| Abstract: | In some investigations on variational principle for coupled thermoelastic problems, the free energy Φ(eij,θ) ,where the state variables are elastic strain eij and temperature increment θ, is expressed as Φ(eij,θ)=λ/2ekkeij=uek1ek1-γekkθ-c/2 p θ2/T0(0.1) This expression is employed only under the condition of |θ|≤T0(absolute temperature of reference) But the value of temperature increment is great, even greater than T0 in thermal shock. And the material properties (λ ,μ ,ν ,c , etc.) will not remain constant, they vary with θ. The expression of free energy for this condition.is derived in this paper. Equation (0.1) is its special case.Euler’s equations will be nonlinear while this expression of free energy has been introduced into variational theorem. In order to linearise, the time interval of thermal shock is divided into a number of time elements Δtk, (Δtk=tk-tk-1,k=1,2…,n), which are so small that the temperature increment θk within it is very small, too. Thus, the material properties may be defined by temperature field Tk-1=T(x1,x2,x3,tk-1) at instant tk-1 , and the free energy Φk expressed by eg. (0.1) may be employed in element Δtk.Hence the variational theorem will be expressed partly and approximately. |
