应用数学和力学2026，Vol.47Issue(2)：145-157,13.DOI:10.21656/1000-0887.450323
变温和荷载作用下正交异性层合梁弹性力学解
Elastic Solutions for Orthotropic Laminated Beams Under Temperature Variations and Loads
摘要
Abstract
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.关键词
正交各向异性层合梁/热弹性理论/状态空间法/Fourier级数Key words
orthotropic laminated beam/theory of thermoelasticity/state space method/Fourier series分类
数理科学引用本文复制引用
钱海,陈佳伟,陆春华..变温和荷载作用下正交异性层合梁弹性力学解[J].应用数学和力学,2026,47(2):145-157,13.基金项目
国家自然科学基金(52108148 （）
52478177) （）
中国博士后科学基金(面上项目)(2021M701483) （面上项目）
江苏省博士后科研资助计划(2021K574C) （2021K574C）
