辛体系下平面热黏弹性圣维南问题的解析解  

ANALYTICAL SOLUTION OF SAINT-VENANT PROBLEM FOR THERMO-VISCOELASTICITY IN THE SYMPLECTIC SYSTEM

作　　者：张维祥[1] 徐新生[2] 王尕平[2] 

机构地区：[1]河南工业大学土木建筑学院,郑州450052 [2]大连理工大学工业装备结构分析国家重点实验室,大连116024

出　　处：《力学与实践》2008年第4期76-78,38,共4页Mechanics in Engineering

基　　金：国家自然科学基金(10272024)．

摘　　要：借助积分变换,将辛体系引入平面热黏弹性问题,建立了基本问题的对偶方程,并将全部圣维南问题归结为满足共轭辛正交关系的零本征值本征解问题.同时,利用变量代换和本征解展开等技术给出了一套求解边界条件问题的具体方法.算例讨论了几种典型边界条件问题,描述了热黏弹性材料的蠕变和松弛特征,体现了这种辛方法的有效性.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.

关 键 词：辛体系 热黏弹性 本征值 本征解 

分 类 号：O343.8[理学—固体力学] V232.1[理学—力学]