Abstract
Although structures made of functionally graded materials have been studied by many researchers, no research may be found in literature on boundary element analysis of the functionally graded viscoelastic structures. In the present paper, a 2D boundary element formulation capable of modeling time-dependent functionally graded materials (FGM) is presented. A numerical implementation of the Somigliana identity in terms of the displacements is developed to solve 2D problems of the exponentially graded viscoelasticity. The FGM concept can be applied to various materials, for structural and functional purposes. In this model, only Green functions of the nonhomogeneous elastostatic problems are needed with material properties that vary continuously along a given dimension. Results reveal that the boundary element approach can successfully be employed for the present complicated problem for arbitrary time histories of the applied loads and arbitrary boundary conditions, without the need to use relaxation functions or mathematical transformations.
Highlights
Structures made of functionally graded materials have been studied by many researchers, no research may be found in literature on boundary element analysis of the functionally graded viscoelastic structures
The fundamental solutions of the functionally graded materials (FGM) for 2D and 3D elasticity problems have been recently developed in some other works (Chan et al 2004; Criado et al 2007, 2008)
In the present paper, a new numerical formulation is presented for accomplishment of the simplified viscoelastic analysis of the functionally graded media by the Boundary element method (BEM)
Summary
Structures made of functionally graded materials have been studied by many researchers, no research may be found in literature on boundary element analysis of the functionally graded viscoelastic structures. A variety of nonhomogeneous engineering media made of polymers, plastics, metals and alloys at elevated temperatures, composites, concrete, etc., exhibit significant rate and history dependencies. Appropriate simulation of these types of structures requires using appropriate viscoelastic models. Boundary element method (BEM) has recently found considerable applications in solving lots of engineering problems, such as viscoelasticity, contact mechanics, elastoplasticity, thermoelasticity, fracture mechanics, elastodynamics, etc. The fundamental solutions of the FGMs for 2D and 3D elasticity problems have been recently developed in some other works (Chan et al 2004; Criado et al 2007, 2008). Extensive works have been developed to effectively model the constitutive behavior of the FG structures, most of these researches have been limited to elastic behavior analysis (Gao et al 2008; Wang and Qin 2012; Ashrafi et al 2013a, 2013b)
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