基于物理中面功能梯度材料板壳结构分析
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摘要
功能梯度材料(FGM),在宏观与微观上都是非均质复合材料,一般是由陶瓷与金属复合而成,其材料组分从纯陶瓷表面到纯金属表面呈连续梯度变化,导致了材料性质与等效物理参数也是梯度平缓变化。这使得FGM在工程应用中,特别在航天工业、聚变堆与核工业等高温环境中,有着传统纤维-基体复合材料无法比拟的优点。本博士学位论文,基于物理中面的概念与经典非线性板壳理论,建立了关于FGM板、圆柱壳与双曲率扁壳的基本方程。物理中面板壳理论具有面内变形与横向弯曲解耦的特点,又因为控制方程与边界条件简洁,使得分析FGM板壳力学行为的难度降低。
在线性分析中,用解析的方法分析了FGM板、圆柱壳与双曲率扁壳弯曲、振动与屈曲等力学行为。分析结果表明,FGM板壳的无量纲挠度随着梯度参数的增加而减小,而无量纲振动频率与临界屈曲载荷随着梯度参数的增加而增加。
在非线性分析中,用Galerkin变分法分析了FGM板壳在热-机载荷作用下的非线性弯曲,大幅度振动,过屈曲等力学行为。主要结论有：
在对FGM板、圆柱壳与双曲率扁壳的非线性弯曲分析中,在机械载荷作用下FGM板壳的弯曲力学行为介于纯金属于与纯陶瓷之间,但是在热-机载荷联合作用下,FGM板壳的弯曲力学行为并不都是如此。在相同的热载作用下,简支FGM板壳都有较大的初始挠度,固支壳只有微小的初始挠度,而固支板在没有发生热过屈曲变形时无初始挠度。当FGM壳的几何参数大于临界几何参数时,FGM壳随着荷载的增加会发生跳跃失稳现象,其中临界几何参数与边界支撑条件,温度载荷、梯度参数有关。
在对FGM板壳非线性振动的分析中,当振幅趋近零时,FGM板壳的振动频率趋近线性解,板的振动频率随着振幅的增大而升高,而FGM壳的振动频率随振幅的变化比较复杂。
在对FGM板过屈曲变形的分析中,简支FGM板的挠度随着边界压力载荷的增加而增加,当压力趋近线性临界屈曲压力时,简支FGM板的挠度趋近零。随着热载荷参数的增加,固支FGM板会发生屈曲分叉,而简支FGM板则不会。在相同热载荷作用的条件下,纯陶瓷的抗热性能高于纯金属板,而具有适当梯度参数的FGM抗热性能可以超过纯陶瓷板,此时可以体现出FGM材料的优越性。
因为比几何中面FGM板壳理论简洁,所以物理中面FGM板壳理论在工程应用中具有一定的优势。
Functionally gradient materials (FGM) are both macroscopically and microscopically heterogeneous composites which are normally made from a mixture of ceramics and metals with continuous composition gradation from pure ceramic on one surface to full metal on the other. This leads to a gradual and smooth change in the material profile as well as the effective physical properties, making them distinguish from the conventional fiber-matrix composites and preferable in many engineering applications, especially in high temperature environments such as aerospace structures, fusion reactors and nuclear industry. In this paper, the concept of physical neutral surface and classical laminated plate and shell theories are employed to formulate the basic equations of the FGM plates, cylindrical shells and double curved shallow shells. In this theory, stretching-bending coupling effects are decoupled, governing equations and boundary conditions have the simple forms, so analysis and solution procedure of FGM plats and shells are simplified.
In linear analysis, FGM plates and shells behaviors, which include bending, vibration, bucking, are discussed using analytical method based on physical neutral surface theories. With increased material constant, deflections of FGM plate and shell are decreased, but frequency and critical bucking loading are increased.
In nonlinear analysis, FGM plates and shells behaviors, which include large deflection bending, large deflection vibration, post-bucking, are discussed using Galerkin variational method. It can be concluded that
In nonlinear bending analysis of FGM plates, cylindrical shells and double-curved shallow shells, if there is no thermal loading, behaviors of FGM plates and shells are intermediate to that of plates and shells made of pure ceramics and metals in mechanical loading, but this is not true while thermo-mechanical loading are applied. Under the same thermal loading, simply support plates have larger initial deflection, and clamped shells have small initial deflection, but clamped plates have not except for in post-bucking state. When geometry parameter of FGM shells is larger than critical geometry parameter, in which are related with material constant, thermal loading and boundary condition, the maximum deflection has a sudden jump with the increased mechanical loads.
Under simply support and clamped boundary conditions, deflections of plates are increased with increased mechanical loading. Deflections of simply support plates are larger than clamped plates with or without thermal loading. Deflections of plates with thermal loading are larger than deflections of plates without thermal loading. Under thermal loading, simply support plates have initial deflection, but clamped plates has not except for in post-bucking state. In nonlinear bending analysis of FGM cylindrical and double curved shallow thin shells, the maximum deflection has a sudden jump with the increased mechanical loads.
In large deflection vibration analysis, when vibration amplitude is closed to zero, nonlinear frequency is closed to linear frequency, frequency of FGM plates are increased with increased vibration amplitude, but frequency of FGM shells are complex with increased vibration amplitude.
In post-bucking analysis, deflection of simply support plates is closed to zero, when boundary pressure is closed to critical pressure. Deflection of simply support plates increased with increased boundary pressure. With increased thermal loading, clamped FGM plates have bifurcation buckling behavior, but simply support plates has not. Under the same thermal loading, heat resistance of ceramics is better than that of metals, but if material constant is properly selected, that of FGM can be better than that of ceramics, so superiority of FGM can be best presented.
Physical neutral surface plate and shell theories about FGM have more merits in the engineering application, because they are easier and simpler than classical laminated plate and shell theories based on geometric middle surface.
在线性分析中,用解析的方法分析了FGM板、圆柱壳与双曲率扁壳弯曲、振动与屈曲等力学行为。分析结果表明,FGM板壳的无量纲挠度随着梯度参数的增加而减小,而无量纲振动频率与临界屈曲载荷随着梯度参数的增加而增加。
在非线性分析中,用Galerkin变分法分析了FGM板壳在热-机载荷作用下的非线性弯曲,大幅度振动,过屈曲等力学行为。主要结论有：
在对FGM板、圆柱壳与双曲率扁壳的非线性弯曲分析中,在机械载荷作用下FGM板壳的弯曲力学行为介于纯金属于与纯陶瓷之间,但是在热-机载荷联合作用下,FGM板壳的弯曲力学行为并不都是如此。在相同的热载作用下,简支FGM板壳都有较大的初始挠度,固支壳只有微小的初始挠度,而固支板在没有发生热过屈曲变形时无初始挠度。当FGM壳的几何参数大于临界几何参数时,FGM壳随着荷载的增加会发生跳跃失稳现象,其中临界几何参数与边界支撑条件,温度载荷、梯度参数有关。
在对FGM板壳非线性振动的分析中,当振幅趋近零时,FGM板壳的振动频率趋近线性解,板的振动频率随着振幅的增大而升高,而FGM壳的振动频率随振幅的变化比较复杂。
在对FGM板过屈曲变形的分析中,简支FGM板的挠度随着边界压力载荷的增加而增加,当压力趋近线性临界屈曲压力时,简支FGM板的挠度趋近零。随着热载荷参数的增加,固支FGM板会发生屈曲分叉,而简支FGM板则不会。在相同热载荷作用的条件下,纯陶瓷的抗热性能高于纯金属板,而具有适当梯度参数的FGM抗热性能可以超过纯陶瓷板,此时可以体现出FGM材料的优越性。
因为比几何中面FGM板壳理论简洁,所以物理中面FGM板壳理论在工程应用中具有一定的优势。
Functionally gradient materials (FGM) are both macroscopically and microscopically heterogeneous composites which are normally made from a mixture of ceramics and metals with continuous composition gradation from pure ceramic on one surface to full metal on the other. This leads to a gradual and smooth change in the material profile as well as the effective physical properties, making them distinguish from the conventional fiber-matrix composites and preferable in many engineering applications, especially in high temperature environments such as aerospace structures, fusion reactors and nuclear industry. In this paper, the concept of physical neutral surface and classical laminated plate and shell theories are employed to formulate the basic equations of the FGM plates, cylindrical shells and double curved shallow shells. In this theory, stretching-bending coupling effects are decoupled, governing equations and boundary conditions have the simple forms, so analysis and solution procedure of FGM plats and shells are simplified.
In linear analysis, FGM plates and shells behaviors, which include bending, vibration, bucking, are discussed using analytical method based on physical neutral surface theories. With increased material constant, deflections of FGM plate and shell are decreased, but frequency and critical bucking loading are increased.
In nonlinear analysis, FGM plates and shells behaviors, which include large deflection bending, large deflection vibration, post-bucking, are discussed using Galerkin variational method. It can be concluded that
In nonlinear bending analysis of FGM plates, cylindrical shells and double-curved shallow shells, if there is no thermal loading, behaviors of FGM plates and shells are intermediate to that of plates and shells made of pure ceramics and metals in mechanical loading, but this is not true while thermo-mechanical loading are applied. Under the same thermal loading, simply support plates have larger initial deflection, and clamped shells have small initial deflection, but clamped plates have not except for in post-bucking state. When geometry parameter of FGM shells is larger than critical geometry parameter, in which are related with material constant, thermal loading and boundary condition, the maximum deflection has a sudden jump with the increased mechanical loads.
Under simply support and clamped boundary conditions, deflections of plates are increased with increased mechanical loading. Deflections of simply support plates are larger than clamped plates with or without thermal loading. Deflections of plates with thermal loading are larger than deflections of plates without thermal loading. Under thermal loading, simply support plates have initial deflection, but clamped plates has not except for in post-bucking state. In nonlinear bending analysis of FGM cylindrical and double curved shallow thin shells, the maximum deflection has a sudden jump with the increased mechanical loads.
In large deflection vibration analysis, when vibration amplitude is closed to zero, nonlinear frequency is closed to linear frequency, frequency of FGM plates are increased with increased vibration amplitude, but frequency of FGM shells are complex with increased vibration amplitude.
In post-bucking analysis, deflection of simply support plates is closed to zero, when boundary pressure is closed to critical pressure. Deflection of simply support plates increased with increased boundary pressure. With increased thermal loading, clamped FGM plates have bifurcation buckling behavior, but simply support plates has not. Under the same thermal loading, heat resistance of ceramics is better than that of metals, but if material constant is properly selected, that of FGM can be better than that of ceramics, so superiority of FGM can be best presented.
Physical neutral surface plate and shell theories about FGM have more merits in the engineering application, because they are easier and simpler than classical laminated plate and shell theories based on geometric middle surface.
引文
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