Flexibility modeling of a beam undergoing large deflection using the assumed mode method

Abstract

We propose a new nonlinear modeling method to conduct the static or dynamic analysis of a flexible beam undergoing large deflection in this paper. In the proposed modeling method, we employ the in-extensible beam assumption which simplifies the expressions of strain energy and geometric constraints among deformation variables. Deformation variables are approximated using modal coordinates and quasi-comparison functions. Governing equations are derived based on the extended Hamilton's principle and used to solve various kinds of nonlinear static and dynamic analysis problems. The accuracy of the proposed modeling method is validated by comparing numerical results to those obtained with a commercial nonlinear finite element code. The efficiency and solution convergence robustness of the proposed modeling method are also compared.