| 辛体系下平面热黏弹性圣维南问题的解析解 |
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| 引用本文： | 张维祥,徐新生,王尕平.辛体系下平面热黏弹性圣维南问题的解析解[J].力学与实践,2008,30(4):76-78. |
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| 作者姓名： | 张维祥 徐新生 王尕平 |
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| 作者单位： | 大连理工大学力学系 |
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| 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.
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| 关 键 词： | 辛体系 热粘弹性 本征值 本征解 |
| 收稿时间： | 2007-5-8 |
| 修稿时间： | 2007-8-21 |
ANALYTICAL SOLUTION OF SAINT-VENANT PROBLEM FOR THERMO-VISCOELASTICITY IN THE SYMPLECTIC SYSTEM |
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| ZHANG Weixiang,XU Xinsheng,WANG Gaping.ANALYTICAL SOLUTION OF SAINT-VENANT PROBLEM FOR THERMO-VISCOELASTICITY IN THE SYMPLECTIC SYSTEM[J].Mechanics and Engineering,2008,30(4):76-78. |
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| Authors: | ZHANG Weixiang XU Xinsheng WANG Gaping |
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| Abstract: | 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. |
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| Keywords: | symplectic system thermo-viscoelasticity eigenvalue eigensolution |
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