Symmetry of the stiffness matrices for geometrically non‐linear analysis

Abstract

AbstractThe efficiency is compared of three procedures developed for geometrically non‐linear analysis with a Lagrangian co‐ordinate system and leading to the formulation of a symmetric secant stiffness matrix. The first, based upon the principle of total potential energy with a special form of the strain energy expression, is due to Mallett and Marcal.1 The second, due to Wood and Schrefler,2 achieved symmetry of the secant matrix by correlation of a procedure based on the virtual work principle with the Mallett–Marcal procedure. The authors3 have recently developed a new symmetric secant matrix procedure also based on the virtual work principle.The aim of this paper is to draw attention to the time‐consuming operations involved in the Mallett–Marcal procedure and to highlight the new secant and tangential stiffness matrix formulations, which are different from those of Wood and Schrefler and easier to compose. This paper also demonstrates how the Wood–Schrefler procedure can be modified to accommodate the new formulation.