三维单域弹性问题虚边界无网格伽辽金法分析

Analysis on Three-dimensional Single-domain Elastic Problem Based on Virtual Boundary Meshless Galerkin Method

针对更具一般性的三维问题,虚边界无网格伽辽金法被进一步推广研究,提出了三维单域弹性问题虚边界无网格伽辽金法,包括ANSYS有限元软件提取面单元、节点数据信息,给出的命令流具有动态数组的优点,输出的节点坐标达到28bit。详细推导了三维单域弹性问题虚边界无网格伽辽金积分方程,并为了便于编程实现进行数值离散,得到积分方程对应的离散格式。最后计算三维混凝土立方体受压试块应力分析,取中间四个截面上的应力进行验证。结果表明,三维单域弹性问题虚边界无网格伽辽金法计算可行、精确性好;给出的ANSYS命令流,能够提前准备编程数据,通用性强,大大简化任意面的单元划分与节点坐标信息提取工作,利于建议方法的推广应用。

The virtual boundary meshless Galerkin method for the analysis of three-dimensional single-domain elastic problem was presented and further researched for more general three-dimensional problems.Specific research contents include that data information of surface elements and nodes was obtained by the command flow of ANSYS finite element software,which had the advantage of dynamic array and the output node coordinates reach 28 bits.The virtual boundary meshless Galerkin method for three-dimensional single-domain elastic problem was given in detail and dispersed to conveniently program.Finally,the stress analysis of three-dimensional concrete cubic compression test block was calculated.The stresses on the middle four sections were taken to verify.The conclusiones:the virtual boundary meshless Galerkin method for three-dimensional single-domain elastic problems is feasible and accurate.The given command flow can prepare the programming data in advance.and has strong generality,greatly simplifies the work of element division and node coordinate information extraction for any plane.it is beneficial to the popularization and application of the proposed method.