| 热黏弹性梁拟静态弯曲问题的解析分析 |
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| 引用本文： | 王松,李晶晶,张能辉. 热黏弹性梁拟静态弯曲问题的解析分析[J]. 力学季刊, 2011, 32(1) |
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| 作者姓名： | 王松 李晶晶 张能辉 |
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| 作者单位： | 上海市应用数学和力学研究所;上海大学理学院力学系; |
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| 基金项目： | 国家自然科学基金重大项目(90816001); 国家杰出青年基金(10725209); 上海市重点学科建设(S30106) |
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| 摘 要： | 基于平面应力假设和热黏弹性材料的积分型本构关系,建立了以位移分量为未知量的热黏弹性梁静动力学分析的二维数学模型。针对拟静态弯曲问题,首先,在Laplace变换域,引入位移势函数,将控制方程解耦;其次,根据给定的平面温度场和边界条件,采用分离变量法,引入热应力函数,得到了热黏弹性梁的热应力分布;最后,利用Laplace逆变换,获得了热黏弹性梁拟静态弯曲热应力响应的解析解,考察了热载荷作用下几何、黏弹性等参数对梁应力和位移的影响。
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| 关 键 词： | 热黏弹性梁 拟静态弯曲 Laplace变换法 解析解 |
Analytical Analysis for Quasi-static Bending Problem of Thermo-viscoelastic Beam |
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| WANG Song,LI Jing-jing,ZHANG Neng-hui. Analytical Analysis for Quasi-static Bending Problem of Thermo-viscoelastic Beam[J]. Chinese Quarterly Mechanics, 2011, 32(1) |
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| Authors: | WANG Song LI Jing-jing ZHANG Neng-hui |
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| Affiliation: | WANG Song1,LI Jing-jing1,2,ZHANG Neng-hui1,2(1.Shanghai Institute of Applied Mathematics and Mechanics,Shanghai 200072,China,2.Department of Mechanics,College of Sciences,Shanghai University,Shanghai 200444,China) |
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| Abstract: | The two-dimensional mathematical model of static/dynamic analysis of a thermo-viscoelastic beam with displacement components as unknown variables was established based on the plane stress hypothesis and thermo-viscoelastic integral constitutive relationship.For quasi-static bending problems,the governing equations were decoupled by introducing displacement functions in Laplace transformation domain.The thermal stress distributions of the thermo-viscoelastic beam were obtained by using the method of separati... |
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| Keywords: | thermo-viscoelastic beam quasi-static bending Laplace transformation method analytical solution |
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