Three-Dimensional Fundamental Solution for Transversely Isotropic Electro-Magneto-Thermo-Elastic Materials

2009 ◽  
Vol 32 (9) ◽  
pp. 887-904 ◽  
Author(s):  
Peng-Fei Hou ◽  
Hao-Ran Chen ◽  
Sha He
Keyword(s):  
Fundamental Solution ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Elastic Materials

scholarly journals Recent developments in the evaluation of the 3D fundamental solution and its derivatives for transversely isotropic elastic materials

2012 ◽  
Vol 10 (1) ◽  
Author(s):  
V. Mantič ◽  
L. Távara ◽  
J.E. Ortiz ◽  
F. París
Keyword(s):  
Fundamental Solution ◽  
Rotational Symmetry ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Real Variable ◽  
Radius Vector ◽  
Linear Elastic ◽  
Plane Normal ◽  
Starting Point ◽  
Recent Developments

<p class="p1">Explicit closed-form real-variable expressions of a fundamental solution and its derivatives for three-dimensional problems in transversely linear elastic isotropic solids are presented. The expressions of the fundamental solution in displacements <span class="s1">U</span><span class="s2">ik </span>and its derivatives, originated by a unit point force, are valid for any combination of material properties and for any orientation of the radius vector between the source and field points. An ex- pression of <span class="s1">U</span><span class="s2">ik </span>in terms of the Stroh eigenvalues on the oblique plane normal to the radius vector is used as starting point. Working from this expression of <span class="s1">U</span><span class="s2">ik</span>, a new approach (based on the application of the rotational symmetry of the material) for deducing the first and second order derivative kernels, <span class="s1">U</span><span class="s2">ik,j </span>and <span class="s1">U</span><span class="s2">ik,jl </span>respectively, has been developed. The expressions of the fundamental solution and its derivatives do not suffer from the difficulties of some previous expressions, obtained by other authors in different ways, with complex valued functions appearing for some combinations of material parameters and/or with division by zero for the radius vector at the rotational symmetry axis. The expressions of <span class="s1">U</span><span class="s2">ik</span>, <span class="s1">U</span><span class="s2">ik,j </span>and <span class="s1">U</span><span class="s2">ik,jl </span>are presented in a form suitable for an efficient computational implementation in BEM codes.</p>

scholarly journals Stress field formulation of linear electro-magneto-elastic materials

2019 ◽  
Vol 24 (12) ◽  
pp. 3806-3822
Author(s):  
A Amiri-Hezaveh ◽  
P Karimi ◽  
M Ostoja-Starzewski
Keyword(s):  
Equations Of Motion ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Governing Equations ◽  
Field Equations ◽  
Elastic Solids ◽  
Elastic Materials ◽  
Transversely Isotropic Media ◽  
Isotropic Media ◽  
Sufficient Set

A stress-based approach to the analysis of linear electro-magneto-elastic materials is proposed. Firstly, field equations for linear electro-magneto-elastic solids are given in detail. Next, as a counterpart of coupled governing equations in terms of the displacement field, generalized stress equations of motion for the analysis of three-dimensional (3D) problems Are obtained – they supply a more convenient basis when mechanical boundary conditions are entirely tractions. Then, a sufficient set of conditions for the corresponding solution of generalized stress equations of motion to be unique are detailed in a uniqueness theorem. A numerical passage to obtain the solution of such equations is then given by generalizing a reciprocity theorem in terms of stress for such materials. Finally, as particular cases of the general 3D form, the stress equations of motion for planar problems (plane strain and Generalized plane stress) for transversely isotropic media are formulated.

scholarly journals Unified analytical expressions of the three-dimensional fundamental solutions and their derivatives for linear elastic anisotropic materials

2016 ◽  
Vol 472 (2186) ◽  
pp. 20150272 ◽  
Author(s):  
Longtao Xie ◽  
Chuanzeng Zhang ◽  
Jan Sladek ◽  
Vladimir Sladek
Keyword(s):  
Three Dimensional ◽  
Transversely Isotropic ◽  
Fundamental Solutions ◽  
Higher Order ◽  
The Novel ◽  
Elastic Materials ◽  
Linear Elastic ◽  
Second Derivatives ◽  
Analytical Expressions ◽  
Derivatives Of

Novel unified analytical displacement and stress fundamental solutions as well as the higher order derivatives of the displacement fundamental solutions for three-dimensional, generally anisotropic and linear elastic materials are presented in this paper. Adequate integral expressions for the displacement and stress fundamental solutions as well as the higher order derivatives of the displacement fundamental solutions are evaluated analytically by using the Cauchy residue theorem. The resulting explicit displacement fundamental solutions and their first and second derivatives are recast into convenient analytical forms which are valid for non-degenerate, partially degenerate, fully degenerate and nearly degenerate cases. The correctness and the accuracy of the novel unified and closed-form three-dimensional anisotropic fundamental solutions are verified by using some available analytical expressions for both transversely isotropic (non-degenerate or partially degenerate) and isotropic (fully degenerate) linear elastic materials.

scholarly journals Three-dimensional fundamental solution in transversely isotropic thermoelastic diffusion material

2012 ◽  
Vol 39 (2) ◽  
pp. 165-184 ◽  
Author(s):  
Rajneesh Kumar ◽  
Vijay Chawla
Keyword(s):  
Fundamental Solution ◽  
Transverse Isotropy ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Fundamental Solutions ◽  
Thermoelastic Diffusion ◽  
Diffusion Media ◽  
Stress Components ◽  
Steady State Problem ◽  
Special Case

The aim of the present investigation is to study the fundamental solution for three dimensional problem in transversely isotropic thermoelastic diffusion medium. After applying the dimensionless quantities, two displacement functions are introduced to simplify the basic threedimensional equations of thermoelastic diffusion with transverse isotropy for the steady state problem. Using the operator theory, we have derived the general expression for components of displacement, mass concentration, temperature distribution and stress components. On the basis of general solution, three dimensional fundamental solutions for a point heat source in an infinite thermoelastic diffusion media is obtained by introducing four new harmonic functions. From the present investigation, a special case of interest is also deduced to depict the effect of diffusion.

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