New analytic solutions to 2D transient heat conduction problems with/without heat sources in the symplectic space

作     者：Dian XU Xinran ZHENG Dongqi AN Chao ZHOU Xiuwen HUANG Rui LI Dian XU;Xinran ZHENG;Dongqi AN;Chao ZHOU;Xiuwen HUANG;Rui LI

作者机构：State Key Laboratory of Structural Analysis for Industrial EquipmentDepartment of Engineering Mechanicsand International Research Center for Computational MechanicsDalian University of TechnologyDalianLiaoning Province116024China 

出 版 物：《Applied Mathematics and Mechanics(English Edition)》 (应用数学和力学（英文版）)

年 卷 期：2022年第43卷第8期

页      面：1233-1248页

核心收录：

学科分类：07[理学] 08[工学] 070104[理学-应用数学] 0701[理学-数学] 0702[理学-物理学] 0801[工学-力学（可授工学、理学学位）] 

基　　金：Project supported by the National Natural Science Foundation of China(Nos.12022209,11972103,and U21A20429) the Fundamental Research Funds for the Central Universities of China(No.DUT21LAB124)。 

主　　题：heat conduction heat source symplectic superposition method(SSM) 

摘      要：The two-dimensional(2D)transient heat conduction problems with/without heat sources in a rectangular domain under different combinations of temperature and heat flux boundary conditions are studied by a novel symplectic superposition method(SSM).The solution process is within the Hamiltonian system framework such that the mathematical procedures in the symplectic space can be implemented,which provides an exceptional direct rigorous derivation without any assumptions or predetermination of the solution forms compared with the conventional inverse/semi-inverse methods.The distinctive advantage of the SSM offers an access to new analytic heat conduction solutions.The results obtained by the SSM agree well with those obtained from the finite element method(FEM),which confirms the accuracy of the SSM.