Derivation of Stress Functions for Two?Dimensional Elasticity and Properties of Solutions

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  • 二次元弾性の応力関数の誘導と解の性質
  • 2ジゲン ダンセイ ノ オウリョク カンスウ ノ ユウドウ ト カイ ノ セイ
  • Effects of boundary conditions on the solution of foundation problems
  • 地盤問題の解に及ぼす境界条件の影響

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Abstract

There exist several methods for analyzing two-dimensional elastic bodies, and sometimes photoelastic studies have been carried out for foundation problems. In the photoelastic studies a finite plate with free side ends is usually used. Accordingly, boundary conditions for this study do not correspond to those for foundation problems. In addition, the former is plane stress but the latter is plane strain. For these reasons, the results of the photoelastic study may not correspond to those of foundation problems. The main objective of this paper is to investigate discrimination of two-dimensional elastic solutions by the stress function method. The stress functions for plane strain and plane stress were derived separately in this paper. The results obtained indicated the stresses and the displacements were expressed by only one biharmonic function. The formulae for the plane strain corresponded to those of Love's stress function for an axially symmetric elastic body. Several numerical examples were presented, and one of these was compared with the result of the photoelastic study. It was shown that an elastic body with stress only as the boundary condition yielded identical stresses for plane strain and plane stress, but an elastic body with stress and displacement as boundary conditions yielded different stresses for plane strain and plane stress.

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