Interface Models in Coupled Thermoelasticity

This work proposes new interface conditions between the layers of a three-dimensional composite structure in the framework of coupled thermoelasticity. More precisely, the mechanical behavior of two linear isotropic thermoelastic solids, bonded together by a thin layer, constituted of a linear isotropic thermoelastic material, is studied by means of an asymptotic analysis. After defining a small parameter ε, which tends to zero, associated with the thickness and constitutive coefficients of the intermediate layer, two different limit models and their associated limit problems, the so-called soft and hard thermoelastic interface models, are characterized. The asymptotic expansion method is reviewed by taking into account the effect of higher-order terms and defining a generalized thermoelastic interface law which comprises the above aforementioned models, as presented previously. A numerical example is presented to show the efficiency of the proposed methodology, based on a finite element approach developed previously.

Performance of the asymptotic expansion method to derive equations of state for hard polyhedron fluids

The asymptotic expansion method is used to derive analytical expressions for the equations of state of 14 hard polyhedron fluids such as cube, octahedron, rhombic dodecahedron, etc., by knowing the values of only the first eight virial coefficients.

A survey on fractional asymptotic expansion method: A forgotten theory

This survey applies the fractional asymptotic expansion to analyze some differential equations with boundary value problem. The method leads to the approximate solution in a wide range of applications, and avoids the limitations of algorithms based on Taylor expansion and the perturbation technique. The new method gives approximation series efficiently and overcomes the problems revealed by other analytical schemes that were proposed in the literature.