Elastic–plastic analysis of the plane strain under combined thermal and pressure loads with a new technique in the finite element method

Abstract

Abstract This research aims to find a new way to address thermal loads within the framework of the elastic–plastic relationship, especially when the loads, such as thermal and pressure ones, are combined. While the residual force method was employed to attempt to find the convergence of a nonlinear solution, it was unable to do so. For this purpose, a mathematical relationship was derived to address thermal loads and add them to the hierarchy of the specified elements method as a subroutine. The findings of the developed program were verified by comparing the numerical results with those of the analytical solution of a thick-walled cylinder loaded with heat load and internal pressure; the results proved the correctness and accuracy of the method used. The method offers a way to redevelop old programs that are unable to effectively address the thermal load in elastic–plastic relations without changing said programs significantly but only by adding the subroutine and some very simple modifications. The solution technique provided in this article can be utilized in many related cases, such as plane stress, axisymmetric solid, and three-dimensional stress analyses.