scholarly journals The inverse non-stationary problem of identification of defects in an elastic rod

2021 ◽  
Vol 13 (S) ◽  
pp. 57-66
Author(s):  
Grigory V. FEDOTENKOV ◽  
Dmitry I. MAKAREVSKII ◽  
Yana A. VAHTEROVA ◽  
Trah Quyet THANG
Keyword(s):  
Solid Mechanics ◽  
Initial Conditions ◽  
Practical Interest ◽  
Stationary Problem ◽  
Technical Condition ◽  
Elastic Rod ◽  
Elastic Bodies ◽  
Fundamental Research ◽  
Great Practical Interest ◽  
Elastic Inclusions

Non-stationary inverse problems of deformed solid mechanics are among the most underexplored due to, inter alia, increasing dimension of non-stationary problems per unit as compared with stationary and static problems, as well as necessity to consider the initial conditions. In the context of the continuing progress of the aviation and aerospace industries, the question arises about technical condition monitoring of aircraft for the purposes of their safe operation. A large proportion of an aircraft structure consists of beam and rod elements exposed to various man-made and natural effects which cause defects inaccessible for visual inspection and required to be identified well in advance. It is well known that defects (such as cracks, cavities, rigid and elastic inclusions) are concentrators of stresses and largely cause processes, which lead to the destruction of elastic bodies. Therefore, the problem of identification of such defects and their parameters, i.e. the problem of identification, represents a great practical interest. Mathematically, the problem of identification represents a non-linear inverse problem. The development of methods of solving such problems is currently a live fundamental research issue.

An Analog of Einstein’s General Relativity Emerging from Classical Finite Elasticity Theory: Analytical and Computational Issues

2013 ◽  
Vol 14 (3) ◽  
pp. 801-818 ◽  
Author(s):  
C. Cherubini ◽  
S. Filippi
Keyword(s):  
Solid Mechanics ◽  
Finite Elasticity ◽  
Quantum Systems ◽  
Curved Space ◽  
The Past ◽  
Strain Energy Density Function ◽  
Elastic Bodies ◽  
Numerical Studies ◽  
Analogue Gravity ◽  
Nonlinear Constitutive Relation

AbstractThe “analogue gravity formalism”, an interdisciplinary theoretical scheme developed in the past for studying several non relativistic classical and quantum systems through effective relativistic curved space-times, is here applied to largely de-formable elastic bodies described by the nonlinear theory of solid mechanics. Assuming the simplest nonlinear constitutive relation for the elastic material given by a Kirchhoff-St Venant strain-energy density function, it is possible to write for the perturbations an effective space-time metric if the deformation is purely longitudinal and depends on one spatial coordinate only. Theoretical and numerical studies of the corresponding dynamics are performed in selected cases and physical implications of the results obtained are finally discussed.

A MODEL HIERARCHY FOR IONOSPHERIC PLASMA MODELING

2004 ◽  
Vol 14 (03) ◽  
pp. 393-415 ◽  
Author(s):  
CHRISTOPHE BESSE ◽  
PIERRE DEGOND ◽  
FABRICE DELUZET ◽  
JEAN CLAUDEL ◽  
GÉRARD GALLICE ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Plasma Density ◽  
Maxwell Equations ◽  
Ionospheric Plasma ◽  
Practical Interest ◽  
Plasma Modeling ◽  
Model Hierarchy ◽  
Great Practical Interest ◽  
Two Fluid ◽  
Insight Into

This paper deals with the modeling of the ionospheric plasma. Starting from the two-fluid Euler–Maxwell equations, we present two hierarchies of models. The MHD hierarchy deals with large plasma density situations while the dynamo hierarchy is adapted to lower density situations. Most of the models encompassed by the dynamo hierarchy are classical ones, but we shall give a unified presentation of them which brings a new insight into their interrelations. By contrast, the MHD hierarchy involves a new (at least to the authors) model, the massless-MHD model. This is a diffusion system for the density and magnetic field which could be of great practical interest. Both hierarchies terminate with the "classical" Striation model, which we shall investigate in detail.

scholarly journals Sticky Thermals: Evidence for a Dominant Balance between Buoyancy and Drag in Cloud Updrafts

2015 ◽  
Vol 72 (8) ◽  
pp. 2890-2901 ◽  
Author(s):  
David M. Romps ◽  
Alexander B. Charn
Keyword(s):  
Large Eddy Simulation ◽  
Practical Interest ◽  
Momentum Equation ◽  
Severe Weather ◽  
Convective Clouds ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Great Practical Interest ◽  
Natural Boundaries ◽  
Drag Law

Abstract The vertical velocities of convective clouds are of great practical interest because of their influence on many phenomena, including severe weather and stratospheric moistening. However, the magnitudes of forces giving rise to these vertical velocities are poorly understood, and the dominant balance is in dispute. Here, an algorithm is used to extract thousands of cloud thermals from a large-eddy simulation of deep and tropical maritime convection. Using a streamfunction to define natural boundaries for these thermals, the dominant balance in the vertical momentum equation is revealed. Cloud thermals rise with a nearly constant speed determined by their buoyancy and the standard drag law with a drag coefficient of 0.6. Contrary to suggestions that cloud thermals might be slippery, with a dominant balance between buoyancy and acceleration, cloud thermals are found here to be sticky, with a dominant balance between buoyancy and drag.

About injuries with a chemical (ink) pencil

1930 ◽  
Vol 26 (8) ◽  
pp. 841-843
Author(s):  
S. I. Rizvash
Keyword(s):  
Human Tissue ◽  
Practical Interest ◽  
Russian Literature ◽  
Medical Institutions ◽  
Great Practical Interest ◽  
Treatment Of Wounds ◽  
Type Of Injury

In Russian literature, very little attention has been paid to this type of injury. I managed to find only 2 articles in which this issue is treated. In the manuals on general and private surgery, both translated and original, there is no indication of the action of aniline pencils on human tissue. Nothing is said about this even in the largest Russian monographs on the treatment of wounds (Trinkler, Petrov). Meanwhile, the injuries caused by a chemical pencil, due to their peculiar course and often even a difficult outcome, are undoubtedly of great practical interest. This prompts me to report two cases of such an injury, which I observed in different medical institutions at almost the same time.

scholarly journals Parametric evaluation of the technical object suitability based on analyze the quality of its maintenance and use taking into account the initial conditions

2018 ◽  
Vol 182 ◽  
pp. 01006
Author(s):  
Rafał Grądzki
Keyword(s):  
Equations Of State ◽  
Initial Conditions ◽  
Technical Condition ◽  
Operation Condition ◽  
Technical Object ◽  
Coupled Equations ◽  
Reliability Parameters ◽  
Operation Conditions ◽  
Operational Data

In this paper, the comparison of three various technical objects (engines of public transport buses) exploitation research for different initial conditions are presented. Object researches were carried out in 2012 and then repeated in 2013. Gathered operational data is presented in three sets (1 – concerning object, 2 – concerning driving conditions, 3 – concerning driver, where set 1 is the collection of diagnostic information Dk, and sets 2 and 3 are the information about object environment U) in form of conventional points (experts numerical assessments). Relation between point information of object and point information of environment was described by coupled equations of state (describing relations between operation condition and technical condition including initial conditions for each analyzed exploitation period). That method allows to determine parameters of technical condition aT and operation condition aR and next, from the course of aT parameter, set of parametrical damage mT(t) and from course of parameter aR – set of momentary damage aR(t). Thus it is possible to evaluate exploitation, technical and operation conditions of each object (bus engine). Received reliability parameters allows to properly control exploitation and service of particular objects and set of objects (fleet of buses) and its elements.

Evaluation of bond strength of cross-laminated LSL specimens under short-span bending

Holzforschung ◽  
2019 ◽  
Vol 73 (8) ◽  
pp. 789-795
Author(s):  
Meng Gong ◽  
Ling Li ◽  
Ying-Hei Chui
Keyword(s):  
Bond Strength ◽  
Test Procedure ◽  
Practical Interest ◽  
Adhesive Bond ◽  
Bond Quality ◽  
Block Shear ◽  
The Face ◽  
Great Practical Interest ◽  
Short Span ◽  
Mass Timber

AbstractMass timber panels (MTPs) have a great potential in the construction of mid- and high-rise buildings. Evaluation of the face-bond strength of MTPs is of great practical interest for this kind of products. This study aimed at developing an appropriate test procedure for evaluating the adhesive bond strength of cross-laminated laminated strand lumber (CL-LSL). Three-point short-span bending tests were conducted on two-layer asymmetric CL-LSL specimens (2LasymCL-LSL), which were adhesively bonded by two-component resins of the type polyurethane (PUR) or polyvinyl acetate (PVAc). For comparison, block shear specimens were tested as well. It was found that the 2LasymCL-LSL assembly was better suitable under the short-span bending for differentiating between good and poor bond quality of MTPs.

Godunov-Conte Method for Solution of Eigenvalue Problems and Its Applications

1977 ◽  
Vol 44 (4) ◽  
pp. 776-779 ◽  
Author(s):  
I. Elishakoff ◽  
M. Charmats
Keyword(s):  
Vibration Analysis ◽  
Eigenvalue Problems ◽  
Annular Plate ◽  
Initial Conditions ◽  
Isotropic Case ◽  
Orthotropic Plates ◽  
Elastic Bodies ◽  
Kronecker Delta ◽  
Parallel Integration ◽  
Polar Orthotropic

The method originally presented by Godunov and modified by Conte for solution of two-point boundary-value problems, is outlined here as applied to eigenvalue problems. The method (which avoids the loss of accuracy resulting from the numerical treatment, often associated with stability and vibration analysis of elastic bodies) consists of parallel integration of the set of k homogeneous equations under the Kronecker-delta initial conditions which are orthogonal (k being the number of “missing” conditions), after each step. Subject to Conte’s test, the set of solutions is reorthogonalized by the Gram-Schmidt procedure and integration continues. The procedure prevents flattening of the base solutions, which otherwise become numerically dependent. The method is applied to stability analysis of polar orthotropic plates, and as in the isotropic case (as shown by Yamaki), it is seen that assumption of symmetric buckling results in a stability overestimate for an annular plate.

scholarly journals Numerical investigation of the Carleman system

Vestnik MGSU ◽  
2015 ◽  
pp. 7-15
Author(s):  
Ol’ga Aleksandrovna Vasil’eva
Keyword(s):  
Cauchy Problem ◽  
Equilibrium State ◽  
Numerical Investigation ◽  
Initial Conditions ◽  
Practical Interest ◽  
Statistical Characteristics ◽  
Stabilization Time ◽  
System Solution ◽  
Stochastic Solution ◽  
The Cauchy Problem

In the article the Cauchy problem of the Carleman equation is considered. The Carleman system of equations is a model problem of the kinetic theory of gases. It is a discrete kinetic model of one-dimensional gas consisting of identical monatomic molecules. The molecules can have one of two speeds, which have equal values and opposite directions. This system of the equations is quasi-linear hyperbolic system of partial differential equations. There is no analytic solution for this problem in general case. So, the numerical investigation of the Cauchy problem of the Carleman system solution is very important.The paper presents and discusses the results of the numerical investigation of the Cauchy problem for the studied system solution with periodic initial conditions. The dependence of the stabilization time of the solution and the time dependence of energy exchange from small parameter are obtained.The second point of the paper is numerical investigation of the solution of the Cauchy problem with non-periodic initial conditions. The solution stabilization to the equilibrium state is obtained. The solution stabilization time is compared with stabilization time in periodic case.The final point of the paper is numerical investigation of the Cauchy problem with stationary normal processes as initial conditions. The solution to this problem is two stationary stochastic processes for any fixed value of time variable. As a rule, the practical interest is not a stochastic solution but its statistical characteristics. The stochastic solution realization is presented and discussed. The dependence of the mathematical expectation of the solution deviation modulus from equilibrium state is obtained. It demonstrates the process of the solution stabilization.

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