Derivation of Plate and Rod Equations for a Piezoelectric Body from a Mixed Three-Dimensional Variational Principle

2000 ◽  
pp. 23-50 ◽  
Author(s):  
S. Vidoli ◽  
R. C. Batra
Keyword(s):  
Variational Principle ◽  
Three Dimensional ◽  
Piezoelectric Body

Modified Mixed Variational Principle and the State-Vector Equation for Elastic Bodies and Shells of Revolution

1992 ◽  
Vol 59 (3) ◽  
pp. 587-595 ◽  
Author(s):  
Charles R. Steele ◽  
Yoon Young Kim
Keyword(s):  
Variational Principle ◽  
Equations Of State ◽  
Classical Mechanics ◽  
Three Dimensional ◽  
Shells Of Revolution ◽  
Elastic Bodies ◽  
Mixed Variational Principle ◽  
Stress Components ◽  
Independent Variable ◽  
Nonsymmetric Deformation

A modified mixed variational principle is established for a class of problems with one spatial variable as the independent variable. The specific applications are on the three-dimensional deformation of elastic bodies and the nonsymmetric deformation of shells of revolution. The possibly novel feature is the elimination in the variational formulation of the stress components which cannot be prescribed on the boundaries. The result is a form exactly analogous to classical mechanics of a dynamic system, with the equations of state exactly in the form of the canonical equations of Hamilton. With the present approach, the correct scale factors of the field variables to make the system self-adjoint are readily identified, and anisotropic materials including composites can be handled effectively. The analysis for shells of revolution is given with and without the transverse shear deformation considered.

A Numerical Three-Dimensional Model for the Contact of Rough Surfaces by Variational Principle

1996 ◽  
Vol 118 (1) ◽  
pp. 33-42 ◽  
Author(s):  
Xuefeng Tian ◽  
Bharat Bhushan
Keyword(s):  
Variational Principle ◽  
Contact Problem ◽  
Rough Surfaces ◽  
Three Dimensional ◽  
Computation Time ◽  
Inversion Method ◽  
Three Dimensional Model ◽  
Perfectly Plastic ◽  
Contact Points ◽  
Uniqueness Of The Solution

A new numerical method for the analysis of elastic and elastic-plastic contacts of two rough surfaces has been developed. The method is based on a variational principle in which the real area of contact and contact pressure distribution are those which minimize the total complementary potential energy. The present variational approach guarantees the uniqueness of the solution of the contact problem and significantly reduces the computation time as compared with the conventional matrix inversion method, and thus, makes it feasible to solve 3-D contact problem with large number of contact points. The model is extended to elastic-perfectly plastic contacts. The model is used to predict contact statistics for computer generated surfaces.

Coulomb traction on a penny-shaped crack in a three dimensional piezoelectric body

2010 ◽  
Vol 81 (6) ◽  
pp. 685-700 ◽  
Author(s):  
Qun Li ◽  
Andreas Ricoeur ◽  
Meinhard Kuna
Keyword(s):  
Three Dimensional ◽  
Piezoelectric Body ◽  
Penny Shaped Crack ◽  
Shaped Crack

The Cosserat Spectrum Theory in Thermoelasticity and Application to the Problem of Heat Flow Past a Rigid Spherical Inclusion

1998 ◽  
Vol 65 (3) ◽  
pp. 614-618 ◽  
Author(s):  
Wensen Liu ◽  
X. Markenscoff ◽  
M. Paukshto
Keyword(s):  
Variational Principle ◽  
Heat Flow ◽  
Displacement Field ◽  
Elastic Energy ◽  
Rigid Inclusion ◽  
Spherical Inclusion ◽  
Three Dimensional ◽  
Practical Method ◽  
Cosserat Spectrum ◽  
Thermoelastic Displacement

We apply the Cosserat Spectrum theory to boundary value problems in thermoelasticity and show the advantages of this method. The thermoelastic displacement field caused by a general heat flow around a spherical rigid inclusion is calculatedand the results show that the discrete Cosserat eigenfunctions converge fast and thus provide a practical method for solving three-dimensional problems in thermoelasticity. In the case of uniform heat flow, the solution is obtained analytically in closed form and a variational principle within the frame of the Cosserat Spectrum theory shows that the solution maximizes the elastic energy.

Another look at unidirectional turbulent flow

1995 ◽  
Vol 287 ◽  
pp. 75-92 ◽  
Author(s):  
A. J. Reynolds ◽  
K. Wieghardt
Keyword(s):  
Variational Principle ◽  
Velocity Profile ◽  
Turbulent Flow ◽  
Three Dimensional ◽  
Core Region ◽  
Flat Channel ◽  
Mean Velocity ◽  
Channel One ◽  
The Core ◽  
The Mean

Here we consider the mean velocity profile in the core region of a unidirectional turbulent flow, that is, a flow in which the turbulent motion is superposed upon parallel time-averaged streamlines. A kinematical variational principle, originally developed for three-dimensional free-turbulent motions, is shown to be applicable to significant parts of the velocity profiles for flows of both Couette and Poiseuille types. In addition to pure plane Couette and pure plane Poiseuille flows, the motions considered include a variety of admixtures produced by blowing through a wide flat channel one of whose walls comprises a belt which moves either in the direction of the blowing or counter to it.

scholarly journals Three-Dimensional Inviscid Flow Computations in a Spatial Turbopump Inducer Using a Distributed Loss Model

1992 ◽  
Author(s):  
E. M. El Ghazzani ◽  
G. Bois ◽  
P. Geai ◽  
F. Leboeuf
Keyword(s):  
Finite Element ◽  
Variational Principle ◽  
Euler Equations ◽  
Flow Model ◽  
Three Dimensional ◽  
Inviscid Flow ◽  
Finite Element Discretization ◽  
Element Discretization ◽  
Rotational Part ◽  
Inviscid Flow Model

A Clebsch formulation, completely equivalent to the Euler equations is implemented from an Eulerian type variational principle. It leads to the decomposition of the velocity field into a potential and a rotational part and, thus, provides a unified solution scheme for potential and Euler equations. Although based on an inviscid flow model, this formulation includes a loss scheme. The numerical method uses a finite element discretization. Particular treatment of convection terms allows a low numerical diffusion. A pseudo time evolution enables a better stability behaviour. Numerical calculations have been performed on an industrial configuration of spatial turbopump. Different comparisons ere showed between measurements, calculations without and with distributed losses.

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