Applying Mixed FEM in Non-linear Dynamic Analysis of Plane Truss with Imperfection in Length

The article presents the dynamic analysis of plane trusses with the imperfection in the length of elements. The establishment of the finite element method is formulated on the basis of a mixed model. To study plane trusses with element imperfection in length under dynamic loading, taking into account the geometrical nonlinearity, the establishment procedure of the calculation algorithm can be performed by assuming that the imperfection length is a parameter. The article proposes an approach based on mixed FEM formulation to solve the trusses with imperfection in the length of elements subjected to dynamic loads. The article establishes the dynamic equilibrium equation for the proposed mixed finite element formulation of trusses based on the compatibility equation considering the geometrical nonlinearity. The Newmark and iterative Newton-Raphson methods are applied in solving the nonlinear system of dynamic equations of trusses. The established incremental-iterative algorithm based on these methods is used to write a program for dynamic analysis with imperfections in element length in trusses. The obtained results verify the efficiency and accurateness of the mixed FEM formulation that proposed by authors in the dynamic analysis of trusses with imperfection in length.