Comment on Y.-H. Hsu et al., "Electrical and mechanical fully coupled theory and experimental verification of rosen-type piezoelectric transformers"

2007 ◽  
Vol 54 (4) ◽  
pp. 699-700 ◽  
Author(s):  
Jiashi Yang
Keyword(s):  
Experimental Verification ◽  
Piezoelectric Transformers ◽  
Fully Coupled ◽  
Coupled Theory

Linear thermoelasticity

2020 ◽  
pp. 257-285
Author(s):  
Lallit Anand ◽  
Sanjay Govindjee
Keyword(s):  
Linear Theory ◽  
Mechanical Response ◽  
Thermal Response ◽  
Engineering Applications ◽  
Temperature Changes ◽  
Weakly Coupled ◽  
Linear Thermoelasticity ◽  
Basic Equations ◽  
Fully Coupled ◽  
Coupled Theory

This chapter presents a theory for the coupled thermal and mechanical response of solids under circumstances in which the deformations are small and elastic, and the temperature changes from a reference temperature are small --- a framework known as the theory of linear thermoelasticity. The basic equations of the fully-coupled linear theory of anisotropic thermoelasticity are derived. These equations are then specialized for the case of isotropic materials. Finally, as a further specialization a weakly-coupled theory in which the temperature affects the mechanical response, but the deformation does not affect the thermal response, are discussed; this is a specialization which is of importance for many engineering applications, a few of which are illustrated in the examples.

Small deformation theory of species diffusion coupled to elasticity

2020 ◽  
pp. 286-298
Author(s):  
Lallit Anand ◽  
Sanjay Govindjee
Keyword(s):  
Linear Theory ◽  
Chemical Potential ◽  
Chemical Species ◽  
Small Deformation ◽  
Species Concentration ◽  
Species Transport ◽  
Reference Concentration ◽  
Basic Equations ◽  
Fully Coupled ◽  
Coupled Theory

This chapter presents a coupled theory for transport of a single atomic (or molecular) chemical species through a solid that deforms elastically. Consideration is limited to isothermal conditions and circumstances in which the deformations are small and elastic, and the changes in species concentration from a reference concentration are small --- a framework known as the theory of linear chemoelasticity. Underlying the presented approach is the notion that the solid can deform elastically but it retains its connectivity and does not itself diffuse. To account for the energy flow due to species transport, the notion of chemical potential of the species is introduced. First the basic equations of the fully-coupled linear theory of anisotropic linear chemoelasticity are derived, and then these equations are specialized for the case of isotropic materials.

A Finite Element Implementation of a Fully Coupled Mechanical–Chemical Theory

2017 ◽  
Vol 09 (03) ◽  
pp. 1750040 ◽  
Author(s):  
Jianyong Chen ◽  
Hailong Wang ◽  
Pengfei Yu ◽  
Shengping Shen
Keyword(s):  
Finite Element ◽  
Irreversible Thermodynamics ◽  
Mass Diffusion ◽  
Chemical Processes ◽  
Gibbs Function ◽  
Finite Element Implementation ◽  
Chemical Theory ◽  
Fully Coupled ◽  
Finite Element Formulations ◽  
Coupled Theory

A finite element implementation with UEL user-defined element (UEL) subroutines in ABAQUS for fully coupled mechanical–chemical processes, which accounts for deformation, mass diffusion, and chemical reactions based on irreversible thermodynamics, is presented. The finite element formulations are deduced from the Gibbs function variational principle. To demonstrate the robustness of the numerical implementation, one- and two-dimensional numerical simulations with different boundary conditions are conducted. The results present the validity and capability of the UEL subroutines and the coupled theory, and show the interaction among deformation, mass diffusion and chemical reaction. This work provides a valuable tool to the researchers for the study of coupled problems.

Dynamic Thermoelastic Response of Cylindrical Shells

1970 ◽  
Vol 37 (3) ◽  
pp. 661-670 ◽  
Author(s):  
E. J. McQuillen ◽  
M. A. Brull
Keyword(s):  
Shell Theory ◽  
Cylindrical Shells ◽  
Infinite Length ◽  
Dynamic Effects ◽  
Thermoelastic Response ◽  
Shell Equations ◽  
Thermoelastic Problems ◽  
Thin Shell Theory ◽  
Fully Coupled ◽  
Coupled Theory

The dynamic, thermoelastic response of cylindrical shells to suddenly applied and rotating thermal inputs is investigated. Fully coupled, dynamic, thermoelastic cylindrical shell equations are derived using Galerkin’s method. Identical results were obtained independently using a variational theorem. Analytical solutions to these equations are formulated for finite-length and infinite-length cylinders. Numerical results for the response of infinite-length cylindrical shells to suddenly applied and rotating longitudinal lines of heat flux are presented. It is shown that for many thermoelastic problems involving moving thermal inputs that the maximum ratio of dynamic to quasi-static deflection can be much greater than two, that dynamic effects can be important for all thicknesses within the realm of thin shell theory, and that semicoupled theory gives incorrect results in some cases for which a fully coupled theory is required.

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