【作者】 杨萌；

【导师】 梁斌；

【作者基本信息】 河南科技大学 ， 机械设计及理论， 2021， 博士

【摘要】 近些年,功能梯度材料(Functionally graded materials,简写FGM)圆柱壳在航空航天、潜水器、化工、通信和工程领域等得到推广使用,相应理论研究也成为热点,各国都投入相当大科研资金进行支持。本文的工作是国家自然科学基金资助项目和河南省科技攻关基金项目的一部分研究内容,重点研究FGM圆柱壳与均匀材料圆柱壳力学行为的相似性,利用得到的成果来解决其实际工程应用问题,以达到用成熟的均匀材料圆柱壳理论来解决繁琐的FGM圆柱壳问题的目的。经与参考文献数据分析对比,验证本文方法是准确有效的,并且应用便捷,适合工程应用推广。对FGM圆柱壳各种使用条件下的工况进行分析讨论,总结一些有意义的规律,指导理论研究和工程应用。论文首先回顾了均匀材料圆柱壳国内外研究现况,从研究的理论方法、静水压力下固有频率求解、加肋圆柱壳等几个角度进行了总结与归纳,为FGM圆柱壳研究工作开展提供背景材料。接着对FGM材料的诞生、优势、适用范围等方面进行了简单介绍,然后对FGM圆柱壳应用领域国内外研究现况进行了系统的阐述,重点在理论研究方面进行了较为详细的列举与分析,最后提出本文研究目的及意义。第二部分指出由于FGM圆柱壳材料性质在厚度方向连续性变化而表现出与均匀材料圆柱壳结构不同特性,导致FGM圆柱壳力学行为分析比相应均匀材料圆柱壳更为复杂,但是两者使用理论分析方法可以一致,并因此可以进行力学行为对比分析。针对FGM材料与均匀材料在数学和力学模型上相似性,通过数学物理方法让二者建立紧密联系,探究它们之间固有关系,实现FGM圆柱壳宏观力学行为“均匀化”转换计算。对FGM圆柱壳力学行为“均匀化”转换后,避开了繁琐的数学推导过程,简化了计算,同时能够保证足够计算精度,在理论上揭示FGM圆柱壳力学行为共同特性和规律,为FGM圆柱壳宏观力学行为分析提供新的探索途径。第三部分基于Flügge和Love一阶经典薄壳理论,采用波动法振动方程作为振动位移函数,通过分析比较寻找FGM圆柱壳数学模型与均匀材料圆柱壳数学模型之间相似关系,将FGM圆柱壳固有频率求解转化为同样几何尺寸、边界条件及载荷工况下均匀材料求解,实现功能梯度材料固有频率求解的均匀化转换计算。利用相对简单均匀材料圆柱壳力学问题解答来获得相对复杂FGM圆柱壳力学问题解答,避免求解复杂偏微分方程边值问题,为工程应用提供便捷公式。对影响FGM圆柱壳自由振动固有频率的各项参数进行算例分析,总结规律。第四部分利用静水压力下FGM圆柱壳与均匀材料圆柱壳力学和数学模型之间相似关系,采用经典Flügge壳体理论,利用成熟的波动法来求解静水压力下FGM圆柱壳自由振动固有频率问题,并给出静水压力下的FGM圆柱壳临界压力求解办法,为FGM圆柱壳无损检测提供理论支持。通过实际算例,对相同边界下和不同边界条件下,影响静水压力下FGM圆柱壳性能的几何物理参数进行分析总结,得出规律变化曲线,总结经验。第五部分通过对经典壳体Flügge理论、Donnell薄壳理论研究,分析了加肋圆柱壳的振动特性,考虑了壳体的旋转惯性和肋骨在其平面内外的运动,运用均匀化理论,分别采用波动法和能量法推导水下加肋功能梯度圆柱壳振动特征方程,并利用MATLAB求解特征方程得到加肋圆柱壳固有频率。算例分析了静水压力下纵横加肋功能梯度圆柱壳在不同壳体尺寸、材料组分、纵横肋肋骨截面长宽比和肋骨间距等情况下固有频率的变化规律。第六部分鉴于含裂纹均匀材料的裂纹尖端应力强度因子是含裂纹构件安全性的重要参数,在前几部分FGM薄圆柱壳均匀化研究基础上,探寻FGM圆筒与均匀材料圆筒这两者裂纹尖端应力与应力强度因子之间存在的相似比值关系,提出了一种适用于含环状裂纹FGM圆筒的应力强度因子高精度快速计算方法。将计算结果与参考文献计算结果进行对比,验证了本文方法的可行性和优越性。最后部分对本文研究内容进行了总结与展望,并提出了创新点。更多还原

【Abstract】 In recent years,functionally graded cylindrical shell(FGM)has been widely used in the fields of aerospace,submersibles,chemical industry,communications and engineering.The corresponding theoretical research has also become a hot spot,and various countries have invested considerable scientific research funds to support.The work of this paper is part of the research content of the projects funded by the National Natural Science Foundation of China and the Henan Science and Technology Research Fund.This article is mainly to study the similarity of mechanical behavior between FGM cylindrical shells and homogeneous material cylindrical shells,and use the results obtained to solve their practical engineering application problems,so as to achieve the purpose of solving the FGM cylindrical shell problems with the familiar theory of homogeneous material cylindrical shells.After analyzing and comparing with reference data,it is verified that the method in this paper is accurate and effective,and the application is convenient,and it is suitable for engineering application promotion.The working conditions of the FGM cylindrical shell under various conditions of use are analyzed and discussed,and some meaningful laws are drawn to guide theoretical research and engineering applications.The thesis first reviews the current research status of homogeneous material cylindrical shells at home and abroad,summarizes and summarizes the theoretical methods,hydrostatic pressure,and ribbed cylindrical shells from various perspectives,and provides background materials for the development of FGM cylindrical shells.The second step is a brief introduction to the birth,advantages,and scope of application of FGM materials.Then the application field of FGM cylindrical shell is systematically explained the current research situation at home and abroad,especially in the theoretical research.Finally,the purpose and significance of the research in this article are put forward.The second part of the article points out that because the material properties of FGM cylindrical shells continuously change in the thickness direction,they exhibit different characteristics from the uniform material cylindrical shells,which makes the mechanical behavior analysis of FGM cylindrical shells more complicated than the corresponding uniform material cylindrical shells.However,the theoretical analysis method of the two materials can be consistent,and therefore the mechanical behavior can be compared and analyzed.Aiming at the similarity between FGM material and homogeneous material in mathematical and mechanical models,the two materials are closely related through mathematical and physical methods,revealing the inherent relationship between them,and realizing the "homogenization" conversion calculation of the macro-mechanical behavior of FGM cylindrical shells.After "homogenizing" the mechanical behavior of the FGM cylindrical shell,the tedious mathematical processing is avoided,and the calculation is simplified.At the same time,it can ensure sufficient calculation accuracy,reveal the common characteristics and laws of the mechanical behavior of FGM cylindrical shells theoretically,and provide a new exploration way for the analysis of the macroscopic mechanical behavior of FGM cylindrical shells.The third part is based on the first-order classic thin shell theory of Flügge and Love,using the wave method as the vibration displacement function.Through analysis and comparison to find the similar relationship between the FGM cylindrical shell and the uniform material cylindrical shell in the mathematical model,the natural frequency of the FGM cylindrical shell is converted into the uniform material solution under the same geometric size,boundary conditions and load conditions,so as to realize the homogenization of functionally graded materials.This method uses a relatively simple solution to the mechanics problem of a uniform material cylindrical shell to obtain a relatively complex solution to the mechanics problem of the FGM cylindrical shell.It avoids solving boundary problems of complex partial differential equations and provides convenient formulas for engineering applications.Finally,a calculation example is carried out to analyze the various parameters that affect the natural frequency of the FGM cylindrical shell in the vacuum,and the rules are summarized.The fourth part of the article uses the similar relationship between the mechanics and mathematical models of the FGM cylindrical shell and the homogeneous material cylindrical shell under hydrostatic pressure,and uses the classic Flügge shell theory to solve the natural frequency problem of the free vibration of the FGM cylindrical shell under hydrostatic pressure.At the same time,a solution to the critical pressure of FGM cylindrical shells under hydrostatic pressure is given,which provides theoretical support for non-destructive testing of FGM cylindrical shells.Through actual calculation examples,the geometric and physical parameters that affect the performance of FGM cylindrical shells under hydrostatic pressure are analyzed and summarized,the regular change curve is drawn,and the experience is summarized.The fifth part analyzes the vibration characteristics of the ribbed cylindrical shell by studying the classical shell Flügge theory and Donnell thin shell theory.Taking into account the rotational inertia of the shell and the movement of the ribs in and out of its plane and applying the homogenization theory,the wave method and the energy method are used to derive the vibration characteristic equations of the underwater stiffened functionally graded cylindrical shell.MATLAB is used to solve the characteristic equation to obtain the natural frequency of the stiffened cylindrical shell.The calculation example analyzes the variation law of natural frequency of circumferential and longitudinally ribbed functionally graded cylindrical shells under hydrostatic pressure with different shell size,material composition,circumferential and longitudinal rib section aspect ratio and rib spacing.The sixth part is that the stress intensity factor at the crack tip of the homogeneous material with cracks is an important parameter for the safety of the cracked components.Based on the research on the homogenization of FGM thin cylindrical shells in the previous parts,it explores the similar ratio relationship between the crack tip stress and the stress intensity factor between the FGM cylinder and the homogeneous material cylinder.A high-precision and fast calculation method for the stress intensity factor of FGM cylinders with annular cracks is proposed.Comparing the calculation results with the calculation results of reference documents,the feasibility and superiority of the method in this paper are verified.The last part summarizes and prospects the research content of this paper,and puts forward innovation points.更多还原