Penalty function method for geometrically nonlinear buckling analysis of imperfect truss with multi-freedom constraints based on mixed FEM

Abstract

This paper is concerned with the approach to implementing the Penalty function method for imposing multi-freedom constraints in geometrically nonlinear analysis of imperfect trusses based on mixed finite element formulation. Using a finite element model based on displacement formulation, it is required to incorporate both the dependent boundary relations and initial length imperfection to the nonlinear master stiffness system of equations for solving the geometrically nonlinear problem of imperfect truss with multi-freedom constraints. For decreasing the mathematical complexion of the incorporating process, the author proposes a novel mixed finite truss element considering initial imperfection, used in building the model for solving the geometrically nonlinear problem of truss with multi-freedom constraints. The modified nonlinear stiffness equation is constructed by employing the penalty function method to convert a constrained problem into an unconstrained problem by extremizing the augmented energy function established based on the proposed mixed finite element formulation. For solving the nonlinear equilibrium equation of imperfect trusses with multi-freedom constraints, the incremental equilibrium equation is constructed, and the incremental-iterative algorithm for calculation is established utilizing the arc-length method, used for writing the calculation program for investigating geometrically nonlinear behavior of imperfect truss with multi-freedom constraints. The results of the numerical test show the influence of initial imperfection and choosing weight values on the equilibrium path of the truss.