Generalized Variational Principles of Quasi-Static Electro-Magneto-Thermo-Elasticity

2009 ◽  
Vol 419-420 ◽  
pp. 153-156 ◽  
Author(s):  
Hai Yan Song ◽  
Zhen Gong Zhou ◽  
Li Fu Liang ◽  
Zong Min Liu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Integral Method ◽  
Variational Principles ◽  
Computational Method ◽  
Variational Integral ◽  
Theoretical Support ◽  
Generalized Variational Principles ◽  
Variational Integral Method ◽  
Element Method

Finite element method is an approximate computational method which is widely used and continuously developed. Variational principles are the foundation of finite element method. In this paper, the generalized variational principles of quasi-static electro-magneto-thermo-elasticity are established using variational integral method. And these variational principles can be degenerated to be variational principles of simple coupling properties materials, which offer theoretical support for finite element method of coupling problems of electro-magneto-thermo-elastic.

Generalized variational principles in the finite-element method.

AIAA Journal ◽  
1969 ◽  
Vol 7 (7) ◽  
pp. 1254-1260 ◽  
Author(s):  
B. E. GREENE ◽  
R. E. JONES ◽  
R. W. McLAY ◽  
D. R. STROME
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Variational Principles ◽  
The Finite Element Method ◽  
Generalized Variational Principles ◽  
Element Method

Generalized Variational Principles of Electro-Magneto-Thermo-Elasto-Dynamics

2009 ◽  
Author(s):  
Haiyan Song ◽  
Zhengong Zhou ◽  
Lifu Liang ◽  
Zongmin Liu
Keyword(s):  
Temperature Field ◽  
Numerical Methods ◽  
Integral Method ◽  
Variational Principles ◽  
Magnetic Behavior ◽  
Coupled Problems ◽  
Variational Integral ◽  
Theoretical Support ◽  
Electric Behavior ◽  
Generalized Variational Principles

Based on coupled properties of electricity, magnetism, heat and force, it is hard to solve the material’s electric behavior, magnetic behavior, temperature field, stress distribution and deformation distribution under the action of all kinds of external fields in usual way. It is necessary that the problems are solved by numerical methods. However variational principle is the foundation of these numerical methods which were widely used. In this paper, the generalized variational principles of electro-magneto-thermo-elasto-dynamics are established by variational integral method. And these variational principles can be degenerated into variational principles of simple coupled properties materials, which offer theoretical support for numerical methods of coupled problems of electro-magneto-thermo-elasticity.

scholarly journals A Variational Finite Element Method for Solving the Blade-to-Blade Flow in Centrifugal Compressor’s Cascades With Splitter Blades on an Arbitrary Streamsheet of Revolution and a Mathematical Treatment to the Region Behind Cascades

1985 ◽  
Author(s):  
Chen Yulin ◽  
Chen Kangmin ◽  
Zhang Dangfang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Flow Field ◽  
Variational Principles ◽  
Computational Method ◽  
Mathematical Treatment ◽  
Exit Angle ◽  
Algebraic Equations ◽  
Kutta Condition ◽  
Element Method

A variational finite element method for solving the blade-to-blade flow in centrifugal compressor’s cascades with splitter blades on an arbitrary streamsheet of revolution is suggested in this paper. At first, the variational principles Ref.(1) is modified, then the variational principle after modification is discretized by eight node isoparametric finite elements to carry out the system of nonlinear algebraic equations for solving the velocity potential function. Finally, the flow field which agrees with Kutta condition and has an region behind the cascade of enough length has been worked out. In this paper, it has been discovered that when the region behind cascade L3 spreads too long the system of equations might become unsolvable as a suitable exit angle β2 can't be found. The linear relation between the velocity defference of the two side of the trailing edge and the exit angle β2 has been found, it shows the range of linear variation of β2 decreases with the increasing of the length of the region behind cascades, in addition, the linear variational relation between tan⁡β2 and L3 has also been obtained. The iterative computational method for the flow field with different length L3 is used to get the solution of flow field satisfying Kutta condition and with enough length L3.

Development of Bifurcation Analysis Method for Rate Dependent Materials

2019 ◽  
Vol 794 ◽  
pp. 220-225
Author(s):  
Daiki Towata ◽  
Yuichi Tadano
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Bifurcation Analysis ◽  
Stiffness Matrix ◽  
Computational Method ◽  
Analysis Method ◽  
The Finite Element Method ◽  
Tangent Stiffness Matrix ◽  
Rate Dependent ◽  
Element Method

In this study, a novel numerical method to analyze the bifurcation problemof a rate dependent material using the finite element method is proposed. The consistent stiffness matrix, which is required for a bifurcation analysis using the finite element method, for a rate dependent material is generally hard to compute, therefore, a computational method to calculate the tangent stiffness matrix based on a numerical differential is introduced so that exact bifurcation analyses for the rate dependent material can be conducted. A numerical example of the proposed method is demonstrated, and the adequacy of the proposed method is discussed.

A Finite Element Method-Based Potential Theory Approach for Optimal Ice Routing

2017 ◽  
Vol 139 (6) ◽  
Author(s):  
Henry Piehl ◽  
Aleksandar-Saša Milaković ◽  
Sören Ehlers
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Fuel Consumption ◽  
Computational Method ◽  
Ice Thickness ◽  
Test Problems ◽  
Theory Approach ◽  
Optimal Route ◽  
Cost Information ◽  
Element Method

Shipping in ice-covered regions has gained high attention within recent years. Analogous to weather routing, the occurrence of ice in a seaway affects the selection of the optimal route with respect to the travel time or fuel consumption. The shorter, direct path between two points—which may lead through an ice-covered area—may require a reduction of speed and an increase in fuel consumption. A longer, indirect route, could be more efficient by avoiding the ice-covered region. Certain regions may have to be avoided completely, if the ice thickness exceeds the ice-capability of the ship. The objective of this study is to develop a computational method that combines coastline maps, route cost information (e.g., ice thickness), transport task, and ship properties to find the optimal route between port of departure, A, and port of destination, B. The development approach for this tool is to formulate the transport task in the form of a potential problem, solve this equation with a finite element method (FEM), and apply line integration and optimization to determine the best route. The functionality of the method is first evaluated with simple test problems and then applied to realistic transport scenarios.

Finite Element Method for Stochastic Beams Based on Variational Principles

1997 ◽  
Vol 64 (3) ◽  
pp. 664-669 ◽  
Author(s):  
Y.-J. Ren ◽  
I. Elishakoff ◽  
M. Shinozuka
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Covariance Function ◽  
Variational Principles ◽  
Joint Probability ◽  
Accurate Solution ◽  
Joint Probability Distribution ◽  
Covariance Functions ◽  
The Mean ◽  
Element Method

This paper proposes a new version (fundamentally different from the existing ones) of finite element method for the mean and covariance functions of the displacement for bending beams with spatially random stiffness. Apart from the conventional finite element method for stochastic problems, which utilizes either perturbation or series expansion technique or the Monte Carlo simulation, the present method is based on the newly established variational principles. The finite element scheme is formulated directly with respect to the mean function and covariance function, rather than perturbed components of the displacement. It takes into account an information on joint probability distribution function of the random stiffness to obtain the covariance function of the displacement. Therefore, the accurate solution can be obtained even if the coefficient of variation of the random stiffness is large, in contrast to conventional technique. Several examples are given to illustrate the advantage of the proposed method, compared with the conventional ones.

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