Improved extended high order analysis of sandwich beams with a bilinear core shear behavior

The response of a sandwich panel with bilinear constitutive behavior for shear stress of a core is presented based on a proposed improved extended high order sandwich panel theory. In this theory the face sheets are analyzed based on the first order shear deformation theory that is hitherto not applied in the conventional extended high order sandwich panel theory. Besides, the two-dimensional (2D) elasticity is used for the core. The field equations are derived using the Ritz-based solution which is suitable for any essential boundary condition. In each type of boundary conditions, the effects of plastic shear modulus of the core on transverse shear stress distribution within the core, transverse normal stresses at top and bottom face sheet-core interfaces, displacement components through the thickness of the core, as well as the force and moment resultants and transverse displacements in the face sheets are studied in detail. Also, all results based on the bilinear material assumption of the core are compared with the linear elastic ones. The results reveal that initial plastic regions are created at core edges. Furthermore, the absolute value of shear stresses in the plastic zones based on the bilinear analysis is lower than those obtained from linear elastic one for both types of the boundary conditions. It is seen that, unlike the case of the clamped edges, the plastic regions predicted by bilinear material behavior are much more extensive than ones resulted from elastic material behavior in the simply supported case. Finally, in the case of the linear elastic analysis, the results of the transverse deflections and shear stresses are compared with finite element simulation.