热载荷作用下S型功能梯度铝-氧化锆复合梁的非线性力学行为  

Nonlinear mechanical behavior of S-type functionally graded aluminum-zirconia composite beamunder thermal load

作　　者：马连生 甘勇天 MA Liansheng;GAN Yongtian(School of Architecture and Art,Weifang University of Science and Technology,University Facilities Horticulture Laboratory in Shandong,262700 Weifang,China;School of Science,Lanzhou University of Technology,730050 Lanzhou,China)

机构地区：[1]潍坊科技学院建筑与艺术学院,山东省高校设施园艺实验室,潍坊262700 [2]兰州理工大学理学院,兰州730050

出　　处：《应用力学学报》2025年第2期378-387,共10页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金资助项目(No.11862012,12062010);山东省自然科学基金重点资助项目(No.ZR2020KA006)。

摘　　要：研究了热载荷作用下对称和非对称S型功能梯度(sigmoid functionally graded materials,S-FGM)梁的过屈曲和弯曲问题,并通过计算结果,分析了两类S型功能梯度梁之间以及S型功能梯度梁与普通功能梯度梁之间力学行为的差异。设梁材料组份沿厚度方向的分布满足sigmoid律,而梁厚度方向上的温度变化用一维热传导方程进行描述且满足sigmoid律。首先利用能量原理推导了功能梯度梁的平衡方程和边界条件;然后利用打靶法对不同边界条件下S-FGM梁的平衡路径进行了数值求解,基于数值结果探究了边界条件、组分材料的分布形式以及外载荷等因素对S-FGM梁力学行为的影响。结果表明:热载荷作用下两端固定夹紧对称和非对称S-FGM梁均发生分支屈曲,而两端固定简支S-FGM梁则是热弯曲(均匀热载荷下对称分布梁除外);梯度指数和上下表面温升比对S-FGM梁的弯曲、屈曲和过屈曲行为有重要影响,而梯度指数和上下表面温升比对两类夹紧S-FGM梁屈曲和过屈曲行为的影响有明显的不同。This paper proposed a numerical evaluation of the postbuckling and bending behavior of the symmetrical and asymmetrical sigmoid functionally graded materials(S-FGM)beams subjected to thermal load,and the numerical results obtained from the present paper are used to analyze the differences of the mechanics behavior between the two types of S-FGM beams and between S-FGM beams and ordinary functionally graded ones.Assuming that the distribution of material components satisfies the sigmoid law,the temperature change in the thickness direction of the beam is described by a one-dimensional heat conduction equation and satisfies the sigmoid law.First,the nonlinear equilibrium equations and boundary conditions of the static problem of the S-FGM beam are derived using the energy method,and then solved numerically by applying the shooting method.The influence of factors such as the distribution form of component materials,external loads and boundary conditions on the mechanical behavior of S-FGM beam is discussed in details.These results show that under thermal load,both symmetrical and asymmetrical S-FGM beams clamped at both ends exhibit typical thermal post-buckling behaviors,while bifurcation buckling does not occur for the S-FGM beams simply supported at both ends(except for the symmetrical S-FGM beams under uniform thermal load).The gradient index and the upper and lower surface temperature rise ratio have an important influence on the bending,buckling and postbuckling behavior of S-FGM beams,while there are significant differences between the effects of both the gradient index and the upper and lower surface temperature rise ratio on the buckling and postbuckling behaviors of the two types of S-FGM beams clamped at both ends.

关 键 词：铝-氧化锆复合材料 热载荷 打靶法 弯曲 过屈曲 

分 类 号：TU323.3[建筑科学—结构工程]