In this work, a new mathematical model of thermoelasticity theory has been considered in the context of a new consideration of heat conduction with fractional order theory. A functionally graded isotropic unbounded medium is considered subjected to a periodically varying heat source in the context of space-time non-local generalization of three-phase-lag thermoelastic model and Green-Naghdi mod...

In this paper we describe a numerical method to solve numerically the weakly dispersive fully nonlinear Serre–Green–Naghdi (SGN) celebrated model. Namely, our scheme is based on reliable finite volume methods, proven to be very efficient for the hyperbolic part of equations. The particularity of our study is that we develop an adaptive numerical model using moving grids. Moreover, we use a spec...

We show that although no actual mathematical shell model is explicitly used in ‘general shell element’ formulations, we can identify an implicit shell model underlying these nite element procedures. This ‘underlying model’ compares well with classical shell models since it displays the same asymptotic behaviours—when the thickness of the shell becomes very small—as, for example, the Naghdi mode...

A new method for obtaining the response of a baaed, uid{loaded, nite cylindrical shell using the nite element method is presented. The Galerkin nite element formulation for this problem utilizes a Neumann Green's function representation of the pressure loading on the shell. By representing the pressure loading in this manner, only the structure need be discretized. Both C 0 and C 1 nite element...

In this paper we propose some thermodynamic theories of materials with internal variables. In concrete, we extend the arguments of the theories of the thermoelasticity of type I, II and III proposed by Green and Naghdi to the case of materials with internal variables. We state the system of equations in the linear case when the material is centrosymmetric. We end with an existence and uniquenes...

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We propose a new family of finite element methods for the Naghdi shell model, one method associated with each nonnegative integer k. The methods are based on a nonstandard mixed formulation, and the kth method employs triangular Lagrange finite elements of degree k+2 augmented by bubble functions of degree k+ 3 for both the displacement and rotation variables, and discontinuous piecewise polyno...