Nonlinear Dynamic Analysis of Truss with Initial Member Length Imperfection Subjected to Impulsive Load Using Mixed Finite Element Method

Abstract

This paper is concerned with the dynamic analysis of truss with initial member length imperfection under impulsive load considering geometric nonlinearity. Using displacement-based finite element formulation in solving the nonlinear problem of this truss requires incorporating the initial member length imperfection as a dependent boundary constraint to the master stiffness equation and producing a modified system of equations. For escaping the mathematical difficulties of treating the initial member length imperfection this paper proposes a novel approach to formulate the nonlinear vibration problem based on mixed finite element formulation. The dynamic equilibrium equation containing unknown displacements and forces is obtained using the principle of stationary potential energy. A mixed matrix of truss elements is established based on mixed variational formulation with length imperfection conditions considering nonlinear deformation. Combining the Newmark integration method and Newton Raphson iteration method is employed  to solve the dynamic equations with geometric nonlinearity. Based on the employed method, the research develops the incremental-iterative algorithm and the calculation program for determining the dynamic response of truss with initial member length imperfection under impulsive load. The numerical results are presented to verify the efficiency of the proposed method.