System and method for numerical simulation based on Lagrange integral point finite element

Abstract

The invention discloses a system and a method for numerical simulation based on a Lagrange integral point finite element. The system for numerical simulation comprises: a modeling module which is usedfor sequentially generating a calculation domain, a calculation grid, a geometric model and a physical model according to data inputted by a user, and storing numerical model data; a solver module which is used for receiving the numerical model data, establishing a unit matrix and a large sparse total stiffness matrix according to input geometric physical parameters and boundary conditions, performing total numerical calculation and local calculation, and storing and outputting a simulation analysis result; and a post-processing module which is used for drawing a cloud chart and a curve chartaccording to the output simulation analysis result, and storing text data. Finite element analysis of fluid and incompressible materials can be carried out, the calculation efficiency is greatly improved, and the calculation cost is reduced.

Description

technical field [0001] The invention relates to the technical field of numerical simulation, in particular to a numerical simulation system and method based on Lagrangian integral point finite elements. Background technique [0002] Numerical simulation systems in the prior art are mainly based on traditional finite element method (FEM), finite difference method (FDM), discrete element method (DEM), hydrodynamic method (SPH), material point method (MPM) and so on. The traditional finite element method and finite difference method have powerful functions and stable calculations. Many existing mature commercial simulation systems are based on these methods (such as PLAXIS, ABAQUS, ANASYS, FLAC3D, etc.), and they still occupy a dominant position in the field of computational mechanics. [0003] However, since the Lagrangian grid must be established, the grid must be deformed with the deformation of the material during the calculation process, which is prone to grid distortion...

AI Technical Summary

Problems solved by technology

[0003] However, since the Lagrangian grid must be established, the grid must be deformed with the deformation of the material during the calculation process, which is prone to grid distortion and cannot really deal with the large deformation of the material (it can only handle large deformation to a certain extent). It is even more impossible to simulate the solid-fluid transformation problem; the Euler finite element method has a fixed grid, but it cannot track and calculate the stress-strain history of elastic-plastic materials, and generally can only be used to deal with fluid mechanics problems; the fluid dynamics method does not have grid distortion problems, Moreover, the control equation is easy to solve and has strong adaptability, but there are problems such as tension instability and large calculation time; the discrete element method can deal with large deformation problems of geotechnical materials without limitation (such as PFC3D of ITASCA company), but its Calculation takes a lot of time, and the relationship between macro and micro parameters is not yet clear. At this stage, it is more suitable for the simulation of micro and micro scale problems; material point method, particle finite element method (PFEM), etc. can accurately track and calculate the stress and strain history of elastic plastic materials , can also simulate large deformation phenomena, but the material point method has high computational cost and low calculation accuracy compared with the finite element method. In addition, the use of linear shape functions will cause obvious errors in the movement of material points across the grid. Using high-order shape functions and It will cause greater calculation costs; the contact problem between solid-solid nodes and solid-liquid nodes in the particle finite element method has been unresolved, and it is necessary to continuously refresh all calculation meshes when performing large deformation simulations, and the calculation costs are relatively high

Images