توابع پتانسيل براي مسايل ترموالاستوديناميك در محيط همسانگرد جانبي

THERMOELASTODYNAMIC BOUNDARY VALUE PROBLEMS IN TRANSVERSELY ISOTROPIC MATERIAL WITH POTENTIAL FUNCTIONS

با استفاده از يك روش سيستماتيك، توابع پتانسيل كامل براي حل مسايل ترموالاستوديناميك در محيط ارايه مي شود. اين توابع پتانسيل براي جداسازي معادلات ديفرانسيل كوپل شده تغييرمكان - درجه حرارت برگرفته از معادلات حركت و قانون اول ترموديناميك حاكم بر محيط به كار مي روند. توابع پتانسيل، شامل دو تابع اسكالر مي باشند كه يكي از آن ها معادله ديفرانسيل جزيي از مرتبه شش و ديگري معادله ديفرانسيل جزيي از مرتبه دو را ارضا مي كند. در مورد هم ارز بودن و غيريكتا بودن توابع پتانسيل بحث شده و دو مورد ديگر از توابع پتانسيل غيريكتا ذكر مي شود.

An open region in Euclidean space containing thermoelastic transversely isotropic material is considered, wherein the axes of material symmetry from both mechanical and thermal points of view are identical. The coupled equations of motion and energy equation are considered as governing equations for the problem involved in this paper. The governing equations are a system of partial differential equations that cannot be analytically solved using classical methods. The related boundary value problem may be solved, either with completely numerical methods such as finite element methods, or with semi numerical methods such as the boundary element method. In the latter case, the related Greenʹs functions are needed, which may be determined by solving the governing equations analytically. To do so, the system of partial differential equations governing the boundary value problems should be transformed into some separated partial differential equations. The method of potential functions is the best way to catch the separated partial differential equations. In this paper, based on a systematic method, a set of potential functions is introduced, which transforms the system of coupled partial differential equations into two separated equations. The order of the governing partial differential equations for one of the potential functions is six, and for the other is two. The uniqueness and non-uniqueness of the proposed potential functions are discussed and based on the non-uniqueness rule of the potential functions; two other sets for the potential functions are also introduced. In addition, the two dimensional case of the problem is discussed separately and the related potential functions are introduced. Applications of the results of this paper are seen if one determines the displacements and the temperature Greenʹs function for the related initial boundary value problems, which, themselves, may be used in transient boundary element methods.