位移型板单元内力解的杂交化后处理

AN ENHANCED HYBRID POST-PROCESSING PROCEDURE FOR IMPROVING STRESS SOLUTIONS OF DISPLACEMENT-BASED PLATE BENDING ELEMENTS

  • 摘要: 本文针对如何提高位移型板弯曲单元内力解的问题进行了一些探讨,在总结位移型和杂交型有限元的特点基础之上,提出了利用杂交元原理对位移型单元内力解进行重算的后处理方案:首先由位移型板元求出单元结点位移;其次假设满足平衡方程的单元内力场,并利用杂交能量泛函原理确定其与单元位移之间的联系,进而求出单元内力解。数值算例表明,本文所提出的方法可以明显改善多种板弯曲单元内力解的性态,使单元在获得较精确的位移解的同时,又可获得较好的内力解,而且又不使单元列式过于复杂。本文为改善位移型有限元的内力和应力解提供了一条可行的新途径。

     

    Abstract: In this paper, a new simple enhanced hybrid post-processing procedure is presented in order to improving internal force or stress solutions of displacement-based plate bending elements. Firstly, the displacement solutions are obtained by the standard method for the displacement-based elements. Secondly, the internal force fields, which satisfying the equilibrium equation of plates, are assumed by introducing several unknown parameters. Then by utilizing the Hellinger-Reissner variational principle, the relationships between those parameters and the displacement solutions are established. Thus, the internal force or stress solutions are determined by the new relationships instead of the traditional stress-strain relationships. Numerical examples show that by using the proposed method, the accuracy of the internal force or stress solutions of the displacement-based plate bending elements is improved significantly. The enhance hybrid elements possess the advantages of both displacement elements and hybrid elements, being characterized by relatively simple formulation, high accuracy for both displacements and stresses.

     

/

返回文章
返回