Analysis of 2-D bimodular materials and wrinkled membranes based on the parametric variational principle and co-rotational approach

2014 ◽  
Vol 98 (10) ◽  
pp. 721-746 ◽  
Author(s):  
L. Zhang ◽  
Q. Gao ◽  
H. W. Zhang
Keyword(s):  
Variational Principle ◽  
Parametric Variational Principle

scholarly journals A Numerical Method Based on the Parametric Variational Principle for Simulating the Dynamic Behavior of the Pantograph-Catenary System

2018 ◽  
Vol 2018 ◽  
pp. 1-21 ◽  
Author(s):  
Dongdong He ◽  
Qiang Gao ◽  
Wanxie Zhong
Keyword(s):  
Variational Principle ◽  
Dynamic Behavior ◽  
Integration Method ◽  
Time Integration ◽  
Dynamic Responses ◽  
Precise Integration ◽  
Contact Wire ◽  
Parametric Variational Principle ◽  
The Matrix ◽  
Catenary System

Based on the finite element method (FEM), the parametric variational principle (PVP) is combined with a numerical time-domain integral method to simulate the dynamic behavior of the pantograph-catenary system. Based on PVP, formulations for the nonlinear droppers in the catenary and for the contact between the pantograph and the contact wire are proposed. The formulations can accurately determine the tension state or compression state of the nonlinear droppers and the contact state between the pantograph and the contact wire. Based on the periodicity of the catenary and the precise integration method (PIM), a numerical time-integration method is developed for the dynamic responses of the catenary. For this method, the matrix exponential of only one unit cell of the catenary is computed, which greatly improves the computational efficiency. Moreover, the validation shows that the formulations can compute the contact force accurately and represent the nonlinearity of the droppers, which demonstrates the accuracy and reliability of the proposed method. Finally, the dynamic behaviors of the pantograph-catenary system with different types of catenaries are simulated.

Parametric Variational Principle for Bi-Modulus Materials and Its Application to Nacreous Bio-Composites

2016 ◽  
Vol 08 (06) ◽  
pp. 1650082 ◽  
Author(s):  
Liang Zhang ◽  
Huiting Zhang ◽  
Jian Wu ◽  
Bo Yan ◽  
Mengkai Lu
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Variational Principle ◽  
Principal Stress ◽  
Stress Strain ◽  
Element Analysis ◽  
Parametric Variational Principle ◽  
Strain Relation ◽  
Stress Strain Relation ◽  
Nonlinear Stress

Bi-modulus materials have different moduli in tension and compression and the stress–strain relation depends on principal stress that is unknown before displacement is determined. Establishment of variational principle is important for mechanical analysis of materials. First, parametric variational principle (PVP) is proposed for static analysis of bi-modulus materials and structures. A parametric variable indicating state of principal stress is included in the potential energy formulation and the nonlinear stress–strain relation is evolved into a linear complementarity constraint. Convergence of finite element analysis is thus improved. Then the proposed variational principle is extended to a dynamic problem and the dynamic equation can be derived based on Hamilton’s principle. Finite element analysis of nacreous bio-composites is performed, in which a unilateral contact behavior between two hard mineral bricks is modeled using the bi-modulus stress–strain relation. Effective modulus of composites can be determined numerically and stress mechanism of “tension–shear chain” in nacre is revealed. A delayed effect on stress propagation is found around the “gaps” between mineral bricks, when a tension force is loaded to nacreous bio-composites dynamically.

Parametric Variational Principle of Viscoplastic Lubrication Model

1992 ◽  
Vol 114 (4) ◽  
pp. 731-735 ◽  
Author(s):  
C. W. Wu ◽  
W. X. Zhong ◽  
L. X. Qian ◽  
L. C. Hu ◽  
S. M. Sun
Keyword(s):  
Mathematical Model ◽  
Mathematical Method ◽  
Variational Principle ◽  
Original Problem ◽  
Engineering Application ◽  
Tangential Velocity ◽  
Control Vector ◽  
Parametric Variational Principle ◽  
Variational Process ◽  
The Mathematical Model

An effective mathematical method to deal with the viscoplastic lubrication model is presented here by applying the parametric variational principle (Zhong, 1985). The plastic slippage of lubricant would occur at the lubricated surfaces under isothermal lubrication. The boundary tangential velocity, therefore, can be taken as the parametric vector (or the control vector) in variational process. The mathematical model of the original problem is finally reduced to a complementarity problem. The algorithm presented in this paper is simple and reliable and shows promise in engineering application.

scholarly journals A parametric variational principle and residuality

2009 ◽  
Vol 256 (11) ◽  
pp. 3568-3587 ◽  
Author(s):  
Robert Deville ◽  
Antonín Procházka
Keyword(s):  
Variational Principle ◽  
Parametric Variational Principle

The parametric variational principle for elastoplasticity

1988 ◽  
Vol 4 (2) ◽  
pp. 134-137 ◽  
Author(s):  
Zhong Wanxie ◽  
Zhang Roulei
Keyword(s):  
Variational Principle ◽  
Parametric Variational Principle
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