基于渐近均匀化的梯度板等效刚度数值计算  

Numerical Computation of Effective Stiffness of Gradient Plates Based on Asymptotic Homogenization

作　　者：张德纲 顾铖璋 韦啸 齐鹏飞 徐亮[1] ZHANG Degang;GU Chengzhang;WEI Xiao;QI Pengfei;XU Liang(College of Aerospace Engineering,Nanjing University of Aeronautics&Astronautics,Nanjing 210016,China;Structural System Research Laboratory,Aerospace System Engineering Shanghai,Shanghai 201109,China)

机构地区：[1]南京航空航天大学航空学院,南京210016 [2]上海宇航系统工程研究所结构系统研究室,上海201109

出　　处：《南京航空航天大学学报》2024年第2期341-349,共9页Journal of Nanjing University of Aeronautics & Astronautics

基　　金：国家自然科学基金青年基金(12002159);江苏省自然科学基金青年基金(BK20200411);大连理工大学工业装备结构分析国家重点实验室开放基金(GZ20101)。

摘　　要：基于梯度板结构的渐近均匀化方法,简化梯度板微单胞的单胞方程及等效刚度列式,并推导其有限元求解列式,实现梯度加筋板微结构等效刚度的高效数值求解。相比仅能处理矩形单胞的经典数值均匀化方法,该方法可以处理一般平行四边形微结构,具有更好的普适性。数值算例通过比对梯度加筋板及其对应的等效均质板挠度,最大挠度数值相对误差均在5%以内,验证了所提数值方法的正确性及可行性。Based on the asymptotic homogenization method of gradient plates,the unit cell problems and the effective stiffness of gradient plates are simplified,and the finite element solution is derived to achieve the efficient numerical solution of effective stiffness.Compared with the classical numerical homogenization method which can only deal with rectangular cells,this method can deal with general parallelogram microstructure and has good universality.The numerical examples verifies the correctness and feasibility of the numerical method proposed in this paper by comparing the deflection of the gradient stiffened plate and its corresponding equivalent homogeneous plate,and the relative error of the maximum deflection value is within 5%.

关 键 词：渐近均匀化 梯度加筋板 映射函数 等效刚度 数值求解 

分 类 号：O34[理学—固体力学]