A boundary element formulation for the heterogeneous functionally graded viscoelastic structures

Fung, 2001 Sutradhar, 2008 Aliabadi, 2002 Paris, 1997 S. Suresh, A. Mortensen, Functionally Graded Materials, Institute of Materials, IOM Communications, London, 1998. Miyamoto, 1999 Drozdov, 1998 Schanz, 1999, A boundary element formulation in time domain for viscoelastic solids, Commun. Numer. Methods Eng., 15, 799, 10.1002/(SICI)1099-0887(199911)15:11<799::AID-CNM294>3.0.CO;2-F Pérez-Gavilán, 2001, A symmetric Galerkin boundary element method for dynamic frequency domain viscoelastic problems, Comput. Struct., 79, 2621, 10.1016/S0045-7949(01)00090-6 Huang, 2006, Complex variable boundary integral method for linear viscoelasticity, Eng. Anal. Boundary Elem., 30, 1049, 10.1016/j.enganabound.2005.12.007 Ashrafi, 2009, A mathematical boundary integral equation analysis of standard viscoelastic solid polymers, Comput. Math. Model., 20, 397, 10.1007/s10598-009-9046-x Zhu, 2011, A fast multipole boundary element method for 2D viscoelastic problems, Eng. Anal. Boundary Elem., 35, 170, 10.1016/j.enganabound.2010.05.018 Ashrafi, 2012, Modeling of viscoelastic solid polymers using a boundary element formulation with considering a body load, Adv. Mater. Res., 463, 499, 10.4028/www.scientific.net/AMR.463-464.499 Yue, 2003, Boundary element analysis of crack problems in functionally graded materials, Int. J. Solids Struct., 40, 3273, 10.1016/S0020-7683(03)00094-5 Chan, 2004, Green’s function for a two–dimensional exponentially graded elastic medium, Proc. R. Soc. A, 460, 1689, 10.1098/rspa.2003.1220 Criado, 2007, Boundary element analysis of three-dimensional exponentially graded isotropic elastic solids, CMES – Comput. Model. Eng. Sci., 22, 151 Criado, 2008, Green’s function evaluation for three-dimensional exponentially graded elasticity, Int. J. Numer. Methods Eng., 74, 1560, 10.1002/nme.2223 Gao, 2008, Fracture analysis of functionally graded materials by a BEM, Compos. Sci. Technol., 68, 1209, 10.1016/j.compscitech.2007.08.029 Ashrafi, 2013, Two–dimensional modeling of heterogeneous structures using graded finite element and boundary element methods, Meccanica, 48, 663, 10.1007/s11012-012-9623-5 Mukherjee, 2003, The elastic-viscoelastic correspondence principle for functionally graded materials, revisited, J. Appl. Mech., 70, 359, 10.1115/1.1533805 Hilton, 2005, Optimum linear and nonlinear viscoelastic designer functionally graded materials—characterizations and analysis, Compos. Part A, 36, 1329, 10.1016/j.compositesa.2004.11.015 Khazanovich, 2008, The elastic–viscoelastic correspondence principle for non-homogeneous materials with time translation non-invariant properties, Int. J. Solids Struct., 45, 4739, 10.1016/j.ijsolstr.2008.04.011 Kamran, 2009, A multi–scale model for coupled heat conduction and deformations of viscoelastic functionally graded materials, Compos. Part B, 40, 511, 10.1016/j.compositesb.2009.02.003 Sladek, 2006, Meshless local Petrov–Galerkin method for continuously nonhomogeneous linear viscoelastic solids, Comput. Mech., 37, 279, 10.1007/s00466-005-0715-0 Dave, 2011, Viscoelastic functionally graded finite element method using correspondence principle, J. Mater. Civ. Eng., 23, 39, 10.1061/(ASCE)MT.1943-5533.0000006 Grasso, 2012, Application of the multi-level time-harmonic fast multipole BEM to 3-D visco-elastodynamics, Eng. Anal. Boundary Elem., 36, 744, 10.1016/j.enganabound.2011.11.015 Zhu, 2010, Fast multipole boundary element analysis of 2D viscoelastic composites with imperfect interfaces, Sci. China Technol. Sci., 53, 2160, 10.1007/s11431-010-4023-3 Christensen, 1982 Mase, 1999 Flügge, 1975 Gao, 2002, The radial integration method for evaluation of domain integrals with boundary-only discretization, Eng. Anal. Boundary Elem., 26, 905, 10.1016/S0955-7997(02)00039-5 Simo, 1997 Aliabadi, 2011 Asemi, 2013, Three-dimensional static and dynamic analysis of functionally graded elliptical plates, employing graded finite elements, Acta Mech., 224, 1849, 10.1007/s00707-013-0835-0