Tech Science Press, CMES, vol.58, no.1, pp.75-108, 2010

Locking-free Thick-Thin Rod/Beam Element for Large Deformation Analyses of Space-Frame Structures, Based on the Reissner Variational Principle and A Von Karman Type Nonlinear Theory

Author(s): Y.C. Cai, J.K. Paik and S.N. Atluri

Abstract :
This paper presents a new shear flexible beam/rod element for large deformation analyses of space-frame structures comprising of thin or thick members, based on the Reissner variational principle and a von Karman type nonlinear theory of deformation in the co-rotational reference frame of the present beam element. The C0 continuous trial functions for transverse rotations in two independent directions are used over each element, to derive an explicit expression for the (16x16) symmetric tangent stiffness matrix of the beam element in the co-rotational reference frame. When compared to the primal approach wherein C1 continuous trial functions for transverse displacements over each element are necessary, the trial functions for the transverse bending moments, shear deformations and rotations are very simple in the current approach, and can be assumed to be linear within each element. The present (16×16) symmetric tangent stiffness matrices of the thick/thin beam are much simpler than those of many others in the literature. Numerical examples demonstrate that the present element is free from shear locking in the thin beam limit, and is suitable for the large deformation analysis of spaced frames with thick/thin members. The present methodologies can be extended to study the very large deformations of plates and shells as well.