二维多域弹性问题虚边界无网格伽辽金法分析

Analysis of Two-Dimensional Multi-Domain Elastic Problem Based on Virtual Boundary Meshless Galerkin Method

针对复杂的不同材料属性的多域组合问题(比如复合材料交界面上接触应力的计算),虚边界无网格伽辽金法被进一步研究,提出了二维多域弹性问题虚边界无网格伽辽金法。简要介绍了多域组合思想、子域虚边界元法,详细推导了二维多域弹性问题分析的虚边界无网格伽辽金法,得到具体的离散格式,便于编程,推广研究。方程的加权系数为位移、面力、连续边界上的位移与面力关系式偏导,数值意义明确,公式具体。最后通过计算数值实例为复合材料交界面上接触应力的计算,给出了复合圆盘接触面上的法向、径向应力,分多种方案调整每个子域的虚边界半径值,所得结果与解析解、其他数值方法进行比较。结论是二维多域弹性问题虚边界无网格伽辽金法的方法计算可行、精确性与稳定性好。

The virtual boundary meshless Galerkin method for the analysis of two-dimensional multi-domain elastic problem is put forward and further researched for multi-domain combination problem with the complex different material property,such as the calculation of contact stress.The multi-domain combination idea and the sub-domain virtual boundary element method are briefly introduced,the virtual boundary meshless Galerkin method for the analysis of two-dimensional multi-domain elastic problem is deduced in detail,its specific discrete format is obtained,which is convenient to program and promote research.The weighting coefficients of the equation are the partial derivatives of the displacement,the surface force,the displacement and the surface force on the continuous boundary.Their numerical significances are clear.Their formulas are specific.At last,numerical example is the calculation of contact stress at the composite interface.The normal and radial stresses on the contact surface of the composite disc are given.The multiple schemes are considered by changing the radius of virtual boundary within each subdomain.The obtained results are compared with the analytical solutions and other numerical methods.The conclusion is that the proposed method is feasible,accurate and stable.