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

The article presents the dynamic analysis of plane trusses with the length imperfection of elements. The formulation of the finite element method is established based on a mixed model. To study plane trusses under dynamic loading with element length imperfection taking into account the geometrical nonlinearity, the establishment procedure of the calculation algorithm can be performed by the assumption that the imperfection length is a parameter. In order to deal with the problem of elements with imperfection length, the article proposed an approach based on mixed FEM formulation to solve the trusses with imperfection length of elements subjected to dynamic loading. The paper establishes the dynamic equilibrium equation for the proposed mixed finite element of trusses, formulated based on the compatibility equation considering the geometrical nonlinearity. It applied the Newmark integration and Newton Raphson iteration methods to solve the system of nonlinear dynamic equations of the trusses. The established incremental-iterative algorithm based on these methods is used to write a program for dynamic analysis for trusses with imperfection length of elements. The obtained results verify the effectiveness and accuracy of the proposed mixed FEM formulation in the dynamic analysis of trusses with imperfection length.