A novel symplectic superposition method has been proposed and developed for plate and shell problems in recent years.The method has yielded many new analytic solutions due to its rigorousness.In this study,the first e...A novel symplectic superposition method has been proposed and developed for plate and shell problems in recent years.The method has yielded many new analytic solutions due to its rigorousness.In this study,the first endeavor is made to further developed the symplectic superposition method for the free vibration of rectangular thin plates with mixed boundary constraints on an edge.The Hamiltonian system-based governing equation is first introduced such that the mathematical techniques in the symplectic space are applied.The solution procedure incorporates separation of variables,symplectic eigen solution and superposition.The analytic solution of an original problem is finally obtained by a set of equations via the equivalence to the superposition of some elaborated subproblems.The natural frequency and mode shape results for representative plates with both clamped and simply supported boundary constraints imposed on the same edge are reported for benchmark use.The present method can be extended to more challenging problems that cannot be solved by conventional analytic methods.展开更多
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 symplect...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.展开更多
基金the support from the National Natural Science Foundation of China(Grants 12022209,11972103,and 11825202)the Liaoning Revitalization Talents Program of China(Grant XLYC1807126)the Fundamental Research Funds for the Central Universities(Grant DUT21LAB124).
文摘A novel symplectic superposition method has been proposed and developed for plate and shell problems in recent years.The method has yielded many new analytic solutions due to its rigorousness.In this study,the first endeavor is made to further developed the symplectic superposition method for the free vibration of rectangular thin plates with mixed boundary constraints on an edge.The Hamiltonian system-based governing equation is first introduced such that the mathematical techniques in the symplectic space are applied.The solution procedure incorporates separation of variables,symplectic eigen solution and superposition.The analytic solution of an original problem is finally obtained by a set of equations via the equivalence to the superposition of some elaborated subproblems.The natural frequency and mode shape results for representative plates with both clamped and simply supported boundary constraints imposed on the same edge are reported for benchmark use.The present method can be extended to more challenging problems that cannot be solved by conventional analytic methods.
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)。
文摘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.
