二维非局部线弹性平面问题的辛分析

将二维非局部线弹性理论引入到Hamilton体系下,基于变分原理推导得出了二维线弹性理论的对偶方程和相应的边界条件.在分析验证对偶方程的准确性的基础上,该套方法被应用于二维弹性平面波问题的求解.将精细积分与扩展的W-W算法相结合在Hamilton体系下建立了求解平面Rayleigh波的数值算法.从推导到计算的保辛性确保了辛体系非局部理论与算法的准确性.通过对不同算例的数值计算,分析和对比了非局部理论方法与传统局部理论方法的差别,并进一步指出了该套算法的适用性和优势所在.

Symplectic analysis for two dimensional nonlocal linear elastic plane problems

The two dimensional nonlocal linear elastic theory is derived to the Hamilton system, the corresponding dual equilibrium equations and boundary conditions are presented from the variational principle. After the validity of the dual equations is confirmed; this methodology is applied in solving the 2D linear elastic plane-wave problems. The symplectic algorithm, consists of precise integration method and external Wittrick-Williams algorithm, for solving the plane Rayleigh waves is presented under the Hamilton system. The symplectic conservation characteristic insures the accuracy of the nonlocal symplectic theory and corresponding algorithm. The analysis and comparison between nonlocal theory and classical local theory are given out based on different numerical examples. The advantages and applicability of the nonlocal symplectic methodology are also presented.