An incremental algorithm to trace the non-linear equilibrium paths of pin-jointed structures using the singular value decomposition of the equilibrium matrix

Abstract

This paper is mainly concerned with a new method that analyses the non-linear behaviour of pin-joint structures. Geometrically, non-linear force method (NFM), which is derived from the force method, is now applied instead of geometrically non-linear finite-element method (NFEM). Singular value decomposition operation of the equilibrium matrix is introduced into the calculation of the responses of structures. The relationships between the equilibrium matrix in NFM and the tangent stiffness matrix in NFEM are discussed. The Newton—Raphson method is used in NFM's iteration procedure and the arc-length incremental strategy is also introduced in post-buckling analysis. Two classical structures and an infinitesimal mechanism are used as illustrative examples.

Keywords

equilibrium matrix tangent stiffness matrix singular point singular value decom-position infinitesimal mechanism

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