Near-field dynamics discontinuous Galerkin finite element method for structural deformation analysis

Abstract

The invention belongs to the technical field of near-field dynamics data processing, and discloses a near-field dynamics discontinuous Galerkin finite element method for structural deformation analysis. The near-field dynamics discontinuous Galerkin finite element method comprises the following steps: establishing a solid model, determining each material area and endowing corresponding material attributes; dividing unit grids by adopting a grid generation algorithm of a standard finite element method; copying the node to generate a discontinuous unit matched with the new method; initially calculating and updating coordinates of nodes and Gaussian points in real time; introducing a weight function to construct a weak form of key type near-field dynamics, calculating equivalent loads, equivalent external loads and a mass matrix of unit nodes through Gaussian points, and determining a stress deformation calculation method of a unit; setting initial conditions and applying stress and displacement boundary conditions; submitting static and dynamic calculation; and carrying out stress, strain analysis. According to the near-field dynamics discontinuous Galerkin finite element method, theproblem of structural static and dynamic deformation and damage can be solved by applying a key type near-field dynamics theory in a traditional finite element framework.

Description

technical field [0001] The invention belongs to the technical field of peridynamic data processing, in particular to a peridynamic discontinuous Galerkin finite element method for structural deformation analysis. Background technique [0002] The fracture and failure simulation of solid structures has been a long-term concern in the field of computational mechanics. The conventional modeling and analysis methods for this type of discontinuity problems are based on the traditional continuum mechanics theory and finite element method based on partial differential equations. However, due to the lack of description of fracture The length-scale parameters of the parameters, the crack path and crack growth criteria need to be preset, so it faces the singularity problem at the discontinuity, the grid dependence problem, the inaccurate fracture description and the bottleneck of calculation accuracy; later developed the extended finite element method and various Meshless method, but ...

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Problems solved by technology

[0006] (1) Traditional continuum mechanics theory and numerical methods such as finite elements face bottlenecks in accuracy and efficiency when dealing with discontinuity problems

[0007] (2) The existing meshless particle solution method of peridynamics has a huge amount of calculation and puts forward higher requirements for computer performance; the discrete structure of the meshless particle method has the problem of discrete error of complex boundaries; the existing method still has boundary effects Significant, difficulties in the accurate imposition of stress boundary conditions

[0008] (3) Insufficient research on the non-continuous Galerkin finite element solution of peridynamics, lack of algorithm details for theoretical modeling and numerical implementation of general three-dimensional problems, and insufficient example application and analysis

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