Method and system for calculating material deformation displacement

Abstract

The application discloses a material deformation displacement calculation method and a calculation system. The method comprises the following steps: in response to obtained design parameters, a corresponding structure and a geometric model are constructed, and a stiffness matrix K and a load matrix F are generated; the stiffness matrix K is stored in a sparse form by row compression, the load matrix F is input, and a Krylov subspace dimension m, an initial value U0 and an allowable error ε are selected; a set of standard orthogonal bases of the Krylov subspace is constructed; the best approximation U of the displacement in the Krylov subspace is calculated m ; the residual ||F-KU m || is calculated, and if the residual is less than the allowable error ε, the best approximation U m is output as the material deformation displacement; if the residual is greater than the allowable error ε, the best approximation U m is taken as a new initial value, the Krylov subspace is updated, and the material deformation displacement is recalculated. The application provides a stiffness calculation method which can be flexibly deployed and efficiently parallel, and realizes acceleration of finite element analysis.

Description

Technical Field

[0001] This invention belongs to the field of finite element analysis technology, and in particular relates to a method and system for calculating material deformation and displacement. Background Technology

[0002] Finite element analysis (FEM) involves dividing a real physical system into a finite number of elements and simulating the structure and stress conditions of the real system through approximate calculations of each element. FEM first establishes a mathematical model based on the actual problem, then discretizes it using the finite element method to obtain the stiffness equation KU = F, where K ∈ R. n×n This represents the linear relationship between the resultant force on each element node and the displacement that occurs; U∈R n×1 , where F is the column vector formed by the displacements of the unit nodes; F∈R n×1 , represents the resultant force on each unit node that generates displacement U; n is the number of equations, which can typically reach hundreds of thousands or even millions.

[0003] Solving the stiffness equations is the core underlying technology of various finite element analysis software, consuming most of the computation time. In engineering practice, due to space and computing power limitations, solving this set of equations often relies on submitting tasks to supercomputing centers, which is a complex process, severely disconnected from the industrial site, and affects the progress of industrial production. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of existing technologies by providing a method and system for calculating material deformation and displacement. Under conditions of limited space and computing resources, it enables finite element analysis simulation in industrial settings, guiding industrial design and providing a flexible, efficient, and parallel method to accelerate finite element analysis. This significantly improves the parallelism of the stiffness equation solution process, increases computational efficiency, and reduces computation time, making large-scale finite element analysis simulation in industrial settings possible.

[0005] The objective of this invention is achieved through the following technical solution:

[0006] A method for calculating material deformation displacement, the method comprising:

[0007] In response to the acquired design parameters, the corresponding structural and geometric models are constructed and the stiffness matrix K and load column matrix F are generated;

[0008] The stiffness matrix K is stored in a row-compressed and sparse manner. The load column matrix F is input and the Krylov subspace dimension m, initial value U0 and tolerance ε are selected.

[0009] Construct a set of orthonormal bases for the Krylov subspace;

[0010] Calculate the best approximation U of displacement U in the Krylov subspace.m ;

[0011] Calculate the residual ||F-KU m If the residual is less than the allowable error ε, then the best approximation U is output. m As the material deformation displacement; if the residual is greater than the allowable error ε, then the optimal approximation U is used. m The Krylov subspace is updated with new initial values, and the material deformation displacement is recalculated.

[0012] Furthermore, the generation of the stiffness matrix and load matrix specifically includes:

[0013] The geometric model is divided into element meshes;

[0014] Set physical parameters and boundary conditions;

[0015] Generate the stiffness matrix K and the load matrix F.

[0016] Furthermore, the design parameters include material parameters, structural dimensions, and external force parameters.

[0017] Furthermore, m can be any natural number less than n, where n is the problem size.

[0018] Furthermore, the construction of the Krylov subspace involves a set of orthonormal bases and the calculation of the optimal approximation U of the displacement U in the Krylov subspace. m Parallel computing is employed.

[0019] Furthermore, the calculated displacement U is the best approximation U in the Krylov subspace. m The least squares problem is obtained by solving the least squares problem using the QR decomposition method.

[0020] On the other hand, the present invention also provides a material deformation displacement calculation system, the system being used to implement any of the aforementioned material deformation displacement calculation methods, the system comprising:

[0021] The user terminal includes a processor and an interface conversion card;

[0022] An agile cluster computing accelerator includes an SRIO network switching module, a computing core, a system control module, and an Ethernet network switching module. The SRIO network switching module is communicatively connected to the interface conversion card and the computing core, respectively. The system control module is communicatively connected to the interface conversion card and the Ethernet network switching module, respectively. The Ethernet network switching module is communicatively connected to the computing core.

[0023] Furthermore, the system control module includes a control chip and an Ethernet routing chip controlled by the user terminal.

[0024] Furthermore, the SRIO network switching module includes an extended interface for reading in the stiffness matrix K and the load array F and distributing the data.

[0025] The beneficial effects of this invention are as follows:

[0026] (1) This invention fully utilizes the sparsity of large-scale linear equation systems generated by finite element analysis to reduce memory overhead; at the same time, taking advantage of the advantages of cluster computing systems, it develops a highly parallelized Krylov subspace method, which can select a larger dimension subspace, accelerate algorithm convergence, and improve computing speed.

[0027] (2) The user terminal of this invention is a chassis and a monitor, and is equipped with an environment for installing various industrial application finite element design software, so it can be easily compatible with the original finite element analysis system; the agile cluster computing accelerator is a 1U standard chassis, which can be easily deployed in various industrial sites. Attached Figure Description

[0028] Figure 1 This is a schematic diagram of the material deformation displacement calculation method provided in the embodiments of the present invention;

[0029] Figure 2 This is a structural block diagram of the material deformation displacement calculation system provided in the embodiments of the present invention. Detailed Implementation

[0030] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that, unless otherwise specified, the following embodiments and features described therein can be combined with each other.

[0031] Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0032] Solving the stiffness equations is the core underlying technology of various finite element analysis software, consuming most of the computation time. In engineering practice, due to space and computing power limitations, solving this set of equations often relies on submitting tasks to supercomputing centers, which is a complex process, severely disconnected from the industrial site, and affects the progress of industrial production.

[0033] To address the aforementioned technical problems, the following embodiments of the material deformation displacement calculation method and calculation system of the present invention are proposed.

[0034] Example 1

[0035] Reference Figure 1 ,like Figure 1 The diagram shown is a schematic flowchart of the material deformation displacement calculation method provided in this embodiment. The method specifically includes:

[0036] Step S100: In response to the acquired design parameters, construct the corresponding structural and geometric models and generate the stiffness matrix K and load array F.

[0037] Specifically, it includes the following sub-steps:

[0038] Step S101: In this embodiment, material parameters, structural dimensions, external loads (external forces), and other industrial design problem parameters are input into the finite element design software.

[0039] Step S102: Using finite element design software, construct the structural and geometric model of the actual problem.

[0040] Step S103: Perform element meshing of the model, such as triangulation.

[0041] Step S104: Set physical parameters and boundary conditions.

[0042] Step S105: Generate the stiffness matrix K and the load column matrix F.

[0043] Step S200: Store the stiffness matrix K in the Agile Cluster computing accelerator by row compression sparsification, input the load matrix F and select the Krylov subspace dimension m, initial value U0 and allowable error ε.

[0044] Step S300: Construct a set of orthonormal bases for the Krylov subspace using the Arnoldi process.

[0045] Step S400: Calculate the best approximation U of the displacement U in the Krylov subspace using the least squares method. m .

[0046] Step S500: Calculate the residual ||F-KU m If the residual is less than the allowable error ε, then the best approximation U is output. m As the material deformation displacement; if the residual is greater than the allowable error ε, then the optimal approximation U is used. m The Krylov subspace is updated with new initial values, and the material deformation displacement is recalculated.

[0047] As one implementation method, the initial value U0 in this embodiment can be arbitrarily selected. The closer the initial value U0 is to the exact solution, the faster the algorithm converges. The value of m is usually much smaller than the problem size n. Thanks to the storage and computing power advantages of the cluster computing system, m can be any large natural number less than n to reduce the number of iteration steps, or even achieve the required accuracy in one step. For example, m can be... or

[0048] As one implementation method, in order to give full play to the advantages of the cluster computing system, the matrix-vector multiplication in the Arnoldi process is performed in parallel, and matrix K is distributed to different computing cores by row; similarly, the least squares problem is solved by QR decomposition, and the QR decomposition process also adopts a parallel algorithm.

[0049] This method can quickly obtain the deformation and displacement of materials, thereby assisting in the construction of various product structure models.

[0050] Finite element analysis (FEM) is widely used in engineering to solve problems related to strength, stiffness, buckling, modal dynamics, dynamics, elasticity, and structural optimization in various large and complex structures. It is extensively applied in industries such as petrochemicals, machinery manufacturing, automotive, civil engineering, and aerospace. In industrial design, FEM, through numerical calculations of structural displacements, stresses, strains, and other mechanical quantities, can simulate various experimental scenarios, thereby guiding the optimized design of product structures and reducing material consumption. Furthermore, it can perform mechanical accident analysis on products, identifying the causes of accidents and enabling engineers to proactively identify potential problems before product manufacturing or engineering implementation, thus increasing product reliability.

[0051] This embodiment takes full advantage of the sparsity of large-scale linear equation systems generated by finite element analysis to reduce memory overhead. At the same time, taking advantage of the advantages of cluster computing systems, a highly parallelized Krylov subspace method is developed, which can select a larger-dimensional subspace, accelerate algorithm convergence, and improve computation speed.

[0052] Example 2

[0053] This embodiment provides a material deformation displacement calculation system for implementing the material deformation displacement calculation method provided in the aforementioned embodiment.

[0054] Reference Figure 2 ,like Figure 2 The diagram shown is a structural block diagram of the material deformation displacement calculation system provided in this embodiment. The system includes:

[0055] It consists of two parts: a user terminal and an agile cluster computing accelerator. The user terminal supports a CPU processor and is configured with an environment that installs various industrial application finite element design software. It provides an SRIO interface through an interface conversion card plugged into PCIe for high-speed data transmission. The agile cluster computing accelerator integrates 30 domestically produced M6678 chips as computing cores. (See attached example.) Figure 2 The chip is represented by P, and each chip has 8 cores, which share 8GB of DDR3 memory.

[0056] In one implementation, the system control module includes a domestically produced FT1500 chip and a gigabit Ethernet routing chip. The FT1500 chip receives control from the user terminal via gigabit Ethernet, and also interacts with the network switching module and DSP computing chip via gigabit Ethernet to exchange commands and response data.

[0057] As one implementation, the SRIO network switching module includes a second-generation RIO switching chip for routing a high-speed 20G RIO interconnect network between the user end and the accelerator, and provides an extended RIO interface to enable high-speed reading and data distribution of the stiffness matrix K and load array F.

[0058] As one implementation method, the Ethernet network switching module utilizes a gigabit Ethernet chip to enable the 30 M6678 chips of the agile cluster computing accelerator to connect to a gigabit Ethernet network, thereby realizing data communication between computing cores.

[0059] In this embodiment, the user terminal consists of a chassis and a monitor, and is equipped with an environment for installing various industrial application finite element design software, so it can be easily compatible with the original finite element analysis system; the agile cluster computing accelerator is a 1U standard chassis, which can be easily deployed in various industrial sites.

[0060] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for calculating material deformation displacement, which, in response to acquired design parameters, constructs a corresponding structural and geometric model and generates a stiffness matrix K and a load matrix F, characterized in that, The method includes: The stiffness matrix K is stored in a row-compressed and sparse manner. The load column matrix F is input and the Krylov subspace dimension m, initial value U0 and tolerance ε are selected. Construct a set of orthonormal bases for the Krylov subspace; Calculate the best approximation U of displacement U in the Krylov subspace. m ; Calculate the residual F-KU m If the residual is less than the allowable error ε, then the best approximation U is output. m As the material deformation displacement; if the residual is greater than the allowable error ε, then the optimal approximation U is used. m The Krylov subspace is updated with new initial values, and the material deformation displacement is recalculated.

2. The material deformation displacement calculation method as described in claim 1, characterized in that, The generation of the stiffness matrix and load matrix specifically includes: The geometric model is divided into element meshes; Set physical parameters and boundary conditions; Generate the stiffness matrix K and the load matrix F.

3. The material deformation displacement calculation method as described in claim 1, characterized in that, The design parameters include material parameters, structural dimensions, and external force parameters.

4. The material deformation displacement calculation method as described in claim 1, characterized in that, The value of m is any natural number less than n, where n is the problem size.

5. The material deformation displacement calculation method as described in claim 1, characterized in that, The construction of the Krylov subspace uses a set of orthonormal bases and the calculation of the best approximation U of the displacement U in the Krylov subspace. m Parallel computing is employed.

6. The material deformation displacement calculation method as described in claim 1, characterized in that, The calculated displacement U is the best approximation U in the Krylov subspace. m The least squares problem is obtained by solving the least squares problem using the QR decomposition method.

7. A material deformation displacement calculation system, characterized in that, The system is used to implement the material deformation displacement calculation method according to any one of claims 1-6, and the system includes: The user terminal includes a processor and an interface conversion card; An agile cluster computing accelerator includes an SRIO network switching module, a computing core, a system control module, and an Ethernet network switching module. The SRIO network switching module is communicatively connected to the interface conversion card and the computing core, respectively. The system control module is communicatively connected to the interface conversion card and the Ethernet network switching module, respectively. The Ethernet network switching module is communicatively connected to the computing core.

8. The material deformation displacement calculation system as described in claim 7, characterized in that, The system control module includes a control chip and an Ethernet routing chip controlled by the user terminal.

9. The material deformation displacement calculation system as described in claim 7, characterized in that, The SRIO network switching module includes an extended interface for reading in the stiffness matrix K and the load array F and distributing the data.

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