zbMATH — the first resource for mathematics

A meshfree approach for transient heat conduction analysis of nonlinear functionally graded materials. (English) Zbl 1404.74202

74S30 Other numerical methods in solid mechanics (MSC2010)
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
74A50 Structured surfaces and interfaces, coexistent phases
80A20 Heat and mass transfer, heat flow (MSC2010)
80M22 Spectral, collocation and related (meshless) methods applied to problems in thermodynamics and heat transfer
Full Text: DOI
[1] Asemi, K.; Salehi, M.; Akhlaghi, M., Transient thermal stresses in functionally graded thick truncated cones by graded finite element method, Int. J. Press. Vessels Pip., 119, 52-61, (2014)
[2] Asgari, M.; Akhlaghi, M., Transient heat conduction in two-dimensional functionally graded hollow cylinder with finite length, Heat Mass Transf., 45, 1383-1392, (2009)
[3] Atluri, S. N.; Shen, S. P., The Meshless Local Petrov-Galerkin (MLPG) Method, (2002), Tech Science Press, USA · Zbl 1012.65116
[4] Awaji, H.; Sivakuman, R., Temperature and stress distributions in a hollow cylinder of functionally graded material: the case of temperature-independent material properties, J. Am. Ceram. Soc., 84, 1059-1065, (2001)
[5] Barnett, G. A., Flyer, N. and Wicker, L. J. [2015] “An RBF-FD polynomial method based on polyharmonic splines for the Navier-Stokes equations: Comparisons on different node layouts,” arXiv:1509.02615v1.
[6] Ching, H. K.; Yen, S. C., Transient thermoelastic deformations of 2-D functionally graded beams under non-uniformly convective heat supply, Compos. Struct., 73, 4, 381-393, (2006)
[7] Cox, M., The numerical evaluation of B-spline, J. Instit. Math. Appl., 10, 134-149, (1972) · Zbl 0252.65007
[8] Dai, K. Y.; Liu, G. R.; Han, X.; Lim, K. M., Thermo-mechanical analysis of functionally graded material (FGM) plates using element-free Galerkin method, Comput. Struct., 83, 17-18, 1487-1502, (2005)
[9] Dai, K. Y.; Liu, G. R.; Lim, K. M.; Han, X.; Du, S. Y., A meshfree radial point interpolation method for analysis of functionally graded material (FGM) plates, Comput. Mech., 34, 3, 213-223, (2004) · Zbl 1138.74417
[10] Daneshjou, K.; Bakhtiari, M.; Alibakhshi, R.; Fakoor, M., Transient thermal analysis in 2D orthotropic FG hollow cylinder with heat source, Int. J. Heat Mass Transf., 89, 977-984, (2015)
[11] de Boor, C., On calculating with B-splines, J. Approx. Theory, 6, 1, 50-62, (1972) · Zbl 0239.41006
[12] de Boor, C., A Practical Guide to Splines, (2001), Springer, New York · Zbl 0987.65015
[13] Farin, G., Curves and Surfaces for Computer Aided Geometric Design, (2002), Academic Press, San Diego, CA · Zbl 0835.65020
[14] Goupee, A. J.; Vel, S. S., Multi-objective optimization of functionally graded materials with temperature-dependent material properties, Mater. Des., 28, 1861-1879, (2007)
[15] Goupee, A. J.; Vel, S. S., Transient multiscale thermoelastic analysis of functionally graded materials, Compos. Struct., 92, 1372-1390, (2010)
[16] Gu, Y. T., Meshfree methods and their comparisons, Int. J. Comput. Methods, 2, 4, 477-515, (2005) · Zbl 1137.74302
[17] Hamza-Cherif, S. M.; Houmat, A.; Hadjoui, A., Transient heat conduction in functionally graded materials, Int. J. Comput. Methods, 4, 4, 603-619, (2007) · Zbl 1257.74046
[18] Han, X.; Liu, G. R., Effects of SH waves in a functionally graded plate, Mech. Res. Commun., 29, 5, 327-338, (2002) · Zbl 1094.74584
[19] Han, X.; Liu, G. R.; Lam, K. Y.; Ohyoshi, T., A quadratic layer element for analyzing stress waves in FGMs and its application in material characterization, J. Sound Vibr., 236, 2, 307-321, (2000)
[20] Han, X.; Liu, G. R.; Xi, Z. C.; Lam, K. Y., Transient waves in a functionally graded cylinder, Int. J. Solids Struct., 38, 17, 3021-3037, (2001) · Zbl 0977.74035
[21] Hidayat, M. I. P.; Ariwahjoedi, B.; Parman, S., A new meshless local B-spline basis functions-FD method for two-dimensional heat conduction problems, Int. J. Numer. Methods Heat Fluid Flow, 25, 225—251, (2015) · Zbl 1356.80064
[22] Hidayat, M. I. P.; Ariwahjoedi, B.; Parman, S.; Rao, T. V. V. L. N., Meshless local B-spline collocation method for two-dimensional heat conduction problems with nonhomogenous and time-dependent heat sources, ASME J. Heat Transf., (2017)
[23] Hidayat, M. I. P.; Wahjoedi, B. A.; Parman, S.; Megat Yusoff, P. S. M., Meshless local B-spline-FD method and its application for 2D heat conduction problems with spatially varying thermal conductivity, Appl. Math. Comput., 242, 236-254, (2014) · Zbl 1334.80012
[24] Hosseini, S. M.; Abolbashari, M. H., A unified formulation for the analysis of temperature field in a thick hollow cylinder made of functionally graded materials with various grading patterns, Heat Transf. Eng., 33, 261-271, (2012)
[25] Hosseini, S. M.; Akhlaghi, M.; Shakeri, M., Transient heat conduction in functionally graded thick hollow cylinders by analytical method, Heat Mass Transf., 43, 669-675, (2007)
[26] Ichikawa, K., Functionally Graded Materials in the 21st Century: A Workshop on Trends and Forecasts, (2001), Springer Science+Business Media LLC, New York, USA
[27] Jabbari, M.; Mohazzab, A. H.; Bahtui, A., One-dimensional moving heat source in a hollow FGM cylinder, J. Press. Vessel Technol., 021202, (2009)
[28] Jiang, B.-N., Least-squares meshfree collocation method, Int. J. Comput. Methods, 9, 2, 1240031-1-1240031-25, (2012) · Zbl 1359.65274
[29] Keles, I.; Conker, C., Transient hyperbolic heat conduction in thick-walled FGM cylinders and spheres with exponentially-varying properties, Eur. J. Mech. A/Solids, 30, 449-455, (2011) · Zbl 1278.80002
[30] Khosravifard, A.; Hematiyan, M. R.; Marin, L., Nonlinear transient heat conduction analysis of functionally graded materials in the presence of heat sources using an improved meshless radial point interpolation method, Appl. Math. Model., 35, 4157-4174, (2011) · Zbl 1225.74033
[31] Kim, K. S.; Noda, N., Green’s function approach to three-dimensional heat conduction equation of functionally graded materials, J. Therm. Stresses, 24, 457-477, (2001)
[32] Lewis, R. W.; Roberts, P. M., Finite element simulation of solidification problems, Appl. Sci. Res., 44, 61-92, (1987) · Zbl 0617.76112
[33] Liang, Xu.; Kou, H.; Lizhong, W.; Palmer, A. C.; Wang, Z.; Liu, G., Three-dimensional transient analysis of functionally graded material annular sector plate under various boundary conditions, Compos. Struct., 192, 584-596, (2015)
[34] Liu, G. R., Meshfree Methods: Moving Beyond the Finite Element Method, (2009), CRC Press, USA
[35] Liu, G. R.; Dai, K. Y.; Han, X.; Ohyoshi, T., Dispersion of waves and characteristic wave surfaces in functionally graded piezoelectric plates, J. Sound Vibr., 268, 1, 131-147, (2003)
[36] Liu, G. R.; Han, X.; Lam, K. Y., Stress waves in functionally gradient materials and its use for material characterization, Compos. Part B, Eng., 30, 4, 383-394, (1999)
[37] Liu, G. R.; Tani, J., Surface waves in functionally gradient piezoelectric plates, J. Vibr. Acoust.-Trans. ASME, 116, 4, 440-448, (1994)
[38] Liu, G. R.; Tani, J.; Ohyoshi, T., Lamb waves in a functionally gradient material plates and its transient response (part 1: theory), Trans. Jpn. Soc. Mech. Eng., 57(A), 535, 603-608, (1991)
[39] Liu, G. R.; Tani, J.; Ohyoshi, T., Lamb waves in a functionally gradient material plates and its transient response (part 2: calculation results), Trans. Jpn. Soc. Mech. Eng., 57(A), 535, 609-614, (1991)
[40] Lyche, T.; Pena, J. M., Optimally stable multivariate bases, Adv. Comp. Math., 20, 149-159, (2004) · Zbl 1041.65017
[41] Miyamoto, Y.; Kaysser, W. A.; Rabin, B. H.; Kawasaki, A.; Ford, R. G., Functionally Graded Materials: Design, Processing and Applications, (1999), Kluwer Academic Publishers, Boston, USA
[42] Noda, M., Thermal stresses in materials with temperature-dependent properties, J. Appl. Mech., 44, 83-97, (1991)
[43] Ootao, Y.; Tanigawa, Y., Three-dimensional transient thermal stresses of functionally graded rectangular plate due to partial heating, J. Therm. Stresses, 22, 35-55, (1999)
[44] Piegl, L.; Tiller, W., The NURBS Book, (1995), Springer, New York · Zbl 0828.68118
[45] Praveen, G. N.; Chin, C. D.; Reddy, J. N., Thermoelastic analysis of a functionally graded ceramic-metal cylinder, ASCE J. Eng. Mech., 125, 1259-1267, (1998)
[46] Qian, L. F.; Batra, R. C., Three-dimensional transient heat conduction in a functionally graded thick plate with a higher-order plate theory and a meshless local Petrov-Galerkin method, Comput. Mech., 35, 214-226, (2005) · Zbl 1143.74321
[47] Reddy, J. N.; Chin, C. D., Thermomechanical analysis of functionally graded cylinders and plates, J. Therm. Stresses, 21, 6, 593-626, (1998)
[48] Shan, Y. Y.; Shu, C.; Qin, N., Multiquadric finite diference (MQ-FD) method and its application, Adv. Appl. Math. Mech., 1, 615-638, (2009)
[49] Shao, Z. S.; Ma, G. W., Thermo-mechanical stresses in functionally graded circular hollow cylinder with linearly increasing boundary temperature, Compos. Struct., 83, 259-265, (2008)
[50] Shariyat, M., A nonlinear Hermitian transfinite element method for transient behavior analysis of hollow functionally graded cylinders with temperature-dependent materials under thermo-mechanical loads, Int. J. Press. Vess. Piping, 86, 280-289, (2009)
[51] Shariyat, M.; Lavasani, S. M. H.; Khaghani, M., Nonlinear transient thermal stress and elastic wave propagation analyses of thick temperature-dependent FGM cylinders, using a second order point-collocation method, Appl. Math. Model., 34, 898-918, (2010) · Zbl 1185.74011
[52] Shu, C.; Ding, H.; Yeo, K. S., Local radial basis function-based differential quadrature method and its application to solve two dimensional incompressible Navier-Stokes equations, Comput. Methods Appl. Mech. Eng., 192, 941-954, (2003) · Zbl 1025.76036
[53] Skouras, E. D.; Bourantas, G. C.; Loukopoulos, V. C.; Nikiforidis, G. C., Truly meshless localized type techniques for the steady-state heat conduction problems for isotropic and functionally graded materials, Eng. Anal. Bound. Elem., 35, 452-464, (2011) · Zbl 1259.80029
[54] Sladek, J.; Sladek, V.; Tan, C. L.; Atluri, S. N., Analysis of transient heat conduction in 3D anisotropic functionally graded solids, by the MLPG method, CMES, 32, 161-174, (2008) · Zbl 1232.80006
[55] Sladek, V.; Sladek, J.; Tanaka, M.; Zhang, Ch., Transient heat conduction in anisotropic and functionally graded media by local integral equations, Eng. Anal. Bound. Elem., 29, 1047-1065, (2005) · Zbl 1182.80016
[56] Sutradhar, A.; Paulino, G. H., The simple boundary element method for transient heat conduction in functionally graded materials, Comput. Methods Appl. Mech. Eng., 193, 4511-4539, (2004) · Zbl 1073.80005
[57] Tani, J.; Liu, G. R., SH surface waves in functionally gradient piezoelectric plates, JSME Int. J. Ser. A-Mech. Mater. Eng., 36, 2, 152-155, (1993)
[58] Tanigawa, Y., Some basic thermoelastic problems for non-homogeneous structural materials, J. Appl. Mech., 48, 377-389, (1995)
[59] Tarn, J. Q.; Wang, Y. M., End effects of heat conduction in circular cylinders of functionally graded materials and laminated composites, Int. J. Heat Mass Transf., 47, 5741-5747, (2004) · Zbl 1121.74355
[60] Thakur, H.; Singh, K. M.; Sahoo, P. K., Meshless local Petrov-Galerkin method for nonlinear heat conduction problems, Numer. Heat Transf. B, 50, 393-410, (2009)
[61] Tolstykh, A. I.; Shirobokov, D. A., On using radial basis functions in a “finite difference mode” with applications to elasticity problems, Comput. Mech., 33, 68-79, (2003) · Zbl 1063.74104
[62] Touloukian, Y. S., Thermophysical Properties of High Temperature Solid Materials, (1976), McMillan, New York
[63] Vel, S. S., Exact thermoelastic analysis of functionally graded anisotropic hollow cylinders with arbitrary material gradation, Mech. Adv. Mater. Struct., 18, 14-31, (2011)
[64] Vel, S. S.; Batra, R., Three-dimensional analysis of transient thermal stresses in functionally graded plates, Int. J. Solids Struct., 40, 7181-7196, (2003) · Zbl 1076.74037
[65] Wang, H. M., An effective approach for transient thermal analysis in a functionally graded hollow cylinder, Int. J. Heat Mass Transf., 67, 499-505, (2013)
[66] Wang, H.; Qin, Q. H.; Kang, Y. L., A meshless model for transient heat conduction in functionally graded materials, Comput. Mech., 38, 51-60, (2006) · Zbl 1097.80001
[67] Zhang, X.; Zhang, P.; Zhang, L., An improved meshless method with almost interpolation property for isotropic heat conduction problems, Eng. Anal. Bound. Elem., 37, 850-859, (2013) · Zbl 1287.80007
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.