On the Thermoelasticity of Non—Linear Discrete and Continuous Constrained Systems

  • Cz. Wozniak
Part of the International Centre for Mechanical Sciences book series (CISM, volume 223)


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.


Heat Flux Discrete Model Material System Stress Vector Deformation Function 
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Copyright information

© Springer-Verlag Wien 1977

Authors and Affiliations

  • Cz. Wozniak
    • 1
  1. 1.WarszawaPoland

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