混合边界矩形薄板静力问题解析研究  

Analytical Study on Static Problems of Rectangular Thin Plates with Mixed Boundary Conditions

作　　者：田宇 常亮[1] 万春华[1] 聂小华[1] TIAN Yu;CHANG Liang;WAN Chunhua;NIE Xiaohua(National Key Laboratory of Strength and Structural Integrity,Aircraft Strength Research Institute of China,Xi'an 710065,Shaanxi,China)

机构地区：[1]中国飞机强度研究所强度与结构完整性全国重点实验室,陕西西安710065

出　　处：《力学季刊》2024年第2期569-580,共12页Chinese Quarterly of Mechanics

摘　　要：本文利用Hamilton体系中的“辛-叠加”方法,基于弹性薄板理论,对两对边固支、另两对边中部固支两端简支这一混合边界条件矩形薄板静力问题进行了解析研究.首先基于Hamilton求解体系辛几何方法对对边简支这一经典边界条件矩形薄板问题进行了解析求解,然后以此为基本体系采用叠加法思想对两对边固支、另两对边中部固支两端简支这一复杂混合边界条件矩形板问题进行了求解,最后采用有限元数值模拟对本文方法的正确性和收敛性进行了验证.本文方法同时具备辛几何方法的理性和叠加法的规律性优点,其求解过程中无需预先假定解的形式,直接由弹性力学基本方程出发,通过逐步严格推导来获得解析解.该方法通用性强,可用于一些传统方法难以解析求解的矩形板问题中.Using the"symplectic superposition"method in the Hamiltonian system and based on the theory of elastic thin plates,an analytically study was carried out for the static problem of rectangular thin plates with mixed boundary conditions of constraint on two opposite sides and middle-constraint ends-simplely-supported on the other two sides.Firstly,based on the Hamiltonian system,the symplectic geometry method was used to analytically solve the problem of classical boundary condition of simply supported edges.Then,based on this solution as the basic system,the superposition method was used to solve the case of complex mixed boundary condition of constraint on two opposite sides and middle-constraint ends-simplely-supported on the other two sides.Finally,the correctness and convergence of the proposed method were verified using the finite element numerical simulations.The method presented in this paper has both advantages of the rationality of symplectic geometry and the regularity of superposition method.During the solving process,there is no need to assume the form of the solution in advance,and the analytical solution is obtained directly from the basic equations of elasticity through strict step-by-step derivation.This method has strong generality and can be used in some rectangular plate problems that are difficult to solve analytically using the traditional methods.

关 键 词：混合边界 弹性薄板理论 HAMILTON体系 辛-叠加方法 静力弯曲 

分 类 号：TU31[建筑科学—结构工程]