Buckling and Postbuckling of Electroconducting Elastic Plates in a Magnetic Field

2002 ◽  
Author(s):  
Davresh Hasanyan ◽  
Liviu Librescu ◽  
Damodar R. Ambur
Keyword(s):  
Magnetic Field ◽  
Electric Current ◽  
Ferromagnetic Material ◽  
Electrical Current ◽  
Elastic Plates ◽  
Postbuckling Behavior ◽  
Field Equations ◽  
Flat Plates ◽  
Theory Of Plates ◽  
Basic Equations

The basic equations of a fully nonlinear theory of electromagnetically conducting flat plates carrying an electric current and exposed to a magnetic field of arbitrary orientation are summarized. The relevant equations have been obtained by considering that both the elastic and electromagnetic media are homogeneous and isotropic. The geometrical nonlinearities are considered in the von-Ka´rma´n sense, and the soft ferromagnetic material of the plate is assumed to feature negligible hysteretic losses. Based on the electromagnetic and elastokinetic field equations, by using the standard averaging methods, the 3-D coupled problem is reduced to an equivalent 2-D one, appropriate to the theory of plates. Having in view that the elastic structures carrying an electric current are prone to buckling, by using the presently developed theory, the associated problems of buckling and post-buckling are investigated. In this context, the problem of the electrical current inducing the buckling instability of the plate, and its influence on the postbuckling behavior are analyzed. In the same context, the problem of the natural-frequencies electrical current interaction of flat plates, as influenced by a magnetic field is also addressed.

Mathematical Theory of Transversally Isotropic Shells of Arbitrary Thickness at Static Load

2019 ◽  
Vol 968 ◽  
pp. 496-510
Author(s):  
Anatoly Grigorievich Zelensky
Keyword(s):  
Mathematical Theory ◽  
Three Dimensional ◽  
Nonlinear Problems ◽  
Theory Of Elasticity ◽  
Elastic Plates ◽  
Dimensional Problem ◽  
Boundary Problems ◽  
Complex Boundary ◽  
Plates And Shells ◽  
Basic Equations

Classical and non-classical refined theories of plates and shells, based on various hypotheses [1-7], for a wide class of boundary problems, can not describe with sufficient accuracy the SSS of plates and shells. These are boundary problems in which the plates and shells undergo local and burst loads, have openings, sharp changes in mechanical and geometric parameters (MGP). The problem also applies to such elements of constructions that have a considerable thickness or large gradient of SSS variations. The above theories in such cases yield results that can differ significantly from those obtained in a three-dimensional formulation. According to the logic in such theories, the accuracy of solving boundary problems is limited by accepted hypotheses and it is impossible to improve the accuracy in principle. SSS components are usually depicted in the form of a small number of members. The systems of differential equations (DE) obtained here have basically a low order. On the other hand, the solution of boundary value problems for non-thin elastic plates and shells in a three-dimensional formulation [8] is associated with great mathematical difficulties. Only in limited cases, the three-dimensional problem of the theory of elasticity for plates and shells provides an opportunity to find an analytical solution. The complexity of the solution in the exact three-dimensional formulation is greatly enhanced if complex boundary conditions or physically nonlinear problems are considered. Theories in which hypotheses are not used, and SSS components are depicted in the form of infinite series in transverse coordinates, will be called mathematical. The approximation of the SSS component can be adopted in the form of various lines [9-16], and the construction of a three-dimensional problem to two-dimensional can be accomplished by various methods: projective [9, 14, 16], variational [12, 13, 15, 17]. The effectiveness and accuracy of one or another variant of mathematical theory (MT) depends on the complex methodology for obtaining the basic equations.

scholarly journals The effect of simplifications of a numerical mesh on the results of electromagnetic analysis of the Nuclotron-type cable

2018 ◽  
Vol 177 ◽  
pp. 08004
Author(s):  
Łukasz Tomków
Keyword(s):  
Magnetic Field ◽  
Electric Current ◽  
Current Density ◽  
Electric Current Density ◽  
Electromagnetic Analysis ◽  
First Case ◽  
Single Region ◽  
The Magnetic Field

The model of a single Nuclotron-type cable is presented. The goal of this model is to assess the behaviour of the cable under different loads. Two meshes with different simplifications are applied. In the first case, the superconductor in the cable is modelled as single region. Second mesh considers individual strands of the cable. The significant differences between the distributions of the electric current density obtained with both models are observed. The magnetic field remains roughly similar.

scholarly journals The Combined Effect of Rotation and Magnetic Field on Finite-Amplitude Thermal Convection

1973 ◽  
Vol 26 (5) ◽  
pp. 617 ◽  
Author(s):  
R Van der Borght ◽  
JO Murphy
Keyword(s):  
Magnetic Field ◽  
Mean Field ◽  
Field Approximation ◽  
Finite Amplitude ◽  
Combined Effect ◽  
Mean Field Approximation ◽  
Free Boundaries ◽  
Wide Range ◽  
The Mean ◽  
Basic Equations

The combined effect of an imposed rotation and magnetic field on convective transfer in a horizontal Boussinesq layer of fluid heated from below is studied in the mean field approximation. The basic equations are derived by a variational technique and their solutions are then found over a wide range of conditions, in the case of free boundaries, by numerical and analytic techniques, in particular by asymptotic and perturbation methods. The results obtained by the different techniques are shown to be in excellent agreement. As for the linear theory, the calculations predict that the simultaneous presence' of a magnetic field and rotation may produce conflicting tendencies.

Research on the delamination wear properties of the pure carbon strip at the high-sliding speed with electric current

2018 ◽  
Vol 70 (1) ◽  
pp. 76-83 ◽  
Author(s):  
Hongjuan Yang ◽  
Lin Fu ◽  
Yanhua Liu ◽  
Weiji Qian ◽  
Bo Hu
Keyword(s):  
Electric Current ◽  
High Speed ◽  
Normal Load ◽  
Copper Wire ◽  
Electrical Current ◽  
Wear Properties ◽  
Sliding Speed ◽  
Content Type ◽  
Delamination Wear ◽  
High Speed Data

Purpose This paper aims to investigate the delamination wear properties of a carbon strip in a carbon strip rubbing against a copper wire at the high-sliding speed (380 km/h) with or without electrical current. Design/methodology/approach The friction and wear properties of a carbon strip in a carbon strip rubbing against a copper wire are tested on the high-speed wear tester whose speed can reach up to 400 km/h. The test data have been collected by the high-speed data collector. The worn surfaces of the carbon strip are observed by the scanning electron microscope. Findings It was found that there was a significant increase of the delamination wear with the decrease of the normal load when the electric current is applied. The size of the flake-like peeling also increases with the decrease of normal load. The delamination wear extends gradually from the edge of the erosion pits to the surrounding area with the decrease of the normal load. However, the delamination wear never appears in the absence of electric current. It is proposed that the decreased normal load and the big electrical current are the major causes of the delamination wear of the carbon strip. Originality value The experimental test at high-sliding speed of 380 km/h was performed for the first time, and the major cause of the delamination was discovered in this paper.

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