Abstract
A typical characteristic of bimodular material beams is that when bending, the neutral layer of the beam does not coincide with its geometric middle surface since the mechanical properties of materials in tension and compression are different. In the classical theory of elasticity, however, this characteristic has not been considered. In this study, a bimodular simply-supported beam under the combination action of thermal and mechanical loads is theoretically analyzed. First, a simplified mechanical model concerning the neutral layer is established. Based on this mechanical model, Duhamel’s theorem is used to transform the thermoelastical problem into a pure elasticity problem with imaginary body force and surface force. In solving the governing equation expressed in terms of displacement, a special solution of the displacement equation is found first, and then by utilizing the stress function method based on subarea in tension and compression, a supplement solution for the displacement governing equation without the thermal effect is derived. Lastly, the special solution and supplement solution are superimposed to satisfy boundary conditions, thus obtaining a two-dimensional thermoelasticity solution. In addition, the bimodular effect and temperature effect on the thermoelasticity solution are illustrated by computational examples.
Highlights
In the classical theory of elasticity [1], it is generally assumed that materials exhibit the same elastic properties in tension and compression, but this is only a simplified result and does not account for the nonlinear characteristics of materials
5, in which the supplement solutionsupplement is obtained by applyat the governing equation, the special solution and corresponding solution ingderived the stress as the wellsupplement as the de Saint-Venant’s
We establish the so-called mechanical model on subarea in tension and compression under mechanical loads. Based on this model, we will analyze the thermal stress of a bimodular beam under the combination action of mechanical and thermal loads
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Negative signs in the longitudinal strain of fibers proposed by Bert [5] This model is mainly applicable to orthotropic materials and is widely used in the analysis of laminated composites [6,7,8,9]. Another model is the criterion of positive–negative signs of principal stress proposed by Ambartsumyan [10], which is mainly applicable to isotropic materials. In structural analysis, this model is of particular significance, since it is this factor that determines whether the point is in tension or in compression. AtSection the governing equation, the special solutionisand corresponding isAiming given in
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