Chinese Journal of Theoretical and Applied Mechanics ›› 2018, Vol. 50 ›› Issue (3): 508-516.DOI: 10.6052/0459-1879-18-079
Special Issue: 热应力专题(2018年第3期)
• Theme Articles on “Thermal Stress” • Previous Articles Next Articles
Received:
2018-03-19
Accepted:
2018-03-21
Online:
2018-06-10
Published:
2018-06-11
Contact:
He Tianhu
CLC Number:
Zhang Pei, He Tianhu. A GENERALIZED THERMOELASTIC PROBLEM WITH NONLOCAL EFFECT AND MEMORY- DEPENDENT DERIVATIVE[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(3): 508-516.
Add to citation manager EndNote|Ris|BibTeX
[1] | Biot MA.Thermoelasticity and irreversible thermodynamics.Journal of Applied Physics, 1956, 27(3): 240-253 |
[2] | 田晓耕, 沈亚鹏. 广义热弹性问题研究进展. 力学进展, 2012, 42(1): 18-28 |
(Tian Xiaogeng, Shen Yapeng. Research progress of the generalized thermoelasticity.Advances in Mechanics, 2012, 42(1): 18-28 (in Chinese)) | |
[3] | Peshkov V.Second sound in helium II.Journal of Physics, 1944, 8: 381-386 |
[4] | Cattaneo C.A form of heat conduction equation which eliminates the paradox of instantaneous propagation.Comptes Rendus Physique, 1958, 247: 431-433 |
[5] | Vernotte PM, Hebd CR.Paradoxes in the continuous theory of the heat conduction.Comptes Rendus de l’Académie des Sciences, 1958, 246: 3154-3155 |
[6] | Wang H, Dai W, Melnik R.A finite difference method for studying thermal deformation in a double-layered thin film exposed to ultrashort pulsed lasers.International Journal of Thermal Sciences, 2006, 45(12): 1179-1196 |
[7] | Chen JK, Beraun JE, Tham CL.Ultrafast thermoelasticity for short-pulse laser heating. International Journal of Thermal Sciences, 2004, 42(8-9): 793-807 |
[8] | Lord HW, Shulman YA.A generalized dynamical theory of thermoelasticity.Journal of the Mechanics and Physics of Solids, 1967, 15: 299-309 |
[9] | Green AE, Lindsay KA.Thermoelasticity.Journal of Elasticity, 1972, 2(1): 1-7 |
[10] | Green AE, Naghdi PM.Thermoelasticity without energy dissipation.Journal of Elasticity, 1993, 31(3): 189-208 |
[11] | Youssef HM.Theory of two-temperature-generalized thermoelasticity.IMA Journal of Applied Mathematics, 2006, 71(3): 383-390 |
[12] | Tzou DY.A unified field approach for heat conduction from macro- to micro-scales.Journal of Heat Transfer, 1995, 117(1): 8-16 |
[13] | Qi XL, Suh CS.Generalized thermo-elastodynamics for semiconductor material subject to ultrafast laser heating. Part I: Model description and validation.International Journal of Heat and Mass Transfer, 2010, 53(1): 41-47 |
[14] | Kuang ZB.Variational principles for generalized dynamical theory of thermopiezoelectricity.Acta Mechanica, 2009, 203(1-2): 1-11 |
[15] | Wang YZ, Zhang XB, Song XN.A generalized theory of thermoelasticity based on thermomass and its uniqueness theorem.Acta Mechanics, 2014, 225(3): 797-808 |
[16] | Podlubny I. Fractional Differential Equations.New York: Academic Press, 1999 |
[17] | Meral FC, Royston TJ, Magin R.Fractional calculus in viscoelasticity: An experimental study.Communications in Nonlinear Science and Numerical Simulation, 2010, 15: 939-945 |
[18] | Sherief HH, El-Sayed AMA, El-Latief AMA.Fractional order theory of thermoelasticity.International Journal of Solids and Structures, 2010, 47(2): 269-275 |
[19] | Youssef HM.Theory of fractional order generalized thermoelasticity.Journal of Heat Transfer, 2010, 132(6): 61301 |
[20] | Ezzat MA, Karamany ASE.Fractional order heat conduction law in magneto-thermoelasticity involving two temperatures.Zeitschrift für angewandte Mathematik und Physik. 2011, 62(5): 937-952 |
[21] | 马永斌. 分数阶广义热弹性理论下多场耦合问题动态响应研究. [博士论文]. 兰州:兰州理工大学, 2017 |
(Ma Yongbin. The dynamic response of multi-field coupling problem under the fractional generalized thermoelasticity. [PhD Thesis]. Lanzhou: Lanzhou University of Technology, 2017 (in Chinese)) | |
[22] | 徐业守,徐赵东,何天虎等. 热冲击下理想黏结三明治板的分数阶广义热弹性问题分析.东南大学学报(自然科学版), 2017, 47(1): 130-136 |
(Xu Yeshou, Xu Zhaodong, He Tianhu, et al. Analysis of the fractional order generalized thermal elasticity of the ideal bonded sandwich board under thermal shock.Journal of Southeast University ( Natural Science Edition), 2017, 47(1): 130-136 (in Chinese)) | |
[23] | Diethelm K.Analysis of Fractional Differential Equation: An Application-Oriented Exposition Using Differential Operators of Caputo Type. Berlin, Heidelberg: Springer-Verlag, 2010 |
[24] | Wang JL, Li HF.Surpassing the fractional derivative: concept of the memory-dependent derivative.Computers & Mathematics with Applications, 2011, 62(3): 1562-1567 |
[25] | Yu YJ, Hu W, Tian XG.A novel generalized thermoelasticity model based on memory-dependent derivative.International Journal of Engineering Science, 2014, 81(811): 123-134 |
[26] | El-Karamany AS, Ezzat MA.Modified Fourier’s law with time-delay and kernel function: Application in thermoelasticity.Journal of Thermal Stresses, 2015, 38(7): 811-834 |
[27] | Ezzat MA, El-Karamany AS, El-Bary AA.Electro-thermoelasticity theory with memory-dependent derivative heat transfer.International Journal of Engineering Science, 2016, 99: 22-38 |
[28] | Yu YJ, Tian XG, Liu XR.Size-dependent generalized thermoelasticity using Eringen’s nonlocal model.European Journal of Mechanics, 2015, 51: 96-106 |
[29] | Lotfy K, Sarkar N.Memory-dependent derivatives for photothermal semiconducting medium in generalized thermoelasticity with two-temperature.Mechanics of Time-Dependent Materials, 2017, 21(4): 519-534 |
[30] | Ezzat MA, El-Karamany AS, El-Bary AA.On dual-phase-lag thermoelasticity theory with memory-dependent derivative.Mechanics of Composite Materials & Structures, 2017, 24(11): 908-916 |
[31] | Ezzat MA, El-Bary AA.Thermoelectric MHD with memory-dependent derivative heat transfer.International Communications in Heat & Mass Transfer, 2016, 75: 270-281 |
[32] | Shaw S.A note on the generalized thermoelasticity theory with memory-dependent derivatives.Journal of Heat Transfer, 2017, 139(9): 092005 |
[33] | Eringen AC.Nonlocal continuum field theories.Applied Mechanics Reviews, 2003, 56(2): 391-398 |
[34] | Aifantis EC.Gradient deformation models at nano, micro, and macro scales.Journal of Materials Processing Technology, 1999, 212: 189-202 |
[35] | Yang F, Chong A, Lam D, et al.Couple stress based strain gradient theory for elasticity.International Journal of Solids & Structures, 2002, 39: 2731-2743 |
[36] | Li CL, Guo HL, Tian XG.A size-dependent generalized thermoelastic diffusion theory and its application.Journal of Thermal Stresses, 2017, 40(5): 603-626 |
[37] | Brancik L. Programs for fast numerical inversion of Laplace transforms in MATLAB language environment//Proceedings of the 7th Conference MATLAB’99, pp. 27-39, Czech Republic, Prague, 1999 |
[1] | Li Zelin, Li Hui, Wang Dongsheng, Ren Chaohui, Zu Xudong, Zhou Jin, Guan Zhongwei, Wang Xiangping. A DYNAMIC RESPONSE PREDICTION MODEL OF FIBER-METAL HYBRID LAMINATED PLATES EMBEDDED WITH VISCOELASTIC DAMPING CORE UNDER LOW-VELOCITY IMPACT EXCITATION 1) [J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(6): 1690-1699. |
[2] | Li Yan, He Tianhu, Tian Xiaogeng. A GENERALIZED THERMOELASTIC DIFFUSION PROBLEM OF THIN PLATE HEATED BY THE ULTRASHORT LASER PULSES 1) [J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(5): 1255-1266. |
[3] | Wang Li'an, Zhao Jianchang, Wang Zuowei. ANALYTICAL STUDY ON GROUND VIBRATION INDUCED BY MOVING VEHICLE 1) [J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(5): 1509-1518. |
[4] | Xiong Chunbao,Hu Qianqian,Guo Ying. DYNAMIC RESPONSE OF SATURATED POROUS ELASTIC FOUNDATION UNDER POROSITY ANISOTROPY$^{\bf 1)}$ [J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(4): 1120-1130. |
[5] | Qiu Zhiping, Jiang Nan. COMPARATIVE STUDY OF STOCHASTIC AND INTERVAL NON-HOMOGENEOUS LINEAR HAMILTONIAN SYSTEMS AND THEIR APPLICATIONS 1) [J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(1): 60-72. |
[6] | Sun Jialiang,Tian Qiang,Hu Haiyan. ADVANCES IN DYNAMIC MODELING AND OPTIMIZATION OF FLEXIBLE MULTIBODY SYSTEMS1) [J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(6): 1565-1586. |
[7] | Yang Hongsheng, Li Yulong, Zhou Fenghua. THE PROPAGATION PROCESS AND THE GEOMETRIC DISPERSION OF A TRAPEZOIDAL STRESS PULSE IN AN ELASTIC ROD 1) [J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(6): 1820-1829. |
[8] | Tu Jiahuang, Tan Xiaoling, Yang Zhilong, Deng Xuhui, Guo Xiaogang, Zhang Ping. EFFECT OF WAKE INDUCED-VIBRATION RESPONSES OF A SQUARE CYLINDER BEHIND THE STATIONARY SQUARE CYLINDER 1) [J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(5): 1321-1335. |
[9] | He Yanli,Zhao Xiang. CLOSED-FORM SOLUTIONS FOR FORCED VIBRATIONS OF CURVED PIEZOELECTRIC ENERGY HARVESTERS BY MEANS OF GREEN'S FUNCTIONS 1) [J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(4): 1170-1179. |
[10] | Jiahuang Tu, Xiaoling Tan, Xuhui Deng, Xiaogang Guo, Jingqun Liang, Ping Zhang. STUDY OF FLOW-INDUCED MOTION CHARACTERISTICS OF THREE TANDEM CIRCULAR CYLINDERS IN PLANAR SHEAR FLOW1) [J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(3): 787-802. |
[11] |
Zheng Baojing, Liang Yu, Gao Xiaowei, Zhu Qianghua, Wu Zeyan.
ANALYSIS FOR DYNAMIC RESPONSE OF FUNCTIONALLY GRADED MATERIALS USING POD BASED REDUCED ORDER MODEL |
[12] | Zhou Chunxiao, Wang Ruiqiong, Nie Zhaokun, Li Gang, Zeng Yan. PROBABILISTIC MODELLING OF DYNAMIC RESPONSE OF UNDERWATER VEHICLE STRUCTURE VIA MAXIMUM ENTROPY METHOD [J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(1): 114-123. |
[13] | Ma Qiang, Zhou Fengxi, Liu Jie. ANALYSIS OF GROUND VIBRATION CONTROL BY GRADED WAVE IMPEDING BLOCK [J]. Chinese Journal of Theoretical and Applied Mechani, 2017, 49(6): 1360-1369. |
[14] | He Chao, Zhou Shunhua, Di Honggui, Xiao Junhua. A 2.5-D COUPLED FE-BE MODEL FOR THE DYNAMIC INTERACTION BETWEEN TUNNEL AND SATURATED SOIL [J]. Chinese Journal of Theoretical and Applied Mechani, 2017, 49(1): 126-136. |
[15] | Liu Fushou, Jin Dongping. EQUIVALENT CIRCULAR RING MODEL FOR THE RADIAL VIBRATION ANALYSIS OF HOOP TRUSS STRUCTURES [J]. Chinese Journal of Theoretical and Applied Mechani, 2016, 48(5): 1184-1191. |
Viewed | ||||||
Full text |
|
|||||
Abstract |
|
|||||