On the Thermoelasticity of Non—Linear Discrete and Continuous Constrained Systems
In the note equations of thermoelasticity of discrete and continuous systems are derived with the aid of the concept of ideal constraints imposed on mechanical as well as non-mechanical quantities. The thermoelastic systems are obtained as models of a certain material system M, in which a set of non-intersecting finite elements is distinguished. We assume that any typical element of M undergoes only homogeneous deformations and linear distributions of temperature; the concept of ideal constraints is applied to derive basic equations of thermoelasticity for this element. The constraints are also introduced to describe the interactions among elements: the stress vector and the heat flux on the corresponding boundaries of interacting elements are assumed to be continuous. The equations of the discrete thermoelastic system are obtained under condition that the pairs of interacting elements form a lattice in RN, 0 < N ≤ 3. The N-th dimensional thermoelastic continuum is derived from the suitable discrete system, provided that elements of M are sufficiently small and that certain regularity conditions hold.
KeywordsHeat Flux Discrete Model Material System Stress Vector Deformation Function
Unable to display preview. Download preview PDF.
- А.А. САМАРСКИЙ, Введение в теорию разностных схем, изд. “Наука”, Москва, 1971.Google Scholar
- C. TRUESDELL, W. NOLL, The Non-Linear Field Theories of Mechanics Handbuch der Physik, III/3, Springer-Verlag 1965.Google Scholar
- Cz. WOZNIAK, On the problem of constraints for deformations and stresses in continuum mechanics, Bull. Acad. Polon. Sci., ser. sci. techn., 1975.Google Scholar
- Cz. WOSNIAK, On the relations between discrete and continuum mechanics, Arch. Mech. Stos., Warszawa, 1976.Google Scholar