Finite Integral Transform Solutions for Free Vibrations of Rectangular Thin Plates With Mixed Boundary Constraints北大核心CSCD

Analytical solutions, with unique research value, can serve as benchmarks for empirical formulas and numerical methods, a tool for rapid parameter analysis and optimization, and a theoretical basis for experimental designs. Conventional analytical methods, e.g., the Lévy solution method, are only applicable to mechanical problems of plates and shells with opposite simply-supported edges, which, however, may fail to obtain analytical solutions for the issues with complex boundary constraints. In recent years, the finite integral transform method for plate and shell problems was developed to deal with non-Lévy-type plates and shells, but it is still infeasible to solve the mixed boundary constrains-induced complex boundary value problems of higher-order partial differential equations. Herein, for the first time, the finite integral transform method was combined with the sub-domain decomposition technique to solve the free vibrations of rectangular thin plates with mixed boundary constraints. The rectangular plate was first divided into 2 sub-domains according to the mixed boundary constraints, and the 2 sub-domains were solved analytically with the finite integral transform method. Finally, the continuity conditions were introduced to obtain the analytical solution of the original problem. Based on the side spot-welded cantilever plates commonly used in engineering, the free vibration problem of a rectangular thin plate with 1 edge subjected to clamped-simply supported constraints and the other 3 edges free, was analyzed. The obtained natural frequencies and mode shapes are in good agreement with those from the finite element method as well as the solutions in literature, thus verifying the accuracy of the proposed method. The solution procedure of the finite integral transform method can be implemented based on the governing equations without any assumption of the solution form. Therefore, this strict analytical method is widely applicable to complex boundary value problems of higher-order partial differential equations for such mechanical problems of plates and shells. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

非Lévy型正交各向异性开口圆柱壳屈曲问题的辛叠加解析解

该文基于笔者提出的辛叠加方法得到了经典解法难以直接获得的典型非Lévy型正交各向异性开口圆柱壳屈曲问题的解析解.首先，基于Donnell薄壳理论建立了正交各向异性开口圆柱壳屈曲问题的Hamilton体系控制方程，然后将非Lévy型边界下的原问题拆分为两个子问题，在Hamilton体系下利用分离变量和辛本征展开等数学手段对子问题进行求解，最后基于原问题边界条件，通过子问题解的叠加求得原问题的解析解.数值算例表明，辛叠加解析解与有限元数值解结果吻合良好.同时，定量研究了长度和厚度等参数对屈曲载荷的影响.相比于半逆解法等传统解析方法，辛叠加方法基于严格的数学推导，无需假定解的形式，可以获得更多类似问题的解析解.     

基于iSIGHT平台的三维机翼气动优化设计

基于iSIGHT设计平台,结合CFD四软件Fluent对三维机翼进行多目标优化设计,以提高其气动性能.设计过程中采用NCCA (neighborhood cultivation)--邻域培植遗传算法,NSGA-Ⅱ(non-dominateda sorting)--非支配解排序遗传算法为优化算法,以N-S方程作为主控方程,对三维机翼优化.经过优化设计后结果表明,机翼的气动性能有了显著改善,该优化方法可推广用于多种翼型和机翼优化.     

Aerodynamic optimization of 3D wing based on iSIGHT

A method for combining the CFD software,Fluent,with the iSIGHT design platform is presented to optimize a three-dimensional wing to ameliorate its aerodynamics performance.In the optimization design,two kinds of genetic algorithms,the Neighborhood Cultivation Genetic Algorithm（NCGA）and the Non-dominated Sorting Genetic Algorithm（NSGAII）,are employed and the Navier-Stoke（N-S）equations are adopted to derive the aerodynamics functions of the 3D wing.The aerodynamic performance of the optimized wing has been significantly improved,which shows that the approach can be extended and employed in other cases.