基于增量本构关系弹塑性分析的无网格伽辽金法

在无网格伽辽金法的基础上，采用增量形式的无网格伽辽金法的插值方法，并利用应力应变增量形式表征材料的弹塑性本构关系，在小变形假设的前提下，提出了基于增量本构关系的弹塑性分析的无网格伽辽金法；采用罚参数修正了能量变分方程式，方便地实现了无网格伽辽金法的本质边界条件．对二维平面问题及轴对称问题的计算结果表明：运用增量形式的无网格伽辽金法进行弹塑性问题的数值分析，具有较高的计算精度，且适应性强，从而为材料的弹塑性分析计算提供了一种实用方法。

Element-Free Galerkin Method for Elasto-Plastic Analysis Based on Incremental Constitutive Equations

On the basis of the element-free Galerkin method (EFGM), the element-free Galerkin method for elasto-plastic analyses was proposed based on the incremental constitutive equations and the small deformation hypothesis. In this proposed method, the incremental interpolation method in the EFGM is adopted, the increments of stress and strain are used to characterize the elasto-plastic constitutive relationship, and the penalty parameters are adopted to revise the energy variation equations to easily realize the essential boundary conditions in the EFGM. The calculating results of 2D plane and axisymmetrical problems show that numerical analysis for elasto-plastic problems by of the incremental EFGM has advantages such as high calculation accuracy and strong adaptability. Therefore, this method can solve the calculation problems of material elasto-plastic analysis.