THE ISOHERMAL PRINCIPLE OF VIRTUAL WORK FOR AN ELASTIC SOLID

Abstract

The aim of the research is the derivation of the isothermal principle of virtual work for an elastic solid. Methodology. By an elastic solid we mean a mathematical model of a continuous medium, in which the specific density of free energy is a function of only temperature and derivatives of displacement vectors. In the framework of equilibrium thermodynamics, the isothermal principle of virtual work for an elastic solid is obtained. Results. The isothermal principle of virtual work for an elastic solid is derived. The conditions for mechanical equilibrium inside and on the surface of an elastic solid are obtained. Research implications. For a given function of the specific density of free energy and the known value of the temperature, it is possible to determine the dependence of the displacement functions on the coordinates that characterize the deformed state of the considered elastic solid.

Keywords

• elastic solid
• virtual work
• virtual displacement
• Lagrangian variation
• free energy density
• Gibbs relation