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

Subject Areas : Engineering

W  Kim ¹ (Department of Mechanical Engineering, Korea Army Academy at Yeong cheon, Yeong cheon, 770-849 South Korea)
J.N  Reddy ² (Department of Mechanical Engineering, Texas A&M University, College Station)

Received: 2010-06-19 Accepted : 2010-07-17 Published : 2010-06-30

Keywords: Finite element models, Least-squares model, Weak-form Galerkin model, Geometric nonlinearity, Timoshenko Beam Theory,

Abstract :

In this paper, a comparison of weak-form Galerkin and least-squares finite element models of Timoshenko beam theory with the von Kármán strains is presented. Computational characteristics of the two models and the influence of the polynomial orders 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 along with those of existing traditional model to compare the performance.

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