Treatment of multi freedom constraints in geometrically nonlinear stability analysis of truss structures using penalty function method

Abstract

Abstract This paper focus on the treating the multi freedom constraints in geometrically nonlinear buckling and post buckling analysis of truss structure using finite element method. The solution of geometrically nonlinear buckling problem of truss structure having multi freedom constraints is required to incorporate the boundary constraints to the nonlinear master stiffness equation. This work proposes approach to impose the multi freedom constraints and construct stiffness equation for solving the nonlinear buckling problems of truss structures using Penalty function method. The nonlinear balanced equations for buckling analysis of truss structures are developed by minimization of the augmented potential energy function of system by incorporating the multi freedom constraints and changing the constrained problem to the non-constrained problem using Penalty objective function. Using the arc length method, this research proposes the incremental-iterative algorithm for solving the nonlinear balanced equations. Based on proposed algorithm, the calculation program for determining equilibrium paths is written. The numerical test results show the efficiency of proposed method in analysing buckling and post buckling behaviour of truss structures.