Accurate thermal stress predictions using C⁰-continuous higher-order shear deformable elements

Abstract

The behavior of C⁰-continuous higher-order shear deformable finite element formulations when applied to thermal stress conditions is analyzed critically. It is shown that, unlike in the first-order formulations, the inconsistent initial strain field can also disturb the displacement recovery in the higher-order shear deformable elements. In this paper, the possible errors due to such inconsistent terms are a priori predicted in an analytical sense and validated by using linear and quadratic beam element formulations. The paper suggests how the total and the thermal strain components have to be consistently reconstituted to get optimal accuracy from higher-order shear-deformable finite elements for thermal stress analysis. A conflict between the consistency and the continuity requirements is noticed in such formulations. The extraneous errors observed in the variationally correct and consistent formulations are attributed to this fact.