热载荷作用下对称S型功能梯度圆板的非线性力学行为  

Nonlinear Mechanical Behavior of Symmetrical S-FGM Circular Plate under Thermal Loading

作　　者：甘勇天 马连生[1] Yongtian Gan;Liansheng Ma(School of Science,Lanzhou University of Technology,Lanzhou,730050)

机构地区：[1]兰州理工大学理学院,兰州730050

出　　处：《固体力学学报》2022年第2期158-167,共10页Chinese Journal of Solid Mechanics

基　　金：国家自然科学基金项目(11862012,12062010);山东省自然科学基金项目(ZR2020KA006)资助。

摘　　要：论文研究了热环境中陶瓷-金属-陶瓷功能梯度圆板(S-FGM)的过屈曲和弯曲行为.圆板材料组分的体积分数符合Sigmoid定律,并承受沿圆板厚度方向变化的温度场作用.基于经典板理论,用能量法导出了对称S-FGM圆板静态问题的非线性平衡方程.用打靶法对所得方程进行了数值求解,并利用数值结果研究了不同边界条件、材料的组分、热载荷等因素对对称S-FGM圆板力学行为的影响.数值结果表明:对称S-FGM圆板相较于普通FGM圆板,其力学行为存在一些不同之处,且板的上下表面温升比对S型功能梯度圆板的力学行为有着显著的影响.This paper presents a numerical investigation on the axisymmetric postbuckling and bending behavior of ceramic-metal-ceramic sigmoid functionally graded material(S-FGM)circular plates subjected to thermal loading.The mechanical and thermal properties of functionally graded circular plate are assumed to vary continuously through the thickness of the plate,and obey the sigmoid law composed of two power laws of the volume fraction of the constituents.First,based on the well-known von Karman plate theory,the nonlinear equilibrium equations and boundary conditions for the static problem of the symmetrical S-FGM circular plate are derived using the energy method.As examples,the clamped and simply-supported S-FGM circular plates are studied,respectively.Then,by applying the shooting method,the bending and postbuckling equilibrium paths for S-FGM circular plates with different boundary conditions are determined.Finally,the effects of material constant n,temperature rise ratio of the upper and lower surfaces,and thermal loading on the nonlinear mechanical behavior of S-FGM plates with different boundary conditions are discussed in detail.After comparing with the results from literature,it can be found that under the action of thermal loading,the clamped S-FGM circular plate appears buckling deformation;while the simply-supported S-FGM circular plate exhibits bending deformation,which is similar to the ordinary FGM circular plate,but the simply-supported S-FGM circular plate subjected to uniform thermal loading exhibits post-buckling behavior.Furthermore,when the material gradient value n is larger,compared with a homogeneous or FGM plate,the ability of the S-FGM circular plate to resist against buckling deformation does not change significantly.With the increase of temperature rise ratio of the upper and lower surfaces,the ability of S-FGM circular plates with different boundaries to resist against deformation gradually weakens,in which,the simply-supported S-FGM circular plates always bend to the side where the temperatu

关 键 词：S-FGM圆板 热载荷 打靶法 弯曲 过屈曲 

分 类 号：O341[理学—固体力学]