Nonlocal thermoelastic analysis of a functionally graded material microbeam

• Published in: Applied mathematics and mechanics Vol. 42; no. 6; pp. 855 - 870
• Main Authors: Peng, Wei, Chen, Like, He, Tianhu
• Format: Journal Article
• Language: English
• Published: Shanghai Shanghai University 01.06.2021; Springer Nature B.V; School of Science,Lanzhou University of Technology,Lanzhou 730050,China; Key Laboratory of Disaster Prevention and Mitigation in Civil Engineering of Gansu Province,Lanzhou University of Technology,Lanzhou 730050,China%School of Civil Engineering and Mechanics,Lanzhou University,Lanzhou 730000,China%Key Laboratory of Disaster Prevention and Mitigation in Civil Engineering of Gansu Province,Lanzhou University of Technology,Lanzhou 730050,China
• Edition: English ed.
• Subjects: Applications of Mathematics; Classical Mechanics; Conduction heating; Conductive heat transfer; Fluid- and Aerodynamics; Functionally gradient materials; Laplace transforms; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Microbeams; Parameters; Partial Differential Equations; Shock resistance; Thermal resistance; Thermal shock; Transient response; size-dependent microbeam; 74F05; ramp-type heating; nonlocal thermoelastic theory; dynamic response; O343.6; functionally graded material (FGM)
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-021-2742-9

In extreme heat transfer environments, functionally graded materials (FGMs) have aroused great concern due to the excellent thermal shock resistance. With the development of micro-scale devices, the size-dependent effect has become an important issue. However, the classical continuum mechanical model fails on the micro-scale due to the influence of the size-dependent effect. Meanwhile, for thermoelastic behaviors limited to small-scale problems, Fourier’s heat conduction law cannot explain the thermal wave effect. In order to capture the size-dependent effect and the thermal wave effect, the nonlocal generalized thermoelastic theory for the formulation of an FGM microbeam is adopted in the present work. For numerical validation, the transient responses for a simply supported FGM microbeam heated by the ramp-type heating are considered. The governing equations are formulated and solved by employing the Laplace transform techniques. In the numerical results, the effects of the ramp-heating time parameter, the nonlocal parameter, and the power-law index on the considered physical quantities are presented and discussed in detail.