利用无网格伽辽金法分析材料稳态蠕变问题

稳态蠕变是高温环境下材料的一个重要的考虑问题，它也是材料破坏的一种重要形式。由于存在划分网格，利用传统有限元法模拟稳态蠕变有一定的不足之处。作为一种新兴的数值模拟方法，无网格法不需要划分单元，只需将求解问题离散成独立的结点，计算过程可以局部细化。利用连续介质的虚功原理，将无网格伽辽金法应用于稳态蠕变的数值模拟，推导了稳态蠕变的无网格伽辽金法控制方程。利用罚参数来实现稳态蠕变的不可压缩条件和本质边界条件，能够保证求解过程中刚度矩阵的对称正定性。通过实例的计算结果表明，无网格伽辽金法在求解稳态蠕变时具有较高的计算精度，结果与理论解结果吻合，而且前后处理较为简单。

Using Element Free Galerkin Method to Analyze Steady State Creep of Material

Steady state creep should be considered for high temperature material, and it is also an important failure mechanism for the material under high temperature. Traditional Finite Element Methods have some obvious shortcomings to simulate the steady state creep for division of elements. As a promising numerical simulation method, the meshless methods only need the node information divided for calculatoin, the grid is considered for pre-process, so the adaptive refinement can be easily achieved. Based on the principles of virtual work for continuum medium, the Element Free Galerkin Method to simulate the numerical calculatoins of steady-state creep was used and the discrete equation was derived in meshless method for steady-state creep. The essential boundary conditions and volume incompressible conditions can be realized by employing the penalty parameters, so the symmetric positive definite system stiffness matrix can be yielded. The numerical example shows that the element free Galerkin method, with high accuracy, is much more convenient to deal with the pre-process and post-process, and the results by meshless method is in good agreement with the exact solution data.