On the elastoplastic cyclic analysis of plane beam structures using a flexibility-based finite element approach

Abstract

a b s t r a c tThis paper presents the extension of a flexibility-based large increment method (LIM) for the case of cyclic loading. In the last few years, LIM has been successfully tested for solving a range of non-linear structural problems involving elastoplastic material models under monotonic loading. In these analyses, the force-based LIM algorithm provided robust solutions and significant computational savings compared to the displacement-based finite element approach by using fewer elements and integration points. Although in cyclic analysis a step-by-step solution procedure has to be adopted to account for the plastic history, LIM will still have many advantages over the traditional finite element method. Before going into the basic idea of this extension, a brief discussion regarding LIM governing equations is presented followed by the proposed solution procedure. Next, the formulation is specified for the treatment of the elastic perfectly plastic beam element. The local stage for the beam behavior is discussed in detail and the required improvement for the LIM methodology is described. Illustrative truss and beam examples are presented for different non-linear material models. The results are compared with those obtained from a standard displacement method and again highlight the potential benefits of the proposed flexibility-based approach.

Quasi-hinge beam element implemented within the hybrid force-based method

“…The LIM was first presented by Zhang and Liu (1997) who demonstrated the ability of this method to converge using less elements and time steps compared to the equivalent displacement-based approach [7,34]. The LIM has been used to analyse structures made of materials with elasto-perfectly plastic behaviour, though so far only for rectangular sections with asymmetric degrees of freedom, conducted by considering the shear force and moment at just one end of the element [14,35]. Flexibility coefficients describing elasto-perfectly plastic behaviour were proposed by , based on an axial force-moment yield surface [13,36].…”

“…To do this a force vector regulator function, ℎ 0 . , is defined following [13,14] and is used to iteratively modify f until the compatibility criterion, . ∆= is satisfied (shown at step 6 of Table 2).…”

“…Both conventional (zero length hinge) and quasi-hinge (finite length hinge) elements have been implemented here to allow comparison of predictions from the two methods. Both elements have been formulated with arbitrary general section geometries and to account for elasto-plastic strain hardening material behaviour in LIM [14].…”

“…The structures of the first two examples are subjected to only axial forces and demonstrate the ability of the solution procedure in analysing two simple structural problems. Results are compared against both theory and previously published work [7,14] and serve to demonstrate the accuracy of the underlying LIM code. The final two examples involve the use of the conventional hinge and quasi-hinge elements.…”

Cyclic Loading of Beams Based on Kinematic Hardening Models: A Finite Element Approach

“…Moreover, equilibrium equation takes the following form, in which [ ] C represents the matrix of elastic moduli, in one, two, or three dimensional forms whichever the case may be. This results into the relation between assembled general stiffness matrix, deformations and load matrix as identified in [20].…”