The relation between the equations of the two-dimensional theory of elasticity for anisotropic and isotropic bodies

The two-dimensional problem of the theory of elasticity for an isotropic body is reduced to the solution of the problem for an anisotropic body. Small additional terms are introduced into the biharmonic operator of the problem of the theory of elasticity of an isotropic body, so that the generalized biharmonic operator obtained has no multiple roots. The general solution is then represented in terms of a function of the generalized complex variables, and numerical investigations for isotropic and anisotropic bodies are carried out using the same algorithms. The effectiveness of such a replacement is demonstrated in numerical investigations for simplify connected and multiply connected regions of arbitrary section. (C) 1998 Elsevier Science Ltd. All rights reserved.