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Acta Mechanica Sinica 2011年第6期27卷 929-937页

作者： Wei-An Yao Xiao-Fei Hu Feng Xiao State Key Laboratory of Structural Analysis for Industrial Equipment Dalian University of Technology 116024 Dalian China Department of Computer Science Dalian Medical University 116044 Dalian China

This paper analyses the bending of rectangular orthotropic plates on a Winkler elastic *** definition of symplectic inner product and symplectic space formed by generalized displacements establish dual variables and dual equations in the symplectic *** operator matrix of the equation set is proven to be a Hamilton operator *** of variables and eigenfunction expansion creates a basis for analyzing the bending of rectangular orthotropic plates on Winkler elastic foundation and obtaining solutions for plates having any boundary *** is discussion of symplectic eigenvalue problems of orthotropic plates under two typical boundary conditions,with opposite sides simply supported and opposite sides *** equations of eigenvalues and symplectic eigenvectors in analytical form *** solutions using two examples are presented to show the use of the new methods described in this *** verify the accuracy and convergence,a fully simply supported plate that is fully and simply supported under uniformly distributed load is used to compare the classical Navier method,the Levy method and the new *** show that the new technique has good accuracy and better convergence speed than other methods,especially in relation to internal forces.A fully clamped rectangular plate on Winkler foundation is solved to validate application of the new methods,with solutions compared to those produced by the Galerkin method.

关键词： Orthotropic plate symplectic space Winklerelastic foundation Analytical solution

STRESS SINGULARITY ANALYSIS OF MULTI-MATERIAL WEDGES UNDER ANTIPLANE DEFORMATION

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Acta Mechanica Solida Sinica 2013年第2期26卷 151-160页

作者： Xiaofei Hu Weian Yao State Key Laboratory of Structural Analysis for Industrial Equipment Dalian University of Technology

With the help of the coordinate transformation technique, the symplectic dual solv- ing system is developed for multi-material wedges under antiplane deformation. A virtue of present method is that the compatibility conditions at interfaces of a multi-material wedge are expressed directly by the dual variables, therefore the governing equation of eigenvalue can be derived easily even with the increase of the material number. Then, stress singularity on multi-material wedges under antiplane deformation is investigated, and some solutions can be presented to show the validity of the method. Simultaneously, an interesting phenomenon is found and proved strictly that one of the singularities of a special five-material wedge is independent of the crack direction.

关键词： analytical method eigenvalues interface crack symplectic space

Automorphism Groups of Some Finite p-Groups

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Algebra Colloquium 2016年第4期23卷 623-650页

作者： Heguo Liu Yulei Wang Department of Mathematics Hubei University Wuhan 430062 China Department of Mathematics Henan University of Technology Zhengzhou 450001 China

The automorphism group of G is determined, where G is a nonabelian p-group given by a central extension as 1→Zpm→G→Zp×…×Zp→1 such that its derived subgroup has order p.

关键词： generalized extraspecial p-group symplectic space orthogonal space auto-morphism central extension

symplectic Structures of Two Kinds of Nonsymmetric Differential Operators

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Acta Mathematicae Applicatae Sinica 2015年第2期31卷 543-556页

作者： Wei-hua YANG School of Mathematics and Physics Beijing University of Technology

Non-self-adjoint quasi-differential expression M and its formal adjoint M＋may generate nonsymmetric ordinary differential operators. Although minimal operators T0, T＋0 generated by M, M＋are not symmetric, they form an adjoint pair. In this paper, author studies regularly solvable operators with respect to the adjoint pair T0, T＋0 in two kinds of conditions and give their geometry description in the corresponding ways.

关键词： regularly solvable operators symplectic space self-adjoint operator pair

PARADOX SOLUTION ON ELASTIC WEDGE DISSIMILAR MATERIALS

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Applied Mathematics and Mechanics(English Edition) 2003年第8期24卷 961-969页

作者：姚伟岸张兵茹 State Key Laboratory of Structural Analysis of Industrial Equipment Dalian University of Technology Dalian 116023 P.R.China State Key Laboratory of Structural Analysis of Industrial Equipment Dalian University of Technology Dalian 116023 P.R.Chinaccording to the Hellinger-Reissner variational principle and introducing proper transformation of variables the problem on elastic wedge dissimilar materials can be led to Hamiltonian system so the solution of the problem can be got by employing the separation of variables method and symplectic eigenfunction expansion under symplectic space which consists of original variables and their dual variables . The eigenvalue - 1 is a special one of all symplectic eigenvalue for Hamiltonian system in polar coordinate . In general the eigenvalue - 1 is a single eigenvalue and the classical solution of an elastic wedge dissimilar materials subjected to a unit concentrated couple at the vertex is got directly by solving the eigenfunction vector for eigenvalue - 1. But the eigenvalue - 1 becomes a double eigenvalue when the vertex angles and modulus of the materials satisfy certain definite relationships and the classical solution for the stress distribution becomes infinite at this moment that is the paradox should occur. Here the Jordan form eigenfunction vector for eigenvalue - 1 exists and solution of the paradox on elastic wedge dissimilar materials subjected to a unit concentrated couple at the vertex is obtained directly by solving this special Jordan form eigenfunction. The result shows again that the solutions of the special paradox on elastic wedge in the classical theory of elasticity are just Jordan form solutions in symplectic space under Hamiltonian system .

According to the Hellinger-Reissner variational principle and introducing proper transformation of variables , the problem on elastic wedge dissimilar materials can be led to Hamiltonian system, so the solution of the problem can be got by employing the separation of variables method and symplectic eigenfunction expansion under symplectic space, which consists of original variables and their dual variables . The eigenvalue - 1 is a special one of all symplectic eigenvalue for Hamiltonian system in polar coordinate . In general, the eigenvalue - 1 is a single eigenvalue, and the classical solution of an elastic wedge dissimilar materials subjected to a unit concentrated couple at the vertex is got directly by solving the eigenfunction vector for eigenvalue - 1. But the eigenvalue - 1 becomes a double eigenvalue when the vertex angles and modulus of the materials satisfy certain definite relationships and the classical solution for the stress distribution becomes infinite at this moment, that is, the paradox should occur. Here the Jordan form eigenfunction vector for eigenvalue - 1 exists, and solution of the paradox on elastic wedge dissimilar materials subjected to a unit concentrated couple at the vertex is obtained directly by solving this special Jordan form eigenfunction. The result shows again that the solutions of the special paradox on elastic wedge in the classical theory of elasticity are just Jordan form solutions in symplectic space under Hamiltonian system .

关键词： paradox symplectic space Jordan form elastic wedge