Upper bound limit analysis of thin plates with a generalized conforming element formulated by the quadrilateral area coordinate method

• Published in: Archive of applied mechanics (1991) Vol. 95; no. 2; p. 65
• Main Authors: Xia, Jiangtao, Chen, Shenshen, Zhu, Pengyu
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2025; Springer Nature B.V
• Subjects: Accuracy; Cartesian coordinates; Classical Mechanics; Engineering; Finite element analysis; Iterative methods; Limit analysis; Load; Original; Plastic zones; Quadrilaterals; Theoretical and Applied Mechanics; Thin plates; Upper bounds; Generalized conforming approach; Quadrilateral area coordinate method; Upper bound limit analysis; Direct iterative method; Thin plates
• ISSN: 0939-1533; 1432-0681
• DOI: 10.1007/s00419-025-02771-1

In this paper, a generalized conforming element formulated by the quadrilateral area coordinate method is developed for upper bound limit analysis of thin plates. This element can prevent loss of accuracy in severely distorted meshes since the transformation between the area and Cartesian coordinates is always linear. Once the deflection field is approximated and the upper bound theorem applied, upper bound limit analysis of thin plates can be formulated by minimizing the dissipation power subject to a set of equality constraints. In order for overcoming the difficulties caused by the nonsmoothness of the goal function, a direct iterative method is utilized to solve this optimization problem, which distinguishes the rigid zones from the plastic zones at each iteration. Numerical examples show that the proposed method for upper bound limit analysis of thin plates is reasonable and effective and possesses the advantages of high accuracy and reliability even for severely distorted meshes.