非均匀变温环境中简支层合拱热弹性力学解  

THERMOELASTIC SOLUTIONS FOR SIMPLY SUPPORTED LAMINATED ARCH IN NON-UNIFORM VARIABLE TEMPERATURE ENVIRONMENT

作　　者：钱海 王页澎 陆春华[1] QIAN Hai;WANG Ye-peng;LU Chun-hua(Faculty of Civil Engineering and Mechanics,Jiangsu University,Zhenjiang 212013,China)

机构地区：[1]江苏大学土木工程与力学学院,镇江212013

出　　处：《工程力学》2024年第11期1-13,共13页Engineering Mechanics

基　　金：国家自然科学基金项目(52108148,51878319);中国博士后科学基金面上项目(2021M701483);江苏省博士后科研计划项目(2021K574C)。

摘　　要：具有轻质高强、可设计强、耐高温等优良特性的复合材料层合结构在我国被广泛应用于航空航天、建筑结构、公路桥梁等工程领域。该文基于热传导方程和热弹性理论,建立变温环境中层合拱结构理论计算模型,研究了变温环境中二维层合拱的热力学行为,得到结构温度、热应力和位移解析解。利用线性叠加原理,将层合拱非齐次温度边界转化为齐次温度边界,基于结构内层间温度和径向热流密度的连续性,建立内、外侧温度和热流密度关系,联合内、外侧温度边界条件,得到层合圆柱拱内温度场解析解。以位移和应力作为状态变量,建立状态空间方程。基于层间位移和径向应力的连续性,借助传递矩阵法,推导出两端简支层合圆柱拱内外侧位移和应力关系,并同时对层合拱内外侧应力边界条件进行傅里叶级数展开,最终得到位移和热应力解析解。收敛性分析和数值结果比对表明了该方法的有效性和准确性。利用该文方法,探讨了外部温度环境、结构尺寸、结构层数及材料组分,对结构内温度、热应力及位移分布的影响,为变温环境下层合拱的设计提供了理论依据。Due to their light weight,high strength,strong designability and high temperature resistance,composite laminated structures are widely used in aerospace,building structures,highway bridges and other engineering fields in China.Based on the heat conduction equation and thermoelasticity theory,built is a theoretical calculation model of laminated arch in variable temperature environment,investigated are the thermal behaviors for two-dimensional laminated arch,and obtained are the analytical solutions of structural temperature,thermal stress and,displacement.By using the linear superposition principle,the inhomogeneous temperature boundaries of the laminated arch is transformed into homogeneous temperature boundaries.Based on the continuities of the temperature and on heat flux at the interfaces between the adjacent layers of the structure,derived is the relationships between the inner and outer layers.The analytical solution of temperature is obtained by using the surface temperature of the laminated cylindrical arch.The state space equation is established by taking displacement and stress as state variables.Based on the continuities of displacements and stresses at the interface,deduced are the relationships between the inner and outer layers of the laminated arch by means of transfer matrix method.The analytical solutions of displacements and thermal stresses are obtained by Fourier series expansion of the surface loads on the laminated arch.The convergence analysis and comparisons of numerical results demonstrate the effectiveness and accuracy of this method.Discussed are the influences of external temperature environment,structure sizes,structure layers and materials on the distributions of temperature,thermal stress and,displacement in the structure in detail,which provides a theoretical reference for designing laminated arches under variable temperature environment.

关 键 词：层合拱 非均匀温度场 傅里叶级数展开 传递矩阵法 热弹性力学理论 

分 类 号：TB332[一般工业技术—材料科学与工程]