| 定常温度热弹性梁的精化理论 |
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| 引用本文： | 高阳,王敏中.定常温度热弹性梁的精化理论[J].工程力学,2006,23(2):34-40. |
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| 作者姓名： | 高阳 王敏中 |
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| 作者单位： | 1. 中国农业大学理学院,北京,100083;北京大学湍流与复杂系统国家重点实验室,力学与工程科学系,北京,100871
2. 北京大学湍流与复杂系统国家重点实验室,力学与工程科学系,北京,100871 |
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| 摘 要： | 首先给出了定常温度热弹性Biot通解的一种新的简化形式,它看起来与各向同性弹性力学的Papkovich-Neuber通解十分相似。不作预先假设,从热弹性理论出发,利用Biot通解和Lur’e算子方法构造了梁的精化理论,得出了自由表面热弹性梁的三个精确方程:四阶方程、超越方程和温度方程。由一般的各向同性弹性梁推广到热弹性梁,导出了在反对称载荷和介质温度作用下热弹性梁的近似控制微分方程。
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| 关 键 词： | 热弹性 控制方程 精化理论 矩形直梁 弹性通解 |
| 文章编号： | 1000-4750（2006）02-0034-07 |
| 收稿时间： | 2004-01-11 |
| 修稿时间： | 2004-01-112004-04-16 |
A REFINED THEORY OF THERMOELASTIC BEAMS UNDER STEADY TEMPERATURE |
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| GAO Yang,WANG Min-zhong.A REFINED THEORY OF THERMOELASTIC BEAMS UNDER STEADY TEMPERATURE[J].Engineering Mechanics,2006,23(2):34-40. |
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| Authors: | GAO Yang WANG Min-zhong |
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| Affiliation: | 1. College of Science, China Agricultural University, Bcijing 100083, China; 2. State Key Laboratory for Turbulence and Complex Systems and Department of Mechanics and Engineering Science, Peking University, Beijing 100871, China |
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| Abstract: | A new simplified form of Biot’s thermoelasticity solution is presented under steady temperature,and it looks like Papkovich-Neuber’s isotropic elasticity solution.Based on thermoelasticity theory,the refined beam theory is derived using Biot’s solution and Lur’e method without ad hoc assumptions.For homogeneous boundary conditions,the thermoelastic beam equations consist of three exact equations: the four-order equation,the transcendental equation and the temperature equation.Generalized from isotropic elastic beam problems,thermoelastic beam problems are focused.Approximate beam equations under anti-symmetrical transverse loadings and temperature distribution are derived. |
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| Keywords: | thermoelasticity governing equation refined theory rectangular beam elastic general solution |
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