Nonlinear Finite Element Analysis of Bending of Straight Beams Using hp-Spectral Approximations

Document Type : Research Paper


SiViRT Center, University of Texas, San Antonio Department of Mechanical Engineering San Antonio


Displacement finite element models of various beam theories have been developed using traditional finite element interpolations (i.e., Hermite cubic or equi-spaced Lagrange functions). Various finite element models of beams differ from each other in the choice of the interpolation functions used for the transverse deflection w, total rotation φ and/or shear strain γxz, or in the integral form used (e.g., weak form or least-squares) to develop the finite element model. The present study is concerned with the development of alternative beam finite elements using hp-spectral nodal expansions to eliminate shear and membrane locking. Both linear and non-linear analysis are carried out using both displacement and mixed finite element models of the beam theories studied. Results obtained are compared with both analytical (series) solutions and non-linear finite element solutions from literature, and excellent agreement is found for all cases.


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