ANALYTICAL SOLUTION OF SAINT-VENANT PROBLEM FOR THERMO-VISCOELASTICITY IN THE SYMPLECTIC SYSTEM
辛体系下平面热黏弹性圣维南问题的解析解

With the aid of the integral transformation, the symplectic system is introduced into the problem of two-dimensional thermo-viscoelasticity and the dual equations of the fundamental problem are constructed. All solutions of Saint-Venant problems can be obtained directly via zero eigenvalue eigensolutions, which satisfy the conjugated relationships of the symplectic orthogonality. Meanwhile, an effective method for boundary problems is provided by the technologies of variable substitution and eigensolution expansion. Numerical examples show that the symplectic method is effective for some typical boundary problems with creep and relaxation characteristics of thermo-viscoelasticity.