功能梯度球壳热屈曲问题研究

发布时间：2018-06-04 09:28

本文选题：功能梯度材料 + 薄球壳　；参考：《太原科技大学》2017年硕士论文

【摘要】：近年来,随着高新技术领域快速发展,对材料的要求越来越高,功能梯度材料特别适用于材料两侧温差较大的环境,其耐热性、再用性和可靠性是以往使用的陶瓷基复合材料无法比拟的。功能梯度材料采用先进的材料复合技术,通过金属、陶瓷、塑料等材料的巧妙组合,使材料的性质和功能沿厚度方向呈梯度变化的一种新型复合材料。因其优异的的力学性能和新颖的设计的思想被广泛的运用在航天、医学、电磁、核工程、光学等领域。板壳结构在各行各业有着广泛的应用,结构的稳定性问题是实际工程应用中需要解决的问题之一。怎样准确的预测到板壳结构发生屈曲时的临界点,一直是现在科研人员需要突破的难题之一。尤其是热屈曲问题,需要同时准确得到临界压力和临界温度。由于功能梯度材料大多运用在高新技术领域,对结构的热稳定性的准确性要求更高。所以对功能梯度材料板壳热屈曲的研究显得非常的重要。本文研究了功能梯度材料薄球壳在线性和非线性情况下的热屈曲问题,为功能梯度材料薄球壳在工程实际运用中提供有价值的参考。1,本文在各向同性完备的非线性热本构方程的基础上,通过christoffel符号表示基矢量对坐标的导数,推导出功能梯度薄球壳在球坐标系下的热本构方程。2,用张量方法推导得到了轴对称球壳稳定性方程。将热本构方程应用到球壳稳定性方程中,得到以位移表示的球壳热屈曲方程组。3,在线性的情况下,分别考虑均布外压和温度作用下,采用伽辽金法和里兹法研究了简支球壳的热屈曲问题。分析了薄球壳厚度和物性参数变化引起的临界压力变化趋势和临界温度的变化趋势。4,在非线性的情况下,应用里兹法分析了简支半球的热屈曲问题。研究了(1)在不同外压温度(没有达到临界温度)作用下,临界压力和厚度的关系;(2)在不同厚度下,临界压力与温度的关系;(3)在不同外压载荷(没有达到临界压力)作用下,临界温度与厚度的关系。
[Abstract]:In recent years, with the rapid development of the field of high and new technology, the demand for materials is becoming higher and higher. FGM is especially suitable for the environment with large temperature difference on both sides of the material, and its heat resistance. The reusability and reliability are unparalleled by the ceramic matrix composites used in the past. The functionally graded material (FGM) is a new kind of composite material, whose properties and functions change along the thickness direction through the clever combination of metal, ceramic, plastic and so on. Because of its excellent mechanical properties and novel design ideas, it has been widely used in aerospace, medicine, electromagnetic, nuclear engineering, optics and other fields. Plate and shell structures are widely used in various industries, and the stability of structures is one of the problems to be solved in practical engineering applications. How to accurately predict the critical point of buckling of plate and shell structure has always been one of the difficult problems that the researchers need to break through. Especially for thermal buckling problem, critical pressure and critical temperature must be accurately obtained simultaneously. As functionally gradient materials are mostly used in high-tech fields, the accuracy of thermal stability of structures is higher. Therefore, it is very important to study the thermal buckling of functionally graded materials (FGM) plates and shells. In this paper, the thermal buckling of thin spherical shells with functionally graded materials under linear and nonlinear conditions is studied. In order to provide a valuable reference for the thin spherical shell with functionally graded materials in engineering application, based on the isotropic complete nonlinear thermal constitutive equation, the derivative of base vector to coordinates is expressed by christoffel symbol. The thermal constitutive equation of functionally graded thin spherical shell in spherical coordinate system is derived. The stability equation of axisymmetric spherical shell is derived by Zhang Liang method. The thermal constitutive equation is applied to the stability equation of spherical shell, and the thermal buckling equation of spherical shell expressed by displacement is obtained. In the linear case, the uniform external pressure and temperature are considered, respectively. The thermal buckling of simply supported spherical shells is studied by Galerkin method and Ritz method. The variation trend of critical pressure and critical temperature caused by the change of thickness and physical parameters of thin spherical shell is analyzed. The thermal buckling problem of simply supported hemispheres is analyzed by using the Ritz method in the case of nonlinearity. The relationship between critical pressure and thickness under different external pressure temperature (not reaching critical temperature) is studied. Under different thickness, the relationship between critical pressure and temperature is studied. (3) under different external pressure loads (no critical pressure is reached), The relation between critical temperature and thickness.
【学位授予单位】：太原科技大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O344.1

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