平面曲梁有限元静力分析的p型超收敛算法  

A p-TYPE SUPERCONVERGENT RECOVERY METHOD FOR FE STATIC ANALYSIS OF PLANAR CURVED BEAMS

作　　者：叶康生[1] 姚葛亮 

机构地区：[1]清华大学土木工程系,土木工程安全与耐久教育部重点实验室,北京100084

出　　处：《工程力学》2017年第11期26-33,58,共9页Engineering Mechanics

基　　金：清华大学自主科研计划项目(2011THZ03)

摘　　要：该文对平面曲梁有限元静力分析提出一种p型超收敛算法,由该法可求得曲梁结构全域超收敛的位移和内力。该法基于有限元解答中结点位移的超收敛特性,通过将单元端部结点位移有限元解设为本质边界条件,在单元上建立单元位移近似满足的线性常微分方程边值问题,对该边值问题采用更高次数的多项式进行有限元求解获得单元上位移的超收敛解,将位移超收敛解代入内力表达式获得内力的超收敛解。该法简单、直接,通过很少量的计算即能显著提高位移和内力的精度和收敛阶。数值结果显示,该法高效、可靠,是一个颇具潜力的方法。A p-type post-processing superconvergent recovery method is proposed for finite element （FE） static analysis of planar curved beams, from which superconvergent displacements and forces on the whole structure can be obtained. Based on the superconvergence property of nodal displacements, a linear ordinary differential boundary value problem （BVP） which approximately governs the displacements on each element is set up by setting the FE solutions of element＇s end nodal displacements as essential boundary conditions. This linear BVP is solved with a higher order element from which the superconvergent displacement on each element is obtained. From the derivatives of the recovered displacements the superconvergent forces are derived. This method is simple and direct. It can enhance the accuracy and convergence order of the displacements and forces significantly with small computational cost. Numerical examples demonstrate that this method is efficient, reliable and promising.

关 键 词：平面曲梁 有限元 后处理 超收敛 边值问题 

分 类 号：TU311.1[建筑科学—结构工程]