Penalty function method for FEM dynamic analysis of trusses with nonlinear multi-node constraints under harmonic load

Abstract

This work introduces the establishment of the FEM model for investigating the dynamic behavior of trusses, subjected to multi-node constraints, under harmonic excitation based on utilizing the method of Penalty function. The technique for treating the nonlinear relationship of multi-node constraints is developed by using the Penalty function to extremum the Hamiltonian augmented potential energy function and to convert the multi-node constrained relation. The method of Newmark integration is utilized to convert dynamic differential equations of a truss system having multi-node boundary constraints subjected to a time-dependent harmonic force to incremental equations. The incremental-iterative algorithm had been developed based on the Newton-Raphson method, used for solving the dynamic incremental equation of motion for the truss system. Utilizing the constructed algorithm, the Matlab program is written to compute the investigated truss system’s internal force-time response and displacement-time response subjected to harmonic load. The advice for choosing the weight value of the Penalty function is proposed based on analyzing numerical results.