Solutions of BVPs in the fully coupled theory of elasticity for the space with double porosity and spherical cavity

2015 ◽  
Vol 39 (8) ◽  
pp. 2136-2145 ◽  
Author(s):  
Lamara Bitsadze ◽  
I. Tsagareli
Keyword(s):  
Spherical Cavity ◽  
Double Porosity ◽  
Theory Of Elasticity ◽  
Fully Coupled ◽  
Coupled Theory

scholarly journals Explicit Solutions of the Boundary Value Problems for an Ellipse with Double Porosity

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Lamara Bitsadze ◽  
Natela Zirakashvili
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Convergent Series ◽  
Double Porosity ◽  
Theory Of Elasticity ◽  
Classical Elasticity ◽  
Dimensional Boundary ◽  
Uniformly Convergent ◽  
Isotropic Bodies ◽  
Fully Coupled

The basic two-dimensional boundary value problems of the fully coupled linear equilibrium theory of elasticity for solids with double porosity structure are reduced to the solvability of two types of a problem. The first one is the BVPs for the equations of classical elasticity of isotropic bodies, and the other is the BVPs for the equations of pore and fissure fluid pressures. The solutions of these equations are presented by means of elementary (harmonic, metaharmonic, and biharmonic) functions. On the basis of the gained results, we constructed an explicit solution of some basic BVPs for an ellipse in the form of absolutely uniformly convergent series.

Axisymmetric Thermal Stresses in a Spherical Shell of Arbitrary Thickness

1957 ◽  
Vol 24 (3) ◽  
pp. 376-380
Author(s):  
E. L. McDowell ◽  
E. Sternberg
Keyword(s):  
Steady State ◽  
Spherical Shell ◽  
Spherical Cavity ◽  
Series Solution ◽  
Thermal Stresses ◽  
Solid Sphere ◽  
Theory Of Elasticity ◽  
Infinite Medium ◽  
Series Solutions ◽  
Arbitrary Thickness

Abstract This paper contains an explicit series solution, exact within the classical theory of elasticity, for the steady-state thermal stresses and displacements induced in a spherical shell by an arbitrary axisymmetric distribution of surface temperatures. The corresponding solutions for a solid sphere and for a spherical cavity in an infinite medium are obtained as limiting cases. The convergence of the series solutions obtained is discussed. Numerical results are presented appropriate to a solid sphere if two hemispherical caps of its boundary are maintained at distinct uniform temperatures.

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.

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