عنوان پایان‌نامه
توابع پتانسیل کامل مسائل ترموالاستودینامیک در محیط ایزوتروپ جانبی
- رشته تحصیلی
- مهندسی عمران - سازه
- مقطع تحصیلی
- کارشناسی ارشد
- محل دفاع
- کتابخانه پردیس یک فنی شماره ثبت: 1341;کتابخانه مرکزی -تالار اطلاع رسانی شماره ثبت: 43741
- تاریخ دفاع
- ۱۱ مهر ۱۳۸۸
- دانشجو
- میثم فراتی
- استاد راهنما
- محمد رحیمیان
- چکیده
- ندارد
- Abstract
- A linear thermoelastic transversely isotropic material in the sense of Green is considered. A complete solution in terms of three potential functions for the coupled displacement-temperature equations of motion and heat equation in transversely isotropic media is presented. The completeness theorem is proved based on retarded Logarithmic potential function, retarded Newtonian potential function, repeated wave equation, the extended Boggio's theorem for the transversely isotropic axially convex domain, the solution of the heat equation and perturbation theory. The number of potential functions is reduced to only one, and the required conditions for this case are discussed. As a special case, the torsionless and rotationally symmetric configuration with respect to the axis of symmetry of the material is discussed. The limiting case of elastodynamics is cited, where the solution for the equations of motion is reduced to the solution given in the literature. In the present paper, thermoelastodynamics in the material possesses an axis which is axis of both elastic and thermal symmetry, transversely isotropy [Eubank and Sternberg, 1954, and Gurtin, 1972, sect. 27] has received attention, and it is the purpose of this paper to present a complete solution for the thermoelastodynamics in transversely isotropic hyperelastic materials in terms of three potential functions satisfying sixth-order and second-order partial differential equations. The solution is reduced to Eskandari-Ghadi solution if an elastodynamic problem is in interest. After the introduction of a solution in terms of a potential function, the immediate concern is to answer to the question related to completeness. The literature includes several studies of completeness of the solutions of linear elastostatics problems in the isotropic material in terms of potential functions, many of which are due to Eubanks and Sternberg [1954], Sternberg and Gurtin [1962], Gurtin [1962] and Stippes [1959]. Additional references have been cited in Truesdell [1995]. This paper deals with the potential function approach, however, the integral transform approach is a commonly used approach in the literature [Sneddon, 1951, 1972]. Burridge [1967] presented Green’s function for the plane wave equation in the form of a Herglotz-Petrowski formula, and investigated different singularities of the Green’s function in detail. In Duffy [2001], the Green's function for heat equation has been given by using Laplace transform. Rajapakse and Wang [1993], by using special potential functions, leaving its completeness unproved, found Green’s functions for a half-space of a transversely isotropic material. Since, their potential functions could not completely uncouple the system of equations of motion; they had to use the integral transform method, as well, to determine the displacement fields. At the end of the paper, we have a brief discussion to compare the approach of this paper with the integral transform approach. As noted by Biot [1956] and mentioned by Verruijt [1967], the theory of thermoelasticity is mathematically analogous to the deformation theory of a fluid-saturated porous elastic material, which is often denoted by the theory of consolidation of porous media. The major difference between the thermoelastodynamics and consolidation of porous media is that in the former theory the displacement-temperature equations of motion are dominant the heat equation, while in the problems of consolidation the usual magnitude of the material constants results in the equation governing the pore water pressure dominants the equations of motion [Verruijt, 1967].
