Lagrange Multiplier Method for Treatment of Nonlinear Multi Freedom Constraints in Dynamic Finite Element Analysis of Truss System Subjected to Harmonic Load

The dynamic finite element analysis of truss with multi freedom nonlinear constraints requires the implementation of constraints to producing the modified dynamic system of equations. Generally, in finite element analysis the mathematical technique for imposing nonlinear boundary constraints based on optimization methods such as the penalty augmentation method and Lagrange multiplier adjunction method. This paper presents an approach to treat the nonlinear multi freedom constraints in dynamic finite element analysis of truss based on the Lagrange multiplier method. Using the Lagrange multiplier method the modified dynamic equilibrium equation is constructed by extremizing the Hamiltonian function and converting a constrained problem into an unconstrained problem. To solve the dynamic equilibrium equation of system under time-dependent harmonic force, the algorithm is established based on the combining Newmark integration method and Newton Raphson method. Using the proposed algorithm the calculation program for dynamic analysis of truss subjected to harmonic load is written. The illustration of numerical example shows the efficiency of the established algorithm.