Finite element analysis of pressure vessel using beam on elastic foundation analysis

Abstract

In this study, we first applied the variation principle to derive a new finite element method (FEM) based on the theory of beam on elastic foundation using line element. The derived FEM was then applied to solve, for the first time, the pressure vessel problems with uniform thickness. Our FEM results, obtained even by using only one line element, agreed exactly with the available closed-form solution, confirming the validity and computing efficiency of our finite element formulation. Moreover, we have applied our new FEM to solve pressure vessel problems with non-uniform thickness where no exact analytical solution is known to exist. The distributions of discontinuity stress in the cylindrical part were obtained. We found that shear force and bending moment were indeed discontinuous at the geometrically discontinuous juncture, due to the bending rigidity and elastic constant change by the non-uniform thickness. Finally, the case of discontinuity stresses in a bimetallic joint was also studied. The locations of maximum shear force and bending moment were found to be affected by the bending rigidity of the material.