自适应无网格伽辽金方法的研究

对基于位移或应变梯度的二阶导数和基于应变能密度的自适应无网格方法进行了研究。利用无网格方法结点排布灵活、结点添加删除方便等特点,给出两种自适应无网格伽辽金方法的原理、计算流程和程序实现。采用基于应变能密度的自适应方法,提出基于背景网格的误差估计和一种由结点组成的四边形局部结点加密技术,计算了悬臂梁拉伸和带小圆孔平板拉伸的算例。结果表明,自适应无网格伽辽金方法可以在较少结点数的情况下获得较准确的结果,具有一定的适用性。

Study of an Adaptive Element-free Galerkin Method

The adaptive Element-Free Galerkin Method(EFGM) procedure based on the gradient of strain energy and derivatives of displacement is analyzed.The meshless method does not require elements to discretize the calculation domain,and the approximate solutions are constructed entirely based on a set of scattered nodes,which can be moved,inserted and deleted flexibly,and is perfectly suitable for adaptive analysis.The schemes,including their principle explanation,arithmetic analysis and programming realization,based on the gradient of strain energy and derivatives of displacement are introduced and compared.A cell error estimate based on background cells and a local domain refinement technique using a quadrilateral composed of nodes is given by mesh intensity.Through analysis of a cantilever beam and an infinite plate with a circular hole problem,the adaptive EFGM procedure correctness is verified.These numerical examples show that the automatic adaptive EFGM procedure is effective and valid.