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Abstract: Some possible modifications of the governing equations of the linear theory of elasticity are considered. The stress–strain relation is specified by an integral equality instead of the local Hooke’s law. The modified integrodifferential boundary value problem is reduced to the minimization of a nonnegative functional under differential constraints. A numerical algorithm based on polynomial approximations of unknown functions (stresses and displacements) is developed and applied to linear elasticity problems. The bilateral estimation criteria of solution errors are proposed in order to analyze the algorithm convergence rate. The numerical results obtained by applying the integrodifferential relation method and the conventional variational method are compared and discussed.

Without Abstract:

The paper deals with the optimization of anisotropic plates loaded by in-plane forces and designed against buckling. The internal structure of the plate is seen as a twodimensional locally orthotropic solid and the orientations of the axes of orthotropy are taken as the design variables. The problem of optimization consists in determining the best orientation of the axes of orthotropy from the condition of the maximum behaviour of the critical buckling loads. General properties of the problem, such as multiplicity of the critical parameters and splitting of multiple eigenvalues, are studied. Optimization algorithms are developed to improve the anisotropic properties of the plate. The results of numerically finding the optimal orientation of orthotropic properties are compared with conventional layouts for square and rectangular plates loaded by normal in-plane forces.