Ln this paper, the super-inverse iterative method is proposed to compute the accurate and complete eigen-solutions for anti-plane cracks/notches with multi-materials, arbitrary opening angles and various surface condi...Ln this paper, the super-inverse iterative method is proposed to compute the accurate and complete eigen-solutions for anti-plane cracks/notches with multi-materials, arbitrary opening angles and various surface conditions. Taking the advantage of the knowledge of the variation forms of the eigen-functions, a series of numerical techniques are proposed to simplify the computation and speed up the convergence rare of the inverse iteration. A number of numerical examples are given to demonstrate the excellent accuracy, efficiency and reliability of the proposed approach.展开更多
Hamiltonian system for the problem on clamped Mindlin plate bending was established by introducing the dual variables for the generalized displacements in this letter. By separation of variables, the transverse eigen-...Hamiltonian system for the problem on clamped Mindlin plate bending was established by introducing the dual variables for the generalized displacements in this letter. By separation of variables, the transverse eigen-problem was derived based on the sympletic geometry method. With the solved sympletic eigen-values, the generalized sympletic eigen-solution was derived through eigenfunction expansion. An example of plate with all edges clamped was given. The sympletic solution system was worked out directly from the Hamiltonian system. It breaks the limitation of traditional analytic methods which need to select basis functions in advance. The results indicate that the sympletic solution method could find its more extensive applications.展开更多
A new state vector is presented for symplectic solution to three dimensional couple stress problem. Without relying on the analogy relationship, the dual PDEs of couple stress problem are derived by a new state vector...A new state vector is presented for symplectic solution to three dimensional couple stress problem. Without relying on the analogy relationship, the dual PDEs of couple stress problem are derived by a new state vector. The duality solution methodology in a new form is thus extended to three dimensional couple stress. A new symplectic orthonormality relationship is proved. The symplectic solution to couple stress theory based a new state vector is more accordant with the custom of classical elasticity and is more convenient to process boundary conditions. A Hamilton mixed energy variational principle is derived by the integral method.展开更多
基金The project is supported by the Natural Science Foundation of China.
文摘Ln this paper, the super-inverse iterative method is proposed to compute the accurate and complete eigen-solutions for anti-plane cracks/notches with multi-materials, arbitrary opening angles and various surface conditions. Taking the advantage of the knowledge of the variation forms of the eigen-functions, a series of numerical techniques are proposed to simplify the computation and speed up the convergence rare of the inverse iteration. A number of numerical examples are given to demonstrate the excellent accuracy, efficiency and reliability of the proposed approach.
文摘Hamiltonian system for the problem on clamped Mindlin plate bending was established by introducing the dual variables for the generalized displacements in this letter. By separation of variables, the transverse eigen-problem was derived based on the sympletic geometry method. With the solved sympletic eigen-values, the generalized sympletic eigen-solution was derived through eigenfunction expansion. An example of plate with all edges clamped was given. The sympletic solution system was worked out directly from the Hamiltonian system. It breaks the limitation of traditional analytic methods which need to select basis functions in advance. The results indicate that the sympletic solution method could find its more extensive applications.
文摘A new state vector is presented for symplectic solution to three dimensional couple stress problem. Without relying on the analogy relationship, the dual PDEs of couple stress problem are derived by a new state vector. The duality solution methodology in a new form is thus extended to three dimensional couple stress. A new symplectic orthonormality relationship is proved. The symplectic solution to couple stress theory based a new state vector is more accordant with the custom of classical elasticity and is more convenient to process boundary conditions. A Hamilton mixed energy variational principle is derived by the integral method.
