Effects of shear deformation on large deflection behavior of elastic frames

Abstract

In this paper, the effects of shear deformation on the large deflection behavior of elastic frames is investigated by the finite element method. A two-node nonlinear beam element with the shear deformation is formulated and employed to analyze some frame structures. The element based on the energy method is developed in the context of the corotational approach. A bracketing procedure u ed the lowest eigenvalue of structural tangent stiffness matrix as indicating parameter is adopted to compute the critical loads. An incremental iterative procedure with the arc-length control technique is employed to trace the equilibrium paths. The numerical results show that the shear deformation plays an important role in the critical load and the large deflection behavior of the frames constructed from the components having low slenderness. A detail investigation is carried out to highlight the influence of slenderness on the behavior of the frames under large deflection.

Nonlinear numerical model of plane frames considering semi-rigid connection and different beam theories

“…Two theories have been used to study deflections of beams and frames, which are the Euler-Bernoulli and Timoshenko theories. In the Euler-Bernoulli theory, the cross-sectional initially normal to the beam neutral axis remains plane and normal to this axis after deformation [7]. This assumption ignores the effects of shear deformation and presents good results for isotropic homogeneous thin beams [8].…”

“…The Timoshenko beam theory, on the other hand, employs a more accurate representation of beam flexure which allows for the inclusion of shear strains and is, therefore, more suited for thick beam analysis [9]. It is considered that the cross-sectional initially normal to center axis of the beam remains plane, but not necessarily normal to the axis after deformation [7].…”

A co-rotational beam element for geometrically nonlinear analysis of plane frames

“…In the previous work, the first author and his co-worker have conducted some research on large displacement analysis of elastic and elasto-plastic frames by developing the co-rotational Bernoulli beam elements [7,8]. The effect of shear deformation on the large displacement response of frames has also investigated by the first author by formulation of the co-rotational Timoshenko element [9]. In the context of the finite element analysis, due to the independence of the transversal displacement and rotation, a Timoshenko beam element for geometrically nonlinear analysis of frames, as discussed by Pacoste and Eriksson in [3] or by the first author in [9,10], can be formulated by linearly interpolating all the kinematic variables, provided that some techniques such as the reduced-order integration are employed to prevent the formulated element from the shear locking.…”

“…The effect of shear deformation on the large displacement response of frames has also investigated by the first author by formulation of the co-rotational Timoshenko element [9]. In the context of the finite element analysis, due to the independence of the transversal displacement and rotation, a Timoshenko beam element for geometrically nonlinear analysis of frames, as discussed by Pacoste and Eriksson in [3] or by the first author in [9,10], can be formulated by linearly interpolating all the kinematic variables, provided that some techniques such as the reduced-order integration are employed to prevent the formulated element from the shear locking. An alternative way for preventing a shear deformable beam element from the shear locking problem, as discussed by Reddy in [11], is to employ appropriate interpolation functions for the kinematic variables.…”