A Comparative Study of Least-Squares and the Weak-Form Galerkin Finite Element Models for the Nonlinear Analysis of Timoshenko Beams

In this paper, a comparison of weak-form gaierkin and least-squares finite element models of timoshenko beam theory with the von karman strains is presented. computational characteristics of the twomodels and the influence of the polynomialorders used on the relative accuracies of the two models are discussed. the degree of approximation functions used varied from linear to the 5th order. in the linear analysis, numerical results of beam bending under different types of boundary conditions are presented along with exact solutions to investigate the degree of shear locking in the newly developed mixed finite element models. in the nonlinear analysis,convergences of nonlinear finite element solutions of newly developed mixed finite element models are presented alongwith those of existing traditional model to comparethe performance.