scholarly journals Structural stability in porous elasticity

2006 ◽  
Vol 462 (2073) ◽  
pp. 2593-2605 ◽  
Author(s):  
S Chiriţă ◽  
M Ciarletta ◽  
B Straughan
Keyword(s):  
Elastic Body ◽  
Structural Stability ◽  
Elastic Deformation ◽  
Coupled System ◽  
System Of Equations ◽  
Coupling Coefficients ◽  
Linearized System

We consider the linearized system of equations for an elastic body with voids as derived by Cowin & Nunziato. We demonstrate that the solution depends continuously on changes in the coefficients, which couple the equations of elastic deformation and of voids. It is also shown that the solution to the coupled system converges, in an appropriate measure, to the solutions of the uncoupled systems as the coupling coefficients tend to zero.

Research of stamping of unequal channel bars. Part 3. Force parameters and shape change of the billet when extruding channels. 2. Determination of the extrusion force, maximum pressure on the matrix wall and the heights of the walls, taking into account the elastic deformation jf the matrix

2021 ◽  
pp. 63-69
Author(s):  
A.L. Vorontsov
Keyword(s):  
Plastic Flow ◽  
Elastic Deformation ◽  
Shape Change ◽  
Plane Deformation ◽  
Maximum Pressure ◽  
Extrusion Force ◽  
System Of Equations ◽  
The Matrix ◽  
Theory Of Plastic Flow

On the basis of the system of equations of the theory of plastic flow, the forces, the maximum pressure on the wall of the matrix and the heights of the obtained walls when extruding channels are determined, taking into account the elastic deformation of the matrix. Keywords: die forging, extrusion, misalignment, punch, matrix, plane deformation, stresses. [email protected]

On structural stability for an elastic body with voids having dipolar structure

2019 ◽  
Vol 32 (1) ◽  
pp. 147-160 ◽  
Author(s):  
Marin Marin ◽  
Andreas Öchsner ◽  
Daniel Taus
Keyword(s):  
Elastic Body ◽  
Structural Stability ◽  
Dipolar Structure

scholarly journals On the Fredholm Property of the Trace Operators Associated with the Elastic Layer Potentials

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 134 ◽  
Author(s):  
Giulio Starita ◽  
Alfonsina Tartaglione
Keyword(s):  
Elastic Body ◽  
Elastic Layer ◽  
Fredholm Property ◽  
System Of Equations ◽  
Layer Potentials ◽  
Connected Set ◽  
Equilibrium Configurations ◽  
Linear Elastostatics ◽  
Class C

We deal with the system of equations of linear elastostatics, governing the equilibrium configurations of a linearly elastic body. We recall the basics of the theory of the elastic layer potentials and we extend the trace operators associated with the layer potentials to suitable sets of singular densities. We prove that the trace operators defined, for example, on W 1 − k − 1 / q , q ( ∂ Ω ) (with k ≥ 2 , q ∈ ( 1 , + ∞ ) and Ω an open connected set of R 3 of class C k ), satisfy the Fredholm property.

The Growth of Vortices in the Vicinity of a Wall of Elastic Moving Airfoils

2013 ◽  
Author(s):  
Masaki Fuchiwaki ◽  
Tomoki Kurinami ◽  
Kazuhiro Tanaka
Keyword(s):  
Flow Field ◽  
Elastic Body ◽  
Elastic Deformation ◽  
Growth Process ◽  
Experimental Studies ◽  
Strain Component ◽  
Pitching Airfoil ◽  
The Impact ◽  
The Relationship ◽  
Significant Attention

There have been a number of studies on the flow field around a pitching airfoil and a heaving airfoil. Especially, the relationship between the wake structure and the characteristics of dynamic thrust has been clarified. Recently, the flow field around an elastic body has been attracted significant attention and the flow field is treated as a coupled problem between the fluid and structure. The flow field around an elastic body has been investigated primarily by numerical means, and there have been experimental studies. However, the details of the impact of elastic deformation effects on the growth process of vortices generated in the vicinity of the wall have not been clarified. In this study, we investigate the growth process of vortices generated in the vicinity of the wall of elastic moving airfoils experimentally. The elastic NACA0010 generates vortices in a large region of a wall and rolls up vortices, with the vortices growing gradually toward the trailing edge as a result of elastic deformation. The elastic NACA0010 has a characteristic whereby vortices having a rotational component that is stronger than the shear-strain component due to the vorticities in the vicinity of a wall of the elastic NACA0010 change not only spatial change of x- and y-components.

Efficient and Flexible Finite Element Procedure for Free and Forced Vibration Problems of a Plate Coupled With Fluid

2020 ◽  
Author(s):  
Ming Ji ◽  
Kazuaki Inaba
Keyword(s):  
Finite Element ◽  
Eigenvalue Problem ◽  
Forced Vibration ◽  
Natural Frequencies ◽  
Coupled System ◽  
Generalized Eigenvalue Problem ◽  
Symmetric System ◽  
System Of Equations ◽  
Generalized Eigenvalue ◽  
Finite Element Procedure

Abstract Identifying the coupled system natural frequencies and dynamic behavior of systems in the presence of fluid-structure interaction is one of the most important issues in the engineering design of buildings, road vehicles and aircraft. This paper presents an efficient and flexible finite element procedure using fully vectorized codes for the free and forced vibration analysis of a rectangular plate in contact with fluid. The 4-node MITC plate finite element (MITC4) based on the Mindlin plate theory is used to simulate the plate, while the 8-node acoustic pressure element is used to simulate the fluid. The derived system of equations using structural displacements and fluid pressures yields a non-symmetric system of equations. Solving the generalized eigenvalue problem for the non-symmetric system is more computationally intensive compared to solving the generalized eigenvalue problem for symmetric systems. The modal expansion technique is used to reduce the model size. Then the reduced non-symmetric system is symmetrized by right eigenvectors. The Newmark method is used to solve the forced vibration problem of the coupled systems. The effect of the height of the fluid on the natural frequencies is discussed. The natural frequencies and transient responses are in good agreement with those obtained from the commercial finite element software. Moreover, the technique is proved to be effective to solve the coupled system.

Application of Generalized Newton-Euler Equations and Recursive Projection Methods to Dynamics of Deformable Multibody Systems

1989 ◽  
Author(s):  
R. A. Wehage ◽  
A. A. Shabana
Keyword(s):  
Euler Equations ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Coupled System ◽  
Projection Methods ◽  
Open Loop ◽  
System Of Equations ◽  
Kinematic Chains ◽  
Deformable Bodies ◽  
Generalized Newton

Abstract A general symbolic-based method is presented for solving equations of motion for open-loop kinematic chains consisting of interconnected rigid and deformable bodies. The method utilizes matrix partitioning, recursive projection based on optimal block U-L factorization and generalized Newton-Euler equations to obtain an order n solution for the constrained equations of motion. Kinematic relationships between the absolute reference, joint and elastic coordinates are used with the generalized Newton-Euler equations for deformable bodies to obtain a large, loosely coupled system of equations. Taking advantage of the inertia matrix structure associated with elastic coordinates yields a recursive solution algorithm whose dimension is independent of the elastic degrees of freedom. The above solution techniques applied to this system of equations yield a much smaller operations count and can more effectively exploit vectorization and parallel processing. The algorithms presented in this paper are illustrated with the aid of cylindrical joints which are easily extended to revolute, prismatic, rigid and other joint types.

The impact of a rigid circular cylinder on an elastic solid

1962 ◽  
Vol 255 (1053) ◽  
pp. 153-191 ◽  
Keyword(s):  
Laplace Transform ◽  
Elastic Body ◽  
Contact Area ◽  
Elastic Solid ◽  
Coupled System ◽  
Poisson's Ratio ◽  
Normal Displacement ◽  
Plane Boundary ◽  
The Laplace Transform ◽  
Perfect Adherence

A method is described for approximating to any degree of accuracy the solution of the following problem: An elastic body which is bounded by a plane on one side, but extends to infinity otherwise, is hit by a circular disk of given mass, radius, and initial speed perpendicular to the plane boundary. The whole surface of the disk enters into contact with the elastic body at the same time and stays in contact at all its points from then on. The disk is assumed to be rigid, i.e. it does not allow the particles of the elastic body in the contact area to move relative to each other in a direction perpendicular to the plane boundary. For the relative motion of these particles parallel to the face of the disk several conditions are considered, representing perfect lubrication, various degrees of viscous friction and perfect adherence. With the help of various Mellin transformations a method is indicated which leads to an expansion of the motion in powers of the Laplace transform variable. The case of perfect adherence needs some special consideration, and a simple approximation for the static problem is found. The case of perfect lubrication is then treated in more detail by a different method which replaces the condition of constant normal displacement in the contact area by an equivalent number of requirements for certain averages over the normal displacement in the contact area. The condition of rigidity for the disk is not exactly satisfied, but it is possible to judge the accuracy of the approximation (with the help of asymptotic expansions in the Laplace transform variable) at the initial time, when discrepancies are largest. The concept of ‘mode of vibration’ is introduced. Any transient in the coupled system of elastic body and rigid disk can be described as superposition of modes, each of which is an exponentially damped harmonic oscillation of the coupled system with a frequency and damping constant independent of the particular transient. The motion of the impinging disk is then seen to be dominated mostly by the lowest mode, provided the mass of the disk is not too small. The displacement perpendicular to the boundary outside of the contact area has been calculated. This calculation is not more difficult than the corresponding one in the case of a point-like source at the plane boundary of an elastic solid. Numerical computations were carried out for the case of perfect lubrication with the help of the Elecom digital computer in order to determine the first two modes and their contributions to the motion of the disk. As long as Poisson’s ratio for the elastic solid exceeds 1/4, the results do not depend strongly on the value of Poisson’s ratio. The ratio of the areal mass densities of the disk to the elastic solid is the main parameter of the theory. The shear wave velocity of the elastic solid determines the time scale of the motion.

scholarly journals The physical and qualitative analysis of fluctuations in air and vapour concentrations in a porous medium

2018 ◽  
Vol 5 (5) ◽  
pp. 171954 ◽  
Author(s):  
Y. Poorun ◽  
M. Z. Dauhoo ◽  
M. Bessafi ◽  
M. K. Elahee ◽  
A. Gopaul ◽  
...  
Keyword(s):  
Transport Model ◽  
Parabolic Type ◽  
Coupled System ◽  
Numerical Approach ◽  
The Body ◽  
Physical Analysis ◽  
System Of Equations ◽  
Ambient Conditions ◽  
Singular Coefficient ◽  
Transport Diffusion

This work presents the development and physical analysis of a sweat transport model that couples the fluctuations in air and vapour concentrations, and temperature, in a one-dimensional porous clothing assembly. The clothing is exposed to inherent time-varying conditions due to variations in the body temperature and ambient conditions. These fluctuations are governed by a coupled system of nonlinear relaxation–transport–diffusion PDEs of Petrovskii parabolic type. A condition for the well-posedness of the resulting system of equations is derived. It is shown that the energy of the diffusion part of the system is exponentially decreasing. The boundedness and stability of the system of equations is thus confirmed. The variational formulation of the system is derived, and the existence and uniqueness of a weak solution is demonstrated analytically. This system is shown to conserve positivity. The difficulty of obtaining an analytical solution due to the complexity of the problem, urges for a numerical approach. A comparison of three cases is made using the Crank–Nicolson finite difference method (FDM). Numerical experiments show the existence of singular coefficient matrices at the site of phase change. Furthermore, the steady-state profiles of temperature, air and vapour concentrations influence the attenuation of fluctuations. Numerical results verify the analytical findings of this work.

scholarly journals Transient setting of relativistic ponderomotive non-linearity and filamentation of ultra-short laser pulses in collisionless plasmas

2019 ◽  
Vol 37 (03) ◽  
pp. 252-259
Author(s):  
R.P. Sharma ◽  
Narender Kumar ◽  
R. Uma ◽  
Ram Kishor Singh ◽  
P.K. Gupta
Keyword(s):  
Laser Beam ◽  
Plasma Oscillation ◽  
Fluid Model ◽  
Coupled System ◽  
Laser Pulses ◽  
Electron Plasma ◽  
Laser Frequency ◽  
Wave Number ◽  
System Of Equations ◽  
Frequency Spectra

AbstractWe study the setting up of relativistic ponderomotive non-linearity in an under-dense collisionless cold plasma. Using the fluid model, coupled system of equations of the laser beam and electron plasma oscillations has been derived. We present the numerical simulation for this coupled system of equations, when the coupling arises through relativistic ponderomotive non-linearity. The filamentation of the laser beam has been found to vary appreciably with perturbation wave number. The results show that with time, localized structures become more complex and the plasma oscillation frequency spectra have several harmonic peaks at terahertz frequencies when the electron plasma frequency is in terahertz range and laser frequency is around 2.35 × 1015 rad/s. We also present the semi-analytical model to capture the underlying physics.

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