A class of strain‐displacement elements in upper bound limit analysis

Abstract

The main restriction in applying the upper bound theorem in limit analysis by means of the finite element method is that once the displacement field has been discretized, the flow rule and the boundary conditions should be satisfied everywhere throughout the discretized structure. This is to secure mathematically that the result will be a rigorous upper bound of the exact limit load multiplier. So far, only the linear and the quadratic displacement elements with straight sides, which result in constant and linear strains, respectively, satisfy this requirement.In this article, it is proven both theoretically and practically that there is a general class of strain-displacement triangular elements with straight sides which provide rigorous upper bounds. The interpolation scheme is based on the Bernstein polynomials, and there is no upper restriction of the polynomial order. Both continuous and discontinuous displacements can be considered. The efficiency is examined through plane strain and Kirchhoff plate examples. The generalization to 3D (i.e., tetrahedral elements with plane faces) and other structural conditions is straightforward.

A dual decomposition of the closest point projection in incremental elasto‐plasticity using a mixed shell finite element

“…Recently, a wide number of mixed FE has been proposed. [13][14][15] An interesting approach for developing mixed FEs is the enhanced assumed strain (EAS) technique, which is effective in improving efficiency and accuracy in linear and nonlinear problems. 7 In particular, FEs based on EAS and solid shell models show many advantages, in both geometrically and material nonlinear problems, especially when complex 3D constitutive laws are used.…”

“…This, generally speaking, means low error in recovering the solution for coarse mesh grids, elevated rate of convergence and equivalent convergence properties for all the unknown fields. Recently, a wide number of mixed FE has been proposed 13‐15 . An interesting approach for developing mixed FEs is the enhanced assumed strain (EAS) technique, which is effective in improving efficiency and accuracy in linear and nonlinear problems 7 .…”