Mixed Finite Element Method for Geometrically Nonlinear Buckling Analysis of Truss with Member Length Imperfection

Abstract

This paper focuses on the numerical method for the geometrically nonlinear buckling analysis of truss with initial member length imperfection. The solution of nonlinear buckling problem of truss with imperfection using a displacement-based finite element is dependent on the imperfection implemented. Generally, the operation of incorporating the initial imperfection to the master stiffness equation develops by master-slave elimination method, penalty augmentation method or Lagrange multiplier adjunction methods. Obviously, the initial imperfection considerably increases the difficulty in finite element formulation nonlinear buckling problem. This research proposes a novel approach to formulate the nonlinear buckling problem of truss with imperfection using mixed finite element method. The mixed balanced equation of truss is formulated using the principle of stationary potential energy. The paper presents novel mixed finite truss element, including initial member length imperfection, considering large displacement. Using the arc length technique, the research develops a new incremental-iterative algorithm for solving the nonlinear buckling problem of truss with initial imperfection in different cases of model formulation, including displacement-based finite element and mixed finite element formulation. The numerical test is presented to investigate the equilibrium path for plan truss with initial member length imperfection. The calculation results in solving problem formulated in both displacement and mixed finite model are converged showing the efficiency and reliability of the proposed method.