Method of Virtual Power Applied to Cosserat Surfaces With Deformable Directors

1993 ◽  
Vol 46 (11S) ◽  
pp. S266-S278
Author(s):  
Boris Krajnc Alves ◽  
Jacob Lubliner
Keyword(s):  
Direct Method ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Momentum Balance ◽  
Power Method ◽  
Virtual Power ◽  
Balance Equations ◽  
Dimensional Theory ◽  
Momentum Balance Equation ◽  
Cosserat Surface

Following a brief outline of the method of virtual power, the local equations of motion for a Cosserat surface with inextensible directors are derived by means of this method. The model obtained coincides with the results derived from three-dimensional theory by Simo and Fox. Subsequently the model is extended so as to account for deformable directors. Besides the linear-momentum and moment-of-momentum balance equations, one additional scalar equation is derived. This equation replaces the director-momentum balance equation of Naghdi and therefore eliminates the necessity of introducing constitutive restrictions. The equivalence between the model derived by the virtual-power method and the results from the direct method of Naghdi are finally noted.

scholarly journals Implicit Euler-Lagrange difference scheme for three-dimensional gasdynamics calculations using concerted approximations to mass and momentum balance equations

2016 ◽  
pp. 1-24 ◽  
Author(s):  
Vladimir Anontol’evich Gasilov ◽  
Alexander Yur’evich Krukovskiy ◽  
Yuri Andreevich Poveschenko ◽  
Ilia Pavlovich Tsygvintsev
Keyword(s):  
Difference Scheme ◽  
Three Dimensional ◽  
Momentum Balance ◽  
Balance Equations

The 2011 Koiter Lecture: The Simple Logic of Classical Nonlinear Thermodynamic Shell Theory

2012 ◽  
Vol 79 (4) ◽  
Author(s):  
J. G. Simmonds
Keyword(s):  
Energy Density ◽  
Constitutive Relations ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Second Law Of Thermodynamics ◽  
Second Law ◽  
Virtual Power ◽  
Ill Conditioning ◽  
Simple Logic ◽  
Reduced Forms

A classical nonlinear thermodynamic theory of elastic shells is derived by specializing the three-dimensional equations of motion and the second law of thermodynamics to a very general, shell-like body. No assumptions are made on how unknowns vary through the thickness. Extensional and bending strains are derived from the equations of motion via the principle of virtual power. The Coleman-Noll procedure plus the second law applied to an assumed form of the first law leads to constitutive relations plus reduced forms of the first and second laws. To avoid potential ill conditioning, a Legendre-Fenchel transformation is used to define a mixed-energy density, the logical place to impose the constitutive Kirchhoff hypothesis, if desired, because such an energy density rests, ultimately, on experiments. The Ladevèze-Pécastaings treatment of three-dimensional edge effects to obtain accurate two-dimensional solutions is discussed.

404 Experimental Study on a Three-Dimensional Wall Jet : Momentum Balance Equation

2009 ◽  
Vol 2009.58 (0) ◽  
pp. 231-232
Author(s):  
Takaaki NISHIZUKA ◽  
Yoshihiro INOUE ◽  
Shintaro YAMASHITA ◽  
Haruhisa YANO
Keyword(s):  
Experimental Study ◽  
Balance Equation ◽  
Three Dimensional ◽  
Momentum Balance ◽  
Wall Jet ◽  
Momentum Balance Equation

A Three-Dimensional Plasticity and Momentum Model for Ship Resistance in Level Ice

1991 ◽  
Vol 113 (1) ◽  
pp. 53-60 ◽  
Author(s):  
C. H. Luk
Keyword(s):  
Numerical Methods ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Analytical Techniques ◽  
Full Scale ◽  
Momentum Balance ◽  
Ship Resistance ◽  
Plastic Limit Analysis ◽  
Level Ice ◽  
Ice Resistance

In this paper, a three-dimensional analysis is presented for calculating the level ice resistance for ships that have conventional hull forms. Comparisons with published ship resistance data and other analytical predictions are also provided. The present approach combines two analytical techniques: 1) plastic limit analysis is used to describe the ice failure mechanism and the associated ice velocity field; and 2) linear and angular momentum balances determine the average ice resistance for a ship. In the momentum balance, potential flow theory is used to describe the water motion induced by the icebreaking process. Existing methods for determining ship resistance in ice include numerical methods which depend on solutions of equations of motion that describe the dynamic interaction between the ice and the ship, and empirical methods which depend on model and full-scale icebreaker data to generate empirical correlations for ship resistance. The present results compare reasonably well with published model-scale and full-scale icebreaker data. Comparisons with predictions based on other numerical methods are also discussed.

Dynamic Variational Principles for Discontinuous Elastic Fields

1979 ◽  
Vol 23 (02) ◽  
pp. 115-122 ◽  
Author(s):  
M. Cengiz Dökmeci
Keyword(s):  
Variational Principles ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Governing Equations ◽  
Natural Boundary ◽  
Dimensional Theory ◽  
Elastic Fields ◽  
Complete Set ◽  
Natural Boundary Conditions

Various forms of variational principles are derived for the three-dimensional theory of elastodynamics. The continuity requirements on the fields of stresses or strains and/or displacements are relaxed through Friedrichs's transformation. Thus, the generalized forms of certain types of earlier variational principles' are systematically constructed using a basic principle of physics. The variational principles derived herein are shown to generate, as the appropriate Euler equations, the complete set of the governing equations of linear elastodynamics, that is, the stress equations of motion, the strain displacement relations, the mixed natural boundary conditions, the constitutive equations, the natural initial conditions, and the jump conditions. Similarly, generalized variational principles are established for the nonlinear theory of elastodynamics, for the incremental motions in linear elasticity, and for an elastic Cosserat continuum, as well.

scholarly journals Modeling strong motions produced by earthquakes with two-dimensional numerical codes

1988 ◽  
Vol 78 (1) ◽  
pp. 109-121
Author(s):  
Donald V. Helmberger ◽  
John E. Vidale
Keyword(s):  
Wave Equation ◽  
Asymptotic Form ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Cylindrical Coordinates ◽  
Dimensional Theory ◽  
Dimensional Solution ◽  
Source Excitation ◽  
Dislocation Sources

Abstract We present a scheme for generating synthetic point-source seismograms for shear dislocation sources using line source (two-dimensional) theory. It is based on expanding the complete three-dimensional solution of the wave equation expressed in cylindrical coordinates in an asymptotic form which provides for the separation of the motions into SH and P-SV systems. We evaluate the equations of motion with the aid of the Cagniard-de Hoop technique and derive close-formed expressions appropriate for finite-difference source excitation.

Theory of Laminated Plates

1971 ◽  
Vol 38 (1) ◽  
pp. 231-238 ◽  
Author(s):  
C. T. Sun
Keyword(s):  
Equations Of Motion ◽  
Three Dimensional ◽  
Continuum Theory ◽  
Laminated Plates ◽  
Harmonic Waves ◽  
Two Dimensional ◽  
Laminated Plate ◽  
Governing Equations ◽  
Dimensional Theory ◽  
Rotatory Inertia

A two-dimensional theory for laminated plates is deduced from the three-dimensional continuum theory for a laminated medium. Plate-stress equations of motion, plate-stress-strain relations, boundary conditions, and plate-displacement equations of motion are presented. The governing equations are employed to study the propagation of harmonic waves in a laminated plate. Dispersion curves are presented and compared with those obtained according to the three-dimensional continuum theory and the exact analysis. An approximate solution for flexural motions obtained by neglecting the gross and local rotatory inertia terms is also discussed.

Validation of a Belt Model for Prediction of Hub Forces from a Rolling Tire4

2009 ◽  
Vol 37 (2) ◽  
pp. 62-102 ◽  
Author(s):  
C. Lecomte ◽  
W. R. Graham ◽  
D. J. O’Boy
Keyword(s):  
Internal Pressure ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Prediction Method ◽  
Analytical Models ◽  
Beam Model ◽  
Impedance Boundary ◽  
Bending Waves ◽  
Tire Rotation ◽  
Three Dimensional Models

Abstract An integrated model is under development which will be able to predict the interior noise due to the vibrations of a rolling tire structurally transmitted to the hub of a vehicle. Here, the tire belt model used as part of this prediction method is first briefly presented and discussed, and it is then compared to other models available in the literature. This component will be linked to the tread blocks through normal and tangential forces and to the sidewalls through impedance boundary conditions. The tire belt is modeled as an orthotropic cylindrical ring of negligible thickness with rotational effects, internal pressure, and prestresses included. The associated equations of motion are derived by a variational approach and are investigated for both unforced and forced motions. The model supports extensional and bending waves, which are believed to be the important features to correctly predict the hub forces in the midfrequency (50–500 Hz) range of interest. The predicted waves and forced responses of a benchmark structure are compared to the predictions of several alternative analytical models: two three dimensional models that can support multiple isotropic layers, one of these models include curvature and the other one is flat; a one-dimensional beam model which does not consider axial variations; and several shell models. Finally, the effects of internal pressure, prestress, curvature, and tire rotation on free waves are discussed.

Membrane theory

2017 ◽  
Author(s):  
David J. Steigmann
Keyword(s):  
Three Dimensional ◽  
Thin Sheets ◽  
Two Dimensional ◽  
Leading Order ◽  
Membrane Theory ◽  
Dimensional Theory ◽  
Small Thickness

This chapter develops two-dimensional membrane theory as a leading order small-thickness approximation to the three-dimensional theory for thin sheets. Applications to axisymmetric equilibria are developed in detail, and applied to describe the phenomenon of bulge propagation in cylinders.

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