The prismatic finite element with the interpolation procedure vector form for the engineering structures’ strength calculations

Abstract

The technique of forming a stiffness matrix of a volume prismatic finite element with a triangular base and with six nodes located at the vertices of the prism is presented. The discretization element is formed on the basis of the interpolation procedure vector form with consideration as the interpolation object of the displacement vector of an arbitrary point of the engineering structure. It is proposed to improve the compatibility of the prismatic discretization element at the boundaries of the docking of the bases by using Lagrange multipliers as additional nodal unknowns, which are introduced in additional nodes located in the middle of the prismatic discretization element bases’ sides. The presented vector form of interpolation allows one to obtain the correct finite element solutions in the problems of determining the stress-strain state of engineering structures using curvilinear coordinate systems.