The complex variable reproducing kernel particle method for bending problems of thin plates on elastic foundations. (English) Zbl 1461.74089
Summary: In this paper, the complex variable reproducing kernel particle method (CVRKPM) for solving the bending problems of isotropic thin plates on elastic foundations is presented. In CVRKPM, one-dimensional basis function is used to obtain the shape function of a two-dimensional problem. CVRKPM is used to form the approximation function of the deflection of the thin plates resting on elastic foundation, the Galerkin weak form of thin plates on elastic foundation is employed to obtain the discretized system equations, the penalty method is used to apply the essential boundary conditions, and Winkler and Pasternak foundation models are used to consider the interface pressure between the plate and the foundation. Then the corresponding formulae of CVRKPM for thin plates on elastic foundations are presented in detail. Several numerical examples are given to discuss the efficiency and accuracy of CVRKPM in this paper, and the corresponding advantages of the present method are shown.
References:
| [1] | Rashed, YF; Aliabadi, MH; Brebbia, CA, The boundary element method for thick plates on a Winkler foundation, Int J Numer Meth Eng, 41, 1435-1462, (1998) · Zbl 0907.73075 · doi:10.1002/(SICI)1097-0207(19980430)41:8<1435::AID-NME345>3.0.CO;2-O |
| [2] | Balas, J; Sladek, J; Sladek, V, The boundary integral equation method for plates resting on a two-parameter foundation, Zamm J Appl Math Mech, 64, 137-146, (1984) · Zbl 0532.73080 · doi:10.1002/zamm.19840640302 |
| [3] | EI-Zafrany, A; Fadhil, S, A modified Kirchhoff theory for boundary element analysis of thin plates resting on two-parameter foundation, Eng Struct, 18, 102-114, (1996) · doi:10.1016/0141-0296(95)00097-6 |
| [4] | Saygun, A; Celik, M, Analysis of circular plates on two-parameter elastic foundation, Struct Eng Mech, 15, 249-267, (2003) · doi:10.12989/sem.2003.15.2.249 |
| [5] | Katsikadelis, JT; Kallivokas, LF, Clamped plates on Pasternak-type elastic foundation by the boundary element method, Int J Appl Mech, 53, 9, (1986) · Zbl 0607.73117 |
| [6] | Katsikadelis, JT; Armenakas, AE, Plates on elastic foundation by BIE method, J Eng Mech, 110, 1086-1105, (1984) · Zbl 0551.73083 · doi:10.1061/(ASCE)0733-9399(1984)110:7(1086) |
| [7] | Sladek, V; Sladek, J, Nonsingular formulation of BIE for plate bending problems, Eur J Mech A/Solids, 11, 335-348, (1992) · Zbl 0761.73114 |
| [8] | Belytschko, T; Krongauz, Y; Organ, K; Fleming, M; Krysl, P, Meshless method: an overview and recent developments, Comput Methods Appl Mech Eng, 139, 3-47, (1996) · Zbl 0891.73075 · doi:10.1016/S0045-7825(96)01078-X |
| [9] | Li, S; Liu, WK, Meshless and particles methods and their applications, Appl Mech Rev, 55, 1-34, (2002) · doi:10.1115/1.1431547 |
| [10] | Liu, WK; Chen, Y; Jun, S; Chen, JS; Belytschko, T, Overview and applications of the reproducing kernel particle methods, Arch Comput Methods Eng, 3, 3-80, (1996) · doi:10.1007/BF02736130 |
| [11] | Liu, WK; Li, S; Belytschko, T, Moving least square reproducing kernel method. (I) methodology and convergence, Comput Methods Appl Mech Eng, 143, 113-154, (1997) · Zbl 0883.65088 · doi:10.1016/S0045-7825(96)01132-2 |
| [12] | Liu, WK; Jun, S; Li, S; Adee, J; Belytschko, T, Reproducing kernel particle methods for structural dynamics, Int J Numer Meth Eng, 38, 1655-1679, (1995) · Zbl 0840.73078 · doi:10.1002/nme.1620381005 |
| [13] | Gan, NF; Li, GY; Long, SY, 3D adaptive RKPM method for contact problems with elastic-plastic dynamic large deformation, Eng Anal Boundary Elem, 33, 1211-1222, (2009) · Zbl 1253.74131 · doi:10.1016/j.enganabound.2008.07.009 |
| [14] | Chen, JS; Chen, C; Wu, CT; Liu, WK, Reproducing kernel particle methods for large deformation analysis of nonlinear structures, Comput Methods Appl Mech Eng, 139, 195-229, (1996) · Zbl 0918.73330 · doi:10.1016/S0045-7825(96)01083-3 |
| [15] | Liu, WK; Jun, S, Multiple-scale reproducing kernel particle methods for large deformation problems, Int J Numer Meth Eng, 41, 1339-1362, (1998) · Zbl 0916.73060 · doi:10.1002/(SICI)1097-0207(19980415)41:7<1339::AID-NME343>3.0.CO;2-9 |
| [16] | Liu, WK; Jun, S; Thomas, SD; Chen, Y; Hao, W, Multiresolution reproducing kernel particle method for computational fluid mechanics, Int J Numer Methods Fluids, 24, 1391-1415, (1997) · Zbl 0880.76057 · doi:10.1002/(SICI)1097-0363(199706)24:12<1391::AID-FLD566>3.0.CO;2-2 |
| [17] | Chen, L; Cheng, YM, Reproducing kernel particle method with complex variables for elasticity, Acta Phys Sin, 57, 1-10, (2008) |
| [18] | Chen, L; Cheng, YM, Complex variable reproducing kernel particle method for transient heat conduction problems, Acta Phys Sin, 57, 6047-6055, (2008) · Zbl 1187.80046 |
| [19] | Chen, L; Cheng, YM, The complex variable reproducing kernel particle method for two-dimensional elastodynamics, Chin Phys B, 19, 090204, (2010) · doi:10.1088/1674-1056/19/9/090204 |
| [20] | Chen, L; Cheng, YM, The complex variable reproducing kernel particle method for elasto-plasticity problems, Sci China Ser Phys Mech Astron, 53, 954-965, (2010) · doi:10.1007/s11433-010-0186-y |
| [21] | Weng, YJ; Zhang, Z; Cheng, YM, The complex variable reproducing kernel particle method for two-dimensional inverse heat conduction problems, Eng Anal Bound Elem, 44, 36-44, (2014) · Zbl 1297.65117 · doi:10.1016/j.enganabound.2014.04.008 |
| [22] | Chen, L; Cheng, YM; Ma, HP, The complex variable reproducing kernel particle method for the analysis of Kirchhoff plates, Comput Mech, 55, 591-602, (2015) · Zbl 1311.74154 · doi:10.1007/s00466-015-1125-6 |
| [23] | Sladek, J; Sladek, V; Mang, HA, Meshless local boundary integral equation method for simply supported and clamped plates resting on elastic foundation, Comput Methods Appl Mech Eng, 191, 5943-5959, (2002) · Zbl 1083.74603 · doi:10.1016/S0045-7825(02)00505-4 |
| [24] | Chinnaboon, B; Katsikadelis, JT; Chucheepsakul, S, A BEM-based meshless method for plates on biparametric elastic foundation with internal supports, Comput Methods Appl Mech Eng, 196, 3165-3177, (2007) · Zbl 1173.74466 · doi:10.1016/j.cma.2007.02.012 |
| [25] | Hu, WJ; Long, SY; Xia, P; Cui, HX, Bending analysis of thick plate on the elastic foundation by the meshless radial point interpolation method, Eng Mech, 26, 58-61, (2009) |
| [26] | Ferreira, A; Roque, C; Neves, A; Jorge, R; Soares, C, Analysis of plates on Pasternak foundations by radial basis functions, Comput Mech, 46, 791-803, (2010) · Zbl 1288.74030 · doi:10.1007/s00466-010-0518-9 |
| [27] | Bahmyari, E; Banatehrani, MM; Ahmadi, M; Bahmyari, M, Vibration analysis of thin plates resting on Pasternak foundations by element free Galerkin method, Shock Vib, 20, 309-326, (2013) · doi:10.1155/2013/532913 |
| [28] | Bahmyari, E; Mohammad, RK, Vibration analysis of nonhomogeneous moderately thick plates with point supports resting on Pasternak elastic foundation using element free Galerkin method, Eng Anal Bound Elem, 37, 1212-1238, (2013) · Zbl 1287.74016 · doi:10.1016/j.enganabound.2013.05.003 |
| [29] | Mohammed, M; Al-Tholaia, Hussein; Al-Gahtani, Husain Jubran, RBF-based meshless method for large deflection of elastic thin plates on nonlinear foundations, Eng Anal Bound Elem, 51, 146-153, (2015) · Zbl 1403.74049 · doi:10.1016/j.enganabound.2014.10.011 |
| [30] | Timoshenco S, Woinowsky-Krieger S (1985) Theory of plates and shell, 2nd edn. McGraw-Hill, New York |
| [31] | Kerr, AD, Elastic and viscoelastic foundation models, J Appl Mech, 31, 491-498, (1964) · Zbl 0134.44303 · doi:10.1115/1.3629667 |
| [32] | Xiong YB, Long SY, Li GY (2005) A local Petrov-Galerkin method for analysis of plates on elastic foundation. China Civ Eng J 38(11):79-83 |
| [33] | Wang, JG; Huang, MG, Boundary element analysis of thin plates on the two-parameter elastic foundation, China Civ Eng J, 25, 51-59, (1992) |
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
