A natural neighbour method based on Fraeijs de Veubeke variational principle for materially non-linear problems

• 来源期刊: 力学学报(英文版)
• 年，卷（期）: 2009,（1）
• 页码范围: 83-93
• 页数: 11页
• 语种: 英文
• DOI: 10.1007/s10409-008-0200-z

摘要

The natural neighbour method can be considered as one of many variants of the meshless methods. In the present paper, a new approach based on the Fraeijs de Veubeke (FdV) functional, which is initially developed for linear elasticity, is extended to the case of geometrically linear but materially non-linear solids. The new approach provides an original treatment to two classical problems: the numerical evaluation of the integrals over the domain A and the enforcement of boundary conditions of the type ui = uion Su. In the absence of body forces (Fi = 0), it will be shown that the calculation of integrals of the type fA .dA can be avoided and that boundary conditions of the type ui = ui on Su can be imposed in the average sense in general and exactly if ui is linear between two contour nodes, which is obviously the case for ui = 0.