摘要
由多种工程材料组成的复合材料层合结构因其卓越的可设计性和优良的力学性能,在建筑工程、航天航空、汽车工业等领域有着广泛的应用.该文研究了温度环境中正交各向异性固支层合梁的热力学行为,并基于热弹性理论推导出了热应力和位移的精确解.该方法适用于荷载和变温环境共同作用下,任意厚度和层数的正交各向异性固支层合梁.首先,引入单位脉冲函数和Dirac函数,将固支边界等效为简支边界和一组纵向边界反力.其次,以位移和应力作为状态变量,并联合基本方程建立状态空间方程,利用Fourier级数将状态空间方程进行简化.然后,根据相邻层界面处位移和应力的连续性关系,推导出层合梁顶层和底层之间的位移和应力关系.最后,利用层合结构上下表面应力和位移的边界条件,最终确定正交各向异性固支层合梁内任意一点的位移和应力.收敛性和对比分析表明了该方法的有效性和准确性.同时,探究了温度环境和长厚比对正交各向异性固支层合梁内位移和应力分布的影响.
Composite laminated structures,composed of multiple engineering materials,have wide-range appli-cations in building engineering,aerospace,automobile industry and other fields,owing to the exceptional des-ignability and mechanical performance.The thermodynamic behaviors of clamped orthotropic laminated beams were investigated in temperature variations and the exact solutions for thermal stresses and displacements were derived based on the theory of thermoelasticity.This method is applicable to laminated beams with arbitrary thickness and number of layers,under both loads and variable temperatures.Firstly,the clamped support was equivalently transformed into a simple support boundary and a pair of transverse boundary reaction forces through introduction of the unit impulse function and the Dirac function.Additionally,the state equation was formulated with the displacement and stress as state variables and the fundamental equations combined.The Fourier series was employed to simplify the state space equation.The relationships of displacements and stres-ses between the top and bottom layers of the laminated beam were sequentially derived based on the continui-ties of displacements and stresses at the interfaces of the adjacent layers.Ultimately,the displacement and stress at any point in the orthotropic laminated beam were determined by means of the stress and displacement boundary conditions at the upper and lower surfaces of the structure.Convergence and comparison analyses demonstrate the effectiveness and accuracy of the proposed method.Furthermore,the effects of the tempera-ture and the length-to-thickness ratio on the distributions of displacements and stresses in the orthotropic lami-nated beams,were discussed in detail.
作者
钱海
陈佳伟
陆春华
QIAN Hai;CHEN Jiawei;LU Chunhua(Faculty of Civil Engineering and Mechanics,Jiangsu University,Zhenjiang,Jiangsu 212013,P.R.China)
出处
《应用数学和力学》
北大核心
2026年第2期145-157,共13页
Applied Mathematics and Mechanics
基金
国家自然科学基金(52108148,52478177)
中国博士后科学基金(面上项目)(2021M701483)
江苏省博士后科研资助计划(2021K574C)。
