The article presents the dynamic analysis of trusses with initial length imperfection of elements under harmonic loading, taking into account the geometrical nonlinearity. The hybrid finite element formulation in the non-linear analysis of the trusses considers the initial length imperfection of elements as a dependent boundary constraint in the master equation of stiffness. Moreover, it is incorporated with the establishment of the modified system of equations. In order to overcome the mathematical complexity in dealing with initial length imperfection, this article recommends a novel approach to solve the non-linear dynamic problems on the basis of hybrid finite element formulation. In this research, the unknowns of the dynamic equilibrium equations are the displacements and forces, which are obtained from the use of virtual work. The hybrid matrix of elements of the truss is established based on the hybrid variation formulation with member length imperfection, taking into account non-linear deformation. The authors applied the Newmark integration and Newton Raphson iteration methods to solve the dynamic equations with consideration of geometrical nonlinearity. The research developed the incremental-iterative algorithm and wrote the calculation programming routine to illustrate dynamic responses of trusses with initial length imperfection under harmonic loading. The obtained results verify the accuracy and effectiveness of the proposed approach.
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