Abstract
A corotational finite element formulation for large displacement analysis of planar functionally graded sandwich (FGSW) beam and frame structures is presented. The beams and frames are assumed to be formed from a metallic soft core and two symmetric functionally graded skin layers. The Euler-Bernoulli beam theory and von Kármán nonlinear strain-displacement relationship are adopted for the local strain. Exact solution of nonlinear equilibrium equations for a beam segment is employed to interpolate the displacement field for avoiding the membrane locking. An incremental-iterative procedure is used in combination with the arc-length control method to compute the equilibrium paths. Numerical examples show that the proposed formulation is capable of evaluating accurately the large displacement response with just several elements. A parametric study is carried out to highlight the effect of the material distribution, the core thickness to height ratio on the large displacement behaviour of the FGSW beam, and frame structures.
Highlights
Large displacement analysis of structures is an important topic in the field of structural mechanics
Many investigations on the large displacement analysis of structures using both analytical and numerical methods are reported in the literature
Various nonlinear beam elements for analysis of planar beam and frame structures are available in the literature
Summary
Large displacement analysis of structures is an important topic in the field of structural mechanics. The first author and his coworkers [12,13,14,15] derived the corotational finite element formulations for large displacement analysis of FGM beam and frame structures In these works, in order to prevent the formulations from the membrane locking, the average strain has been introduced to replace the membrane strain. Investigation on the large displacement behaviour of FGSW beams and frames, to the authors’ best knowledge, has not been reported in the literature, and it is studied in this paper for the first time To this end, a finite element formulation based on EulerBernoulli beam theory is derived in the context of the corotational approach and used in the investigation. Numerical examples are given to show the accuracy of the derived formulation and to illustrate the effect of the material distribution and the core thickness ratio on the large displacement behaviour of the FGSW beam and frame structures
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