Механика машин, механизмов и материалов (Dec 2019)
Isothermal Local Loading of an Elastoplastic Three-Layer Plate
Abstract
The effect of circular, annular and linear uniformly distributed axisymmetric loads on a round three-layer plate with asymmetric thickness is considered. The analytical type of loads is described using the Heaviside function. The materials of the bearing layers of the plate are elastoplastic, the filler is physically nonlinear. For the asymmetric in thickness three-layer plate we have accepted the kinematic hypothesis of a broken normal. In the thin external layers the Kirchhoff’s hypotheses are accepted. The filler is no compressible through thickness. It’s normal subject to the hypothesis Timoshenko. The work of arising shear stresses is taken into account. The formulation of a boundary value problem is given. The equilibrium equations are obtained by the Lagrange variational method. Boundary conditions on the plate contour are formulated. The solution to the boundary problem is reduced to finding the three required functions: deflection, shear and radial displacements of the middle plane of the filler. For these functions, an inhomogeneous system of ordinary nonlinear differential equations is obtained. Its solution was carried out by the Ilyushin elastic solution method. It is shown that the fifth approximation can be taken as the desired solution, since its difference from the previous one does not exceed 1 %. Iterative analytical solutions are obtained in Bessel functions. Their parametric analysis is carried out. Numerical results are obtained for a plate which layers are recruited from D16T–fluoroplast-4–D16T materials which mechanical characteristics, including nonlinearity functions, were obtained earlier. The boundary conditions correspond to the hinge support of the plate contour. The influence of the physical nonlinearity of the layer materials on the displacements in the plate is investigated. It is shown that the increase in calculated displacements during elastoplastic deformation in the plate is up to 20 %.
