A posteriori error estimates for continuous/discontinuous Galerkin approximations of the Kirchhoff-Love buckling problem

TL;DR

This paper develops an a posteriori error estimate for the critical buckling load and mode in Kirchhoff-Love plates, accounting for stress tensor approximation errors, using finite element methods suitable for coupled buckling and stress problems.

Contribution

It introduces a novel a posteriori error estimate for buckling analysis that incorporates stress tensor approximation errors within a finite element framework.

Findings

Provides an error indicator for the buckling load and mode.

Accounts for errors in stress tensor computation.

Uses standard finite element spaces for coupled problems.

Abstract

Second order buckling theory involves a one-way coupled coupled problem where the stress tensor from a plane stress problem appears in an eigenvalue problem for the fourth order Kirchhoff plate. In this paper we present an a posteriori error estimate for the critical buckling load and mode corresponding to the smallest eigenvalue and associated eigenvector. A particular feature of the analysis is that we take the effect of approximate computation of the stress tensor and also provide an error indicator for the plane stress problem. The Kirchhoff plate is discretized using a continuous/discontinuous finite element method which uses standard continuous piecewise polynomial finite element spaces which can also be used to solve the plane stress problem.