COMPARISON OF SOLUTIONS TO THE BENDING PROBLEMS OF THREE-LAYER PLATES ON THE WINKLER AND PASTERNAK FOUNDATIONS

Solutions of problems on axisymmetric bending of an elastic three-layer circular plate on the Winkler and Pasternak foundations are given. The bearing layers are taken as isotropic, for which Kirchhoff’s hypotheses are fulfilled. In a sufficiently thick lightweight, incompressible in thickness aggregate, the Timoshenko model is valid. The cylindrical coordinate system, in which the statements and solutions of boundary value problems are carried out, is connected with the median plane of the filler. On the plate contour, it is assumed that there is a rigid diaphragm that prevents the relative shear of the layers. The system of differential equations of equilibrium is obtained by the variational method. Three types of boundary conditions are formulated. One- and two-parameter Winkler and Pasternak models are used to describe the reaction of an elastic foundation. The solution to the boundary value problem is reduced to finding three desired functions, plate deflection, shear, and radial displacement in the filler. The general analytical solution to the boundary value problem is written out in the case of the Pasternak model in Bessel functions. At the Winkler foundation, the known solution is given in Kelvin functions. A numerical comparison of the displacements and stresses obtained by both models with a uniformly distributed load and rigid sealing of the plate contour is carried out.

Development of High-Order Infinite Element Method for Bending Analysis of Mindlin–Reissner Plates

An approach is presented for solving plate bending problems using a high-order infinite element method (IEM) based on Mindlin–Reissner plate theory. In the proposed approach, the computational domain is partitioned into multiple layers of geometrically similar virtual elements which use only the data of the boundary nodes. Based on the similarity, a reduction process is developed to eliminate virtual elements and overcome the problem that the conventional reduction process cannot be directly applied. Several examples of plate bending problems with complicated geometries are reported to illustrate the applicability of the proposed approach and the results are compared with those obtained using ABAQUS software. Finally, the bending behavior of a rectangular plate with a central crack is analyzed to demonstrate that the stress intensity factor (SIF) obtained using the high-order PIEM converges faster and closer than low-order PIEM to the analytical solution.

The Transverse Shear Effect of a New Strain Based Sector Finite Elements for Plate Bending Problems

In this paper, we present the transverse shear effect on the plate bending. The element used is a sector finite element called SBSP (Strain Based Sector Plate-Kirchhoff Theory-), it used for the numerical analysis of circular thin plate bending., and it based on the strain approach. This element has four nodes and three degrees of freedom per node. Through the numerical applications with different loading cases and boundary conditions; This makes the present element robust, better suitable for computations.