SHEAR DEFORMABLE HYBRID FINITE-ELEMENT FORMULATION FOR BUCKLING ANALYSIS OF THIN-WALLED MEMBERS

Thin-walled members that are used in many industrial and residential structures, are susceptible to buckling due to their slenderness, because of which accurate prediction of their response is required. The effect of shear deformation can gain importance in the buckling behaviour of beams especially with built-up or composite sections or the materials with relatively low shear modulus such as FRP. To include shear deformation effects, in displacement based formulations, the kinematic assumptions of Vlasov should be modified. On the other hand, in complementary energy based formulations, shear deformations can be included by using the strain energy of the shear stresses without modifying the kinematic assumptions, however the assemblage procedure is difficult for such formulations. To overcome the shortcomings of both displacement based and complementary energy based formulations, mixed-hybrid finite element formulations can be used. In this study, the hybrid finite element formulation based on Hellinger-Reissner functional is obtained by introducing the equilibrium and force boundary conditions as auxiliary conditions to the complementary energy functional.