Shear-deformable hybrid finite element method for buckling analysis of composite thin-walled members

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Thin-walled members are widely used in mechanical and civil engineering applications. The use of thin-walled elements made of fibre-reinforced composite materials has increased significantly in the past decades due to the superior features of these materials. However, because of their slenderness, susceptibility of thin-walled composite members to buckling is the main concern in the structural design of these elements. For the buckling analysis of thin-walled members with any loading types and boundary conditions, one tends to use numerical methods rather than the closed-form solutions which are limited to simple loading and boundary conditions. Finite element methods (FEM) as the most commonly used numerical techniques can be categorised into two main groups: single-field FEM and multi-field or hybrid FEM. The first group is further categorised into two types: displacement-based elements and stress-based elements. In buckling analysis of thin-walled members with fibre-reinforced laminated composite materials, shear deformations can have a significant effect. Single-field finite element methods adopt different approaches to include shear deformations. Displacement-based methods take account of the effects of shear deformations by modifying the kinematic assumptions of the thin-walled theory. On the other hand, in stress-based methods, the inter-element equilibrium conditions have to be satisfied a-priori, which further complicates the assemblage procedure. A shear-deformable hybrid finite element method for the buckling analysis of composite thin-walled members is developed in this thesis by enforcing the strain-displacement relations to the potential energy functional. In the developed method, the resulting matrix equations are defined only in terms of the nodal displacement values as unknowns which makes the assemblage procedure as simple as in a displacement-based finite element. The shear deformations are taken into account in the current hybrid finite element method by using the strain energy of the shear stress field which eliminates the mentioned difficulties in the other finite element methods.
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