Time-domain finite element method to generalized diffusion-elasticity problems with the concentration-dependent elastic constants and the diffusivity |
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| Affiliation: | 1. School of Civil Engineering, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, P.R. China;2. State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi''an Jiaotong University, Xi''an 710049, Shaanxi, P.R. China;3. School of Science, Lanzhou University of Technology, Lanzhou 730050, Gansu, P.R. China;1. Department of Computational Mathematics, Oles Honchar Dnipro National University, Gagarin Av., 72, Dnipro 49010, Ukraine;2. Department of Theoretical and Computational Mechanics, Oles Honchar Dnipro National University, Gagarin Av., 72, Dnipro 49010, Ukraine;3. Université Clermont Auvergne, CNRS, SIGMA Clermont (ex- French Institute of Advanced Mechanics), Institut Pascal, Campus de Clermont-Ferrand, 63178 Aubière, France;1. Instituto Tecnológico de Aeronáutica, 12228-900 São José dos Campos, SP, Brazil;2. Diretoria de Infraestrutura da Aeronáutica, 01552-000 São Paulo, SP, Brazil;1. College of Computer Science and Artificial Intelligence, Wenzhou University, Wenzhou, Zhejiang, 325035, China;2. School of Surveying and Geospatial Engineering, College of Engineering, University of Tehran, Tehran, Iran;3. Department of Computer Science, School of Computing, National University of Singapore, Singapore, Singapore;4. Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam;1. Department of Engineering, University of Messina, Villaggio S. Agata, 98166 Messina, Italy;2. Department of Civil, Energy, Environmental and Materials Engineering (DICEAM), University of Reggio Calabria, Via Graziella, 89124 Reggio Calabria, Italy;1. Department of Computer Science and Artificial Intelligence, Wenzhou University, Wenzhou 325035, China;2. School of Surveying and Geospatial Engineering, College of Engineering, University of Tehran, Tehran, Iran;3. Department of Computer Science, School of Computing, National University of Singapore, Singapore |
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| Abstract: | The investigations of mechanical-diffusion coupling are of great importance for the micro-electromechanical devices under non-uniform concentration environment, especially with the development of energy storage technology for a rapid charging system. In recent years there have been many experimental and theoretical studies show that the elastic constants and the diffusivity depend on the concentration of diffusing substances. In view of this, present work aims to study generalized diffusion-elasticity problems considering the concentration-dependent elastic constants and the diffusivity by time-domain finite element method. By using principle of virtual work, the obtained nonlinear finite element equations are solved directly in time domain to minimize precision losses in the application of integrated transformation method, and then the nonlinear solutions can be obtained. As numerical examples, the developed method is used to investigate the transient response of a thick circular plate subjected to the shock loading of the concentration. The results demonstrate that the developed method can faithfully predict the deformation of structure and most importantly the diffusive wave feature in both one-/two-dimensional solids whilst it is commonly difficult to model, especially for two-dimensional case, by using transform method. Parametric studies are performed to evaluate and discuss the effects of concentration-dependent elastic constants and diffusivity on the structural dynamic responses. |
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