Geometrically nonlinear extended high order analysis for sandwich beams based on elastic–plastic core shear behavior

Geometrically nonlinear response of a sandwich panel based on elastic–linear plastic (bilinear) shear behavior of the core is presented. The extended high order sandwich panel theory (EHSAPT) is applied to obtain governing equations. The nonlinear Von Karman type relations for strains of face sheets and the core are adopted. The face sheets follow first order shear deformation theory along with the linear elastic assumption. A Ritz based solution which is suitable for any essential boundary condition is implemented. Two types of boundary conditions are considered simply supported and immovable clamped at both edges. In each type of boundary conditions, the effects of plastic shear modulus of bilinear material behavior on transverse shear stress distribution along with detection of the elastic and plastic regions within the core, force and moment resultants, transverse displacement distributions in the face sheets, in-plane and vertical displacements through the thickness of the core are studied in detail. Besides, all results based on the bilinear material assumption of the core are compared with the linear elastic ones. Finally, for the case study of the simply supported beam, the results of the constitutive model are compared with finite element simulation.