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On the derivation and possibilities of the secant stiffness matrix for nonlinear finite element analysis. (English) Zbl 0826.73059
Summary: The general non symmetric parametric form of the incremental secant stiffness matrix for nonlinear analysis of solids using the finite element method is derived. A convenient symmetric expression for a particular value of the parameters is obtained. The geometrically nonlinear formulation is based on a generalized Lagrangian approach. Detailed expressions of all the relevant matrices involved in the analysis of three-dimensional solids are obtained. The possibilities of application of the secant stiffness matrix for nonlinear structural problems including stability, bifurcation and limit load analysis are also discussed. Examples of application are given for the nonlinear analysis of pin joined frames.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74G60 Bifurcation and buckling
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