摘要
为分析多孔梯度材料圆板在非均匀温度场中的热后屈曲响应,基于经典板理论和物理中面概念建立了梯度多孔材料圆板在热载荷作用下的控制微分方程,其中假设厚度变化沿半径为二次抛物线型且板在其厚度上具有对称和非对称的非均匀孔隙率分布。采用打靶法数值求解了问题的屈曲和后屈曲响应,给出了均匀升温和热传导下的梯度多孔非线性变厚度圆板后屈曲平衡路径。结果显示:变厚度系数、孔隙率系数、孔隙分布方式以及温度场对板的临界载荷和后屈曲平衡路径均有影响;在不同温度场中孔隙率系数越大,屈曲时的临界载荷越小;孔隙率对称分布下的临界载荷大于非对称情况下的。
In order to analyze the thermal post-buckling response of the graded porous material circular plate in the non-uniform temperature field,the governing differential equation of the graded porous material circular plate under thermal load was established on the basis of classical plate theory and the concept of physical neutral plane.It is assumed that the thickness change is quadratic parabolic along the radius and the plate has symmetric and asymmetric non-uniform porosity distribution across their thickness.Using shooting method technique,the buckling and post-buckling responses of the problem was numerically solved,and the post-buckling equilibrium paths of the graded porous nonlinear variable thickness circular plate under different types of thermal loads as heat conduction and uniform temperature rise were obtained.The results show that the variable thickness coefficient,porosity coefficient,pore distribution and temperature field have the effects on the critical load and post buckling equilibrium path of the plate;under different temperature fields,the larger the porosity coefficient,the smaller the critical load during buckling;the critical load under symmetrical porosity distribution is greater than that under asymmetric porosity distribution.
作者
李清禄
苗文帅
张靖华
LI Qinglu;MIAO Wenshuai;ZHANG Jinghua(School of Science,Lanzhou University of Technology,Lanzhou 730050,China)
出处
《机械科学与技术》
CSCD
北大核心
2023年第12期2118-2124,共7页
Mechanical Science and Technology for Aerospace Engineering
基金
国家自然科学基金项目(12062010,12362009)。
关键词
梯度多孔材料
物理中面
圆板
后屈曲
数值解
graded porous materials
physical neutral plane
circular plate
post-buckling
numerical solution
