NONCONVENTIONAL FINITE ELEMENT MODELS FOR NONLINEAR ANALYSIS OF BEAMS
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In this study, mixed finite element models of beam bending are developed to include the membrane forces and shear forces in addition to the bending moments and displacements. Mixed finite element models were developed based on the weighted residual statements of governing equations. The Euler-Bernoulli beam theory (EBT) and the Timoshenko beam theory (TBT) are used. The effectiveness of the new mixed models is evaluated in light of other mixed models to show the advantages. Each newly developed model is examined and compared with other models to verify its performance under various boundary conditions. In the linear analysis, solutions are compared with available analytical solutions and solutions of existing models. In the nonlinear case, direct and Newton-Raphson methods are used to solve the nonlinear equations. The converged solutions are compared with available solutions of the displacement models. Post-processed data of the mixed model developed herein shows better accuracy than the conventional displacement-based model. © 2011 World Scientific Publishing Company.
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