Nonlinear Deformation of Circular Sandwich Plates with Compressible Filler

Here is the formulation of the boundary value problem on the bending of an elastoplastic three-layer circular plate with a compressible filler. To describe the kinematics of the package, the hypotheses of the polyline are accepted. For thin bearing layers, the Kirchhoff hypothesis is accepted. In a relatively thick lightweight filler, the Tymoshenko hypothesis is performed with a linear approximation of radial displacements and deflection along the layer thickness. The work of shear stresses and compression stresses is assumed to be small and is not taken into account. The physical equations of state in the bearing layers correspond to the nonlinear theory of elasticity. The inhomogeneous system of ordinary nonlinear differential equations of equilibrium is obtained by the Lagrange variational method. Boundary conditions are formulated. The solution of the boundary value problem is reduced to finding the four desired functions – the deflection of the lower layer; shear, radial displacement and compression function in the filler. These functions satisfy an inhomogeneous system of ordinary nonlinear differential equations. Here is the formulation of the boundary value problem on the bending of an elastoplastic three-layer circular plate with a compressible filler. To describe the kinematics of the package, the hypotheses of the polyline are accepted. For thin bearing layers, the Kirchhoff hypothesis is accepted. In a relatively thick lightweight filler, the Tymoshenko hypothesis is performed with a linear approximation of radial displacements and deflection along the layer thickness. The work of shear stresses and compression stresses is assumed to be small and is not taken into account. The physical equations of state in the bearing layers correspond to the nonlinear theory of elasticity. The inhomogeneous system of ordinary nonlinear differential equations of equilibrium is obtained by the Lagrange variational method. Boundary conditions are formulated. The solution of the boundary value problem is reduced to finding the four desired functions – the deflection of the lower layer; shear, radial displacement and compression function in the filler. These functions satisfy an inhomogeneous system of ordinary nonlinear differential equations.