory (Dynamic Random Access Memory, DRAM).

The present invention is not limited to the structures that have been described above and shown in the accompanying drawings, and various modifications and changes may be made without departing from the scope thereof. The scope of the present invention is limited only by the appended claims.

Claims (16)

1. a smooth finite element numerical calculation method based on digital twin, is characterized in that, described method comprises: Obtain solid material data and polygon element data for solid materials; Dividing each of the polygonal units within the target range into a plurality of smooth units; Calculate the stiffness matrix of each smooth element, and obtain the stiffness matrix of the polygonal element; obtaining a solid material stiffness matrix and a load matrix based on the stiffness matrix of the polygon element; According to the solid material stiffness matrix and the load matrix, the matrix operation is carried out, and the displacement approximate solution matrix U of the static elastic problem of the solid material is obtained. 2. The smooth finite element numerical calculation method according to claim 1, wherein acquiring the solid material data of the solid material specifically comprises: Obtain Young's modulus and Poisson's ratio for solid materials. 3. smooth finite element numerical calculation method according to claim 1, is characterized in that, acquiring the polygonal element data of solid material specifically comprises: Get the element number, element node number, and node coordinates of a polygonal element. 4 . The smooth finite element numerical calculation method according to claim 3 , wherein the polygonal element is a quadrilateral element. 5 . 5. The smooth finite element numerical calculation method according to claim 4, wherein each of the polygonal elements in the target range is divided into a plurality of smooth elements, specifically: Divide each quadrilateral element in the target range into four smooth elements. 6. The smooth finite element numerical calculation method according to any one of claims 1-5, wherein the stiffness matrix of each smooth element is calculated, and the stiffness matrix of the polygonal element is obtained, specifically comprising: Each of the smooth elements is looped to determine the element area and normal of each smooth element, and a smooth operation is performed based on the element area and normal to obtain the smooth element stiffness matrix. 7. The smooth finite element numerical calculation method according to claim 6, wherein the smooth operation is performed based on the element area and the normal, specifically comprising: Determine the definition domain of the static elasticity problem of the solid material, and obtain the outer boundary normal and boundary displacement of the defined domain based on the preset boundary conditions; obtaining a displacement gradient of the definition domain based on the boundary outer normal and the boundary displacement; A smoothing operation is performed on the displacement gradient of each smoothing element in the domain. 8 . The smooth finite element numerical calculation method according to claim 7 , wherein the definition domain of the static elastic problem of the solid material is determined, and the outer boundary normal of the definition domain and Boundary displacement, including: Assuming a two-dimensional static elastic problem domain Ω, the boundary of the domain is calculated based on the following formula: σ _ij +b _j =0 in Ω Γ = Γ _u + Γ _t

where σ _ij is the stress tensor, b _j is the body force, Γ is the boundary of the definition domain Ω, Γ _u is the forced displacement boundary, Γ _t is the traction force boundary,

is the empty set; At this point, the boundary conditions are: σ _ij n _j =t _i on Γ _t

where t _i is the traction force, n _j is the normal outside the boundary,

is the forced displacement, and _ui is the displacement of the boundary Γ _u . 9 . The smooth finite element numerical calculation method according to claim 8 , wherein the obtaining the displacement gradient of the definition domain based on the outer normal of the boundary and the boundary displacement, specifically comprising: 10 . Variational weak processing is performed using the following formula:

in,

is the symmetrical part of the displacement gradient, D _ijkl is the material matrix, δ is the δ function, k and l are the node numbers; The smoothing operation is performed on the displacement gradient of each smoothing element within each element using the following formula:

Among them, Φ is the smooth function, u ^h (x _C ) is the displacement after the smooth operation, and x _C is the coordinate of the smooth element; According to the distribution integral, the right-hand side of the above formula is transformed into:

Among them, n(x) is the normal vector outside the boundary; The simultaneous formula can be obtained:

where Γ _C is the smooth element boundary,

is the displacement gradient after smooth operation. 10. The smooth finite element numerical calculation method according to claim 9, wherein the variational weak formula satisfies the following conditions:

Among them, B _I is the standard gradient matrix, and N _I is the shape function matrix. 11. The smooth finite element numerical calculation method according to claim 9, wherein the specific form of the smooth function Φ is as follows:

Among them, Ω _C is the smooth element, AC is the area of the smooth element Ω _C , u ^h (x _{C ) is the displacement after the smoothing operation, and x C is} the coordinate of the smooth element. 12. The smooth finite element numerical calculation method according to claim 9, wherein the smooth strain is calculated by the following formula:

in,

is a smooth strain matrix,

is the smoothing strain, and _dI is the elastic modulus. 13. The smooth finite element numerical calculation method according to claim 12, wherein the smooth strain matrix is calculated by the following formula:

where n _k (x) is the normal vector outside the boundary. 14. The smooth finite element numerical calculation method according to claim 6, wherein the obtaining of the solid material stiffness matrix and the load matrix based on the stiffness matrix of the polygonal element specifically comprises: The stiffness matrix of the smooth element is combined to obtain the stiffness matrix of the polygonal element, and the boundary conditions of the static elastic problem of the solid material are loaded to obtain the final stiffness matrix K and load matrix F of the solid material. 15. A computer device, comprising a memory and a processor, wherein the memory stores a computer program, wherein the processor implements the algorithm described in any one of claims 1 to/14 when the processor executes the computer program A step of. 16. A computer-readable storage medium, wherein the computer storage medium contains one or more program instructions, and the one or more program instructions are used to execute any one of claims 1-14. Methods.

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