Symplectic Elasticity

10.1142/6656 ◽  
2009 ◽  
Author(s):  
Weian Yao ◽  
Wanxie Zhong ◽  
Chee Wah Lim
Keyword(s):  
Symplectic Elasticity

Mechanism of Cross Bow in Single-Roll Transmission Temper Mill

2010 ◽  
Vol 145 ◽  
pp. 216-222 ◽  
Author(s):  
Jie Tao Dai ◽  
Qing Dong Zhang
Keyword(s):  
Finite Element ◽  
Analytical Calculation ◽  
Element Model ◽  
Calculation Model ◽  
Vertical Extension ◽  
Width Direction ◽  
Symplectic Elasticity ◽  
The Cross ◽  
The Relationship ◽  
Roll Drive

In a 1220mm temper mill, the cross bow was serious, which seriously affected the unit’s output and efficiency. In order to solve this problem, the mechanism of cross bow is studied in rolling of single-roll transmission temper mill. First, established the FEM of the single-roll drive temper mill rolling, analyzed the distribution factors of vertical extension in thickness. Second, used the method of symplectic elasticity to establish the analytical calculation model to study the relationship between the cross bow with the uneven vertical extension, explained the mechanism of cross bow. Then, used ANSYS to establish finite element model which further analyzed the cross bow under different distribution of extension in width direction. On the basis of analyzed the mechanism, proposed measures to reduce the value of cross bow. These measures have been applied in production; the effect of application was obvious.

Symplectic Elasticity: Theory and Applications

2010 ◽  
Vol 63 (5) ◽  
Author(s):  
C. W. Lim ◽  
X. S. Xu
Keyword(s):  
Eigenvalue Problem ◽  
Body Movement ◽  
Classical Mechanics ◽  
Plane Elasticity ◽  
Theoretical Physics ◽  
Solution Technique ◽  
Inverse Approach ◽  
Symplectic Elasticity ◽  
Elastic Cylinders ◽  
The Many

Many of the early works on symplectic elasticity were published in Chinese and as a result, the early works have been unavailable and unknown to researchers worldwide. It is the main objective of this paper to highlight the contributions of researchers from this part of the world and to disseminate the technical knowledge and innovation of the symplectic approach in analytic elasticity and applied engineering mechanics. This paper begins with the history and background of the symplectic approach in theoretical physics and classical mechanics and subsequently discusses the many numerical and analytical works and papers in symplectic elasticity. This paper ends with a brief introduction of the symplectic methodology. A total of more than 150 technical papers since the middle of 1980s have been collected and discussed according to various criteria. In general, the symplectic elasticity approach is a new concept and solution methodology in elasticity and applied mechanics based on the Hamiltonian principle with Legendre’s transformation. The superiority of this symplectic approach with respect to the classical approach is at least threefold: (i) it alters the classical practice and solution technique using the semi-inverse approach with trial functions such as those of Navier, Lévy, and Timoshenko; (ii) it consolidates the many seemingly scattered and unrelated solutions of rigid body movement and elastic deformation by mapping with a series of zero and nonzero eigenvalues and their associated eigenvectors; and (iii) the Saint–Venant problems for plane elasticity and elastic cylinders can be described in a new system of equations and solved. A unique feature of this method is that bending of plate becomes an eigenvalue problem and vibration becomes a multiple eigenvalue problem.

Sign in / Sign up

Export Citation Format

Share Document