The Mathematical Theory of Thick and Thin Elastic Rectangular Disks in the States of Plane Stress and Plane Strain

摘要

The mathematical theory of thick and thin elastic rectangular disks in the states of plane stress and plane strain is derived from the three- and two? dimensional theories of elasticity. By verifying the three-dimensional strain-displacement relations it is found that the exact state of plane stress in two-dimensional problems of elasticity for thin disks exists only when either Poisson’s ratio＝o or the area dilatation=a constant，and does not exist except under these conditions. Two kinds of the exact stress strain relations of thin disks in the state of plane stress are derived from the conditions. The Exact displacement equilibrium equations of thick and thin disks in three- and two-dimensional problems are stated.The solutions of the displacement equilibrium equations and the stress-strain relations of thick and thin disks in the slates of plane stress and plane strain are given.