Nonlinear dynamic analysis of plan truss with length imperfection under harmonic excitation using mixed FEM

This paper is concerned with the vibration of a harmonically excited plan truss with an element’s length imperfection. Using displacement-based finite element formulation the process of establishing an algorithm for finding the solution of a harmonically excited plan truss with an element’s length imperfection considering geometric nonlinearity can be done with the mathematical operation of treating length imperfection as a dependent boundary constraint. To overcome the treating element’s imperfection in solving process, this work proposes an approach for solving truss with element’s length imperfection under harmonic load based on mixed FEM formulation. The dynamic equilibrium equation is constructed for the proposed mixed truss finite element which is built based on a compatibility equation considering geometric nonlinearity. For solving the nonlinear dynamic system of equations of truss system under harmonic excitation is employed combining the Newmark integration method and Newton Raphson iteration method. The established incremental iterative algorithm based on combining these methods is used to write the calculation program for investigating vibration of the truss system with elements length imperfection subjected to harmonic load. The numerical test results show the efficiency of the mixed FEM formulation in vibration analysis of truss with length imperfection under harmonic excitation.