ASSESSMENT OF THERMAL AND FORCE EFFECTS ON AN ORTHOTROPIC SHELL WITH POSITIVE GAUSSIAN CURVATURE
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Abstract
A mathematical model of thermomechanical deformation is presented for a shell with positive Gaussian curvature, made of an orthotropic composite that develops induced anisotropy during loading. The general formulation of the boundary value problems, as substantiated in a number of studies, is carried out in an uncoupled setting. The occurrence of a temperature gradient is assumed to be one-dimensional, normal to the shell surfaces. Small temperature gradients are assumed, allowing the problem to be solved in a quasi-static manner. To account for the effect of induced heterogeneity—manifested as the dependence of the deformation-strength properties of composites on the nature of the stress state—state equations formulated by one of the authors in the principal material axes of normalized tensor space are used. The developed model is implemented for the thermomechanical analysis of a single-layer shell with positive Gaussian curvature. The main solution parameters are compared with results obtained from similar problems using tested models for the theory of deformation of orthotropic materials with differing resistance proposed by other authors, as well as from the equations of orthotropic linear elasticity theory neglecting differing resistance.
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