二维准晶平面问题中的Hamilton体系求解方法  

A Hamiltonian System Solution Method for Planar Problems of 2D Quasicrystals

作　　者：李彤[1] 屈建龙 王炜[1] 王晨龙 徐新生[1] LI Tong;QU Jianlong;WANG Wei;WANG Chenlong;XU Xinsheng(School of Mechanics and Aerospace Engineering,Dalian University of Technology,Dalian,Liaoning 116023,P.R.China)

机构地区：[1]大连理工大学力学与航空航天学院,辽宁大连116023

出　　处：《应用数学和力学》2024年第11期1359-1371,共13页Applied Mathematics and Mechanics

基　　金：大连理工大学工业装备结构分析优化与CAE软件全国重点实验室探索基金(S22303)。

摘　　要：针对二维准晶平面问题,该文通过导入Hamilton体系,将问题转化为Hamilton体系下的辛本征值和辛本征解问题,即问题的解可由辛本征解组成的级数表示.利用辛本征解之间的辛共轭正交关系,可将满足边界条件的解问题归结为代数方程组的求解问题,从而形成一种解析求解方法.这种方法可直接推广到求解混合边界条件及分段边界条件问题中.Aimed at the planar problem of 2D quasicrystals,the problem was transformed into one of symplectic eigenvalues and symplectic eigensolutions through introduction of the Hamiltonian system.In the Hamiltonian system,the solution to this problem was expressed by a series of symplectic eigensolutions.With the symplectic conjugate orthogonality relationship between symplectic eigensolutions,the solving problem satisfying boundary conditions can be reduced to a problem of solving algebraic equations,thus to form an analytical solution method.The proposed method can be directly extended to solve the problems of mixed boundary conditions and segmented boundary conditions.

关 键 词：二维准晶 HAMILTON体系 辛共轭正交 辛方法 平面问题 

分 类 号：O343.1[理学—固体力学]