An extended smooth meshless Galerkin method

Abstract

The invention discloses an extended smooth meshless Galerkin method, which combines the extended finite element, meshless Galerkin and smooth integration technology, wherein the traditional meshless Galerkin method is modified, and a triangle with stronger topological adaptability is used as a background integration cell, so that the discretization process of a geometric body is more simple and easy to perform. The traditional Gaussian integration method is abandoned and the smooth integration technique is introduced to avoid the tedious derivation process of the shape function, which improvesthe calculation accuracy to some extent. The improved meshless method is applied to the simulation of crack propagation in concrete, and the simulation results are closer to the real situation than the traditional finite element method.

Description

technical field [0001] The invention belongs to the technical field of crack extension analysis and relates to an extended smooth gridless Galerkin method. Background technique [0002] Crack growth refers to the dynamic process of crack nucleation and growth in materials under the action of external factors. For the problem of crack propagation in continuum media, the most common method at present is the extended finite element method (XFEM) meshless method, etc. The problems of these methods are: [0003] 1. XFEM is based on the traditional finite element, developed from the unknown variables of cracks and crack propagation. For the triangular element with the strongest topology adaptability, its simulation accuracy is low, and it is necessary to improve its calculation by subdividing the grid. Accuracy, low computational efficiency. [0004] 2. The most commonly used method for simulating crack growth without mesh is the collocation method, that is, the geometry and cra...

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Problems solved by technology

However, this method has obvious disadvantages: 1) the calculation is oscillating, the calculation accuracy is unstable, and the number of nodes in the node calculation domain is too large, which will reduce its calculation accuracy; 2) the accuracy is low

Collocation method is a strong form of balanced differential equation, its accuracy is lower than conventional Galerkin method; 3) low computational efficiency

The conventional meshless Galerkin method requires Gaussian integration. In order to ensure the calculation accuracy, a large number of integration points are usually arranged in the background integration cell, and the partial derivatives of the shape functions of these integration points are calculated, which greatly affects the gridless The calculation efficiency of Galerkin has become the biggest difficulty in engineering practice

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