热弹性动力学耦合问题的微分代数方法

王林翔; R·V·N·梅尔姆克

热弹性动力学耦合问题的微分代数方法

王林翔¹,
R·V·N·梅尔姆克²

1.
南丹麦大学自然科学与工程学院,丹麦 000;2.威尔费瑞德·劳瑞尔大学耦合动力学与复杂系统研究中心,加拿大 0N2L3C5

详细信息

作者简介:
王林翔(1971- ),男,副教授,博士(E-mail:Wanglinxinang@mci.sdu.dk).

中图分类号: O343.6；O155
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- 被引次数: 0
出版历程
- 收稿日期: 2005-09-19
- 修回日期: 2006-06-17
- 刊出日期: 2006-09-15

Differential-Algebraic Approach to Coupled Problems of Dynamic Thermoelasticity

WANG Lin-xiang¹,
Roderick V. N. Melnik²

1.
MCI, Faculty of Science and Engineering, University of Southern Denmark, Sonderborg, DK-6400, Denmark;

摘要

摘要: 对一般的热机械问题提出了一种有效的数值方法，并对二维的热弹性问题进行了测试．该方法的基本思路是将描述热机械耦合问题的偏微分方程进行降阶，使之成为一组微分代数方程，应力应变关系被写成代数方程．所得到的微分代数系统采用全隐式的向后差分公式进行求解．对该方法进行了详细的说明．为了验证该方法的有效性，将其应用于一个动态非耦合的热弹性问题的求解和一个耦合的二维热弹性问题的求解．
- 热弹性 /
- 二维问题 /
- 微分代数方法
Abstract: An efficient numerical approach for the general thermomechanical problems was developed and it was tested for a two-dimensional thermoelasticity problem. The main idea of the numerical method is based on the reduction procedure of the original system of PDEs describing coupled thermomechanical behavior to a system of Differential Algebraic Equations (DAEs) where the stress-strain relationships are treated as algebraic equations. The resulting system of DAEs were then solved with a Backward Differentiation Formula (BDF) using a fully implicit algorithm. The described procedure was explained in detail. And its effectiveness was demonstrated on the solution of a transient uncoupled thermoelastic problem, for which an analytical solution is known, as well as on a fully coupled problem in the two-dimensional case.
- thermoelasticity /
- two-dimensional /
- differential-algebraic solvers

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参考文献(24)

[1]	Melnik R V N.Convergence of the operator-difference scheme to generalised solutions of a coupled field theory problem[J].J Difference Equations Appl,1998,4(2):185—212. doi: 10.1080/10236199808808136
[2]	Melnik R V N.Discrete models of coupled dynamic thermoelasticity for stress-temperature formulations[J].Appl Math Comput,2001，122(1)：107—132. doi: 10.1016/S0096-3003(00)00026-6
[3]	Melnik R V N,Roberts A J,Thomas K A.Coupled thermomechanical dynamics of phase transitions in shape memory alloys and related hysteresis phenomena[J].Mechanics Research Communications,2001，28(6)：637—651. doi: 10.1016/S0093-6413(02)00216-1
[4]	Melnik R V N,Roberts A J,Thomas K A.Phase transitions in shape memory alloys with hyperbolic heat conduction and differential algebraic models[J].Computational Mechanics,2002，29(1)：16—26. doi: 10.1007/s00466-002-0311-5
[5]	Strunin D V,Melnik R V N,Roberts A J.Coupled thermomechanical waves in hyperbolic thermoelasticity[J].J Thermal Stresses,2001，24(2)：121—140. doi: 10.1080/01495730150500433
[6]	Melnik R V N,Roberts A J,Thomas K A.Computing dynamics of copper-based SMA via center manifold reduction of 3D models[J].Computational Material Science,2000，18(3/4)：255—268. doi: 10.1016/S0927-0256(00)00104-X
[7]	Niezgodka M,Sprekels J.Convergent numerical approximations of the thermomechanical phase transitions in shape memory alloys[J].Numer Math,1991，58：759—778.
[8]	Rawy E K,Iskandar L,Ghaleb A F.Numerical solution for a nonlinear, one-dimensional problem of thermoelasticity[J].J Comput Appl Math,1998，100(1)：53—76. doi: 10.1016/S0377-0427(98)00134-4
[9]	Abd-Alla A N,Ghaleb A F,Maugin G A.Harmonic wave generation in nonlinear thermoelasticity[J].Internat J Engrg Sci,1994，32(7)：1103—1116. doi: 10.1016/0020-7225(94)90074-4
[10]	Jiang S.Numerical solution for the Cauchy problem in nonlinear 1-D thermoelasticity[J].Computig,1990,44(2):147—158. doi: 10.1007/BF02241864
[11]	Abou-Dina M S,Ghaleb A F.On the boundary integral formulation of the plane theory of elasticity with applications (analytical aspects)[J].Journal of Computational and Applied Mathematics,1999，106(1)：55—70. doi: 10.1016/S0377-0427(99)00052-7
[12]	Yang M T,Park K H,Banerjee P K.2D and 3D transient heat conduction analysis by BEM via particular integrals[J].Comput Methods Appl Mech Engrg,2002，191(15/16)：1701—1722. doi: 10.1016/S0045-7825(01)00351-6
[13]	Sherief H H,Megahed F A.A two-dimensional thermoelasticity problem for a half space subjected to heat sources[J].Internat J Solids and Structures,1999，36(9)：1369—1382. doi: 10.1016/S0020-7683(98)00019-5
[14]	Banerjee P K.The Boundary Element Methods in Engineering[M].London:McGrau-Hill,1994，1—100.
[15]	Park K H,Banerjee P K.Two-and three-dimensional transient thermoelastic analysis by BEM via particular integrals[J].Internat J Solids and Structures,2002，39：2871—2892. doi: 10.1016/S0020-7683(02)00125-7
[16]	Hosseini-Tehrani P,Eslami M R.BEM analysis of thermal and mechanical shock in a two-dimensional finite domain considering coupled thermoelasticity[J].Engineering Analysis With Boundary Elements,2000,24(3):249—257. doi: 10.1016/S0955-7997(99)00063-6
[17]	Pawlow I.Three-dimensional model of thermomechanical evolution of shape memory materials[J].Control and Cybernetics,2000，29(1)：341—365.
[18]	Ichitsubo T,Tanaka K,Koiva M,et al.Kinetics of cubic to tegragonal transformation under external field by the time-dependent Ginzburg-Landau approach[J].Phys Rev B,2000，62(9)：5435—5441. doi: 10.1103/PhysRevB.62.5435
[19]	Jacobs A E. Solitons of the square-rectangular martensitic transformation[J].Phys Rev B,1985，31(9):5984—5989. doi: 10.1103/PhysRevB.31.5984
[20]	Jacobs A E.Landau theory of structures in tegragonal-orthorhombic ferroelastics[J].Phys Rev B,2000，61(10):6587—6595. doi: 10.1103/PhysRevB.61.6587
[21]	Chen J,Dargush G F.BEM for dynamic poroelastic and thermoelastic analysis[J].J Solids Struct,1995，32(15):2257—2278. doi: 10.1016/0020-7683(94)00227-N
[22]	Timoshenko S P,Goodier J N.Theory of Elasticity[M].3rd edition.New York:McGraw-Hill,1970，421—480.
[23]	Hairer E,Norsett S P,Wanner G.Solving Ordinary Differential Equations Ⅱ—Stiff and Differential Algebraic Problems[M].Berlin:Springer-Verlag,1996，210—250.
[24]	Jiang S.On global smooth solutions to the one-dimensional equations of nonlinear inhomogeneous thermoelasticity[J].Nonlinear Analysis,1993，20(10)：1245—1256. doi: 10.1016/0362-546X(93)90154-K