摘要
用有限元[1]通用程序进行结构计算时,最常用的是位移法,因而计算得到的位移有较高的精度。由位移计算应力时,有限元法应用的是应力-应变关系和应变-位移关系,其中应变-位移是微商关系。在数值计算中,微商只能转化为差商等用插值近似处理。这样,虽然位移精度高,但应力的计算精度就被大打折扣。本文应用弹性力学辛体系理论[2],解析求解了位移和应力的影响函数。利用有限元程序计算得到的位移,由功互等定理,不需要微分插值,就可以得到指定点的应力,应力精度大大提高。工程实际中有许多问题的最大应力往往发生在构件表面。针对表面应力问题,本文给出了半平面表面应力的影响函数,进行了数值算例计算。计算结果表明,用本文提出的影响函数法求解一点的应力,其精度明显提高,并且计算结果有很好的稳定性。用本文的影响函数法编制成子程序,可作为有限元软件应力计算的一个模块,可以更好地发挥有限元程序的功效。
The displacement method is common used for structural analysis in finite element method （FEM）. The displacements calculated by FEM have high accuracy. When the stresses are calculated from the displacements, the stress-strain relationship and strain-displacement relation are used in FEM. As the strain-displacement relation is differential quotient relation, the differential quotient is translated to interpolation in numerical methods. Thus, the accuracy of stresses is reduced. Based on the sympletie elasticity, the influence functions of displacements and stresses are derived analytically. The stresses of one point are obtained through the reciprocal theorem of works without differential interpolation. The accuracy of stresses is impraved. The maximum stress is often appeared on the surface of structures. The influence functions of surface stress are present in this paper. The numerical results show that the method is feasible and effective. The subroutine, compiled with the influence function method, can be used as a module to add into a finite element software for stress calculation.
出处
《计算力学学报》
EI
CAS
CSCD
北大核心
2010年第2期177-181,共5页
Chinese Journal of Computational Mechanics
基金
国家自然科学基金重点项目(10632032)
国家自然科学基金(10672100
50978162)资助项目
关键词
影响函数
辛
有限元
表面应力
influence function
symplectic
finite element method
surface stress
