Abstract
The paper presents a solid boundary element approach for analysis of time-harmonic elastodynamic problems for isotropic and anisotropic solids containing rigid shell-like inhomogeneities of finite mass (movable inclusions). It presents a novel approach to derivation of the integral formulae and boundary integral equations, which is based on the partial symmetry property of the elasticity tensor (that is typical for quasicrystals). The mathematical models of rigid shell-like inhomogeneities of arbitrary shape are obtained. The paper also provides a solid approach for the boundary element solution of the obtained integral equations for arbitrary-shaped shell-like inclusions, which include numerical evaluation of singular and hypersingular integrals and accurate computation of the generalized stress intensity factors at inclusion’s front line. Numerical examples are also presented.
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References
Achenbach JD (1973) Wave propagation in elastic solids. North-Holland, Amsterdam
Dominguez J (1993) Boundary elements in dynamics. Elsevier, London
Evans GA, Webster JR (1997) A high order, progressive method for the evaluation of irregular oscillatory integrals. Appl Numer Math 23:205–218
Fan TY, Yang W, Cheng H, Sun XH (2022) Generalized dynamics of soft-matter quasicrystals: Mathematical models. Solutions and applications, 2nd edn. Springer, Singapore
Iserles A, Norsett SP (2005) Efficient quadrature of highly oscillatory integrals using derivatives. Proc R Soc A 461:1383–1399
Kachanov M, Sevostianov I (2018) Micromechanics of materials, with applications. Springer, Cham
Kit HS, Khaj MV, Mykhas’kiv VV (1996) Analysis of dynamic stress concentration in an infinite body with parallel penny-shaped cracks by BIEM. Eng Fract Mech 55(2):191–207
Murakami Y (2002) Metal fatigue: Effects of small defects and nonmetallic inclusions. Elsevier
Mykhas’kiv VV, Khay OM (2009) Interaction between rigid-disc inclusion and penny-shaped crack under elastic time-harmonic wave incidence. Int J Solids Struct 46:602–616
Mykhas’kiv V, Khay O, Sladek J, Sladek V, Zhang C (2008) Micromechanical dynamic influence of rigid disk-shaped inclusion on neighboring crack in 3D elastic matrix. Mater Sci Forum 133–136
Pasternak IM, Sulym H (2021) Thermoelasticity of solids containing thread-like inhomogeneities. I. Nondeformable thread-like inclusions. Int J Solids Struct 232(1):111176
Pasternak I, Pasternak R, Pasternak V, Sulym H (2017) Boundary element analysis of 3D cracks in anisotropic thermomagnetoelectroelastic solids. Eng Anal Boundary Elem 74:70–78
Pasternak I, Sulym H, Ilchuk N (2019) Boundary element analysis of 3D shell-like rigid electrically conducting inclusions in anisotropic thermomagnetoelectroelastic solids. Z Angew Math Mech e201800319
Wang CY, Achenbach JD (1995) Three-dimensional time-harmonic elastodynamic green’s functions for anisotropic solids. Proc R Soc Lond A 449:441–458
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Kushnir, R., Pasternak, I., Sulym, H. (2023). 3D Time-Harmonic Elastic Waves Scattering on Shell-Like Rigid Movable Inclusions. In: Guz, A.N., Altenbach, H., Bogdanov, V., Nazarenko, V.M. (eds) Advances in Mechanics. Advanced Structured Materials, vol 191. Springer, Cham. https://doi.org/10.1007/978-3-031-37313-8_18
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DOI: https://doi.org/10.1007/978-3-031-37313-8_18
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