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result(s) for
"Elastic plates"
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On equilibrium problem for two elastic plates with covering and thin junction
The paper addresses the analysis of equilibrium problem for two elastic plates with a thin rigid covering. It is assumed that the plates are connected by a thin elastic junction. We prove a solution existence to the problem and investigate limiting passages as rigidity parameters of the elastic junction and the elastic body converge to infinity. Limit models are analyzed. Both variational and differential statements for all problems are obtained, and their equivalence is proved.
Journal Article
On Equilibrium Problem for T-Shape Elastic Structure
This paper is concerned with an equilibrium problem for an elastic structure consisting of a plate and an elastic beam connected to each other at a given point. We consider two cases: In the first one, the elastic beam is connected to a rigid part of the elastic plate; in the second case, contact occurs between two elastic bodies. The elastic plate may contain a thin rigid delaminated inclusion. Neumann-type boundary conditions are considered at the external boundary of the plate. The existence of a solution to the considered problems is proven. A sufficient and necessary condition imposed onto the external forces for the solvability of the problems is found. Passages to the limit with respect to the rigidity parameter of the elastic beam are justified. For all problems, we analyze variational statements as well as differential ones.
Journal Article
Non-coercive problems for Kirchhoff–Love plates with thin rigid inclusion
In the paper, we consider a boundary value problem for an elastic plate with a thin rigid inclusion in a non-coercive case. Both vertical and horizontal displacements of the plate are considered in the frame of the considered model. The inclusion is assumed to be delaminated from the plate which provides a crack between the inclusion and the surrounding elastic body. To guarantee a mutual non-penetration between crack faces, we consider inequality type boundary conditions with unknown set of a contact. A solution existence of the equilibrium problems is proved. Displacements of the plate in the x3 -direction can be fixed at one or two points. In these cases, we also prove a solution existence of the boundary value problems.
Journal Article
Methods for Reducing Stress Concentration Around Holes in Thin Plates and Cylindrical Shells with Annular Radially Inhomogeneous Inclusions
This study involves computer simulations and finite-element analyses of the stress–strain state of thin elastic plates and cylindrical shells weakened by a circular hole and reinforced by an annular inclusion made of a functionally graded material. Over one hundred configurations of the FGM inclusions of various sizes and mechanical properties have been analyzed to evaluate the influence of the inclusion geometry and the modulus variation law on the concentration of parameters of the stress–strain state of plates and shells around the hole. The resulting distributions of stress and strain intensity in zones of local stress concentration have been determined, and optimal parameters for the geometry and elastic properties of radially inhomogeneous FGM inclusions have been identified. These parameters have enabled a significant reduction in the stress concentration factor.
Journal Article
Analytical modeling for nonlinear vibration analysis of partially cracked thin magneto-electro-elastic plate coupled with fluid
A nonlinear analytical model for the transverse vibration of cracked magneto-electro-elastic (MEE) thin plate is presented using the classical plate theory (CPT). The MEE plate material selected is fiber-reinforced
BaTiO
3
–
CoFe
2
O
4
composite, which contains a partial crack at the center. The CPT and the simplified line spring model for crack terms are modified to accommodate the effect of electric and magnetic field rigidities. The analysis considers in-plane forces for the MEE plate, which makes the model nonlinear. The derived governing equation is solved by expressing the transverse displacement in terms of modal coordinates. An approximate solution for forced vibration of cracked MEE plate is also obtained using a perturbation technique. The effect of part-through crack, volume fraction of the composite on the vibration frequencies and structure response is investigated. The frequency response curves presented shows the phenomenon of hard or soft spring. Furthermore, the devised model is extended to the case of cracked MEE plate submerged in fluid. Velocity potential function and Bernoulli’s equation are used to incorporate the inertia effect of surrounding fluid. Both partially and totally submerged plate configurations are considered. The validation of the present results is carried out for intact submerged plate as to the best of the author’s knowledge the literature lacks in results for submerged-cracked plates. New results for cracked MEE plate show that the vibration characteristics are affected by volume fraction, crack length, fluid level and depth of immersion.
Journal Article
Composite wave models for elastic plates
The long-term challenge of formulating an asymptotically motivated wave theory for elastic plates is addressed. Composite two-dimensional models merging the leading or higher-order parabolic equations for plate bending and the hyperbolic equation for the Rayleigh surface wave are constructed. Analysis of numerical examples shows that the proposed approach is robust not only at low- and high-frequency limits but also over the intermediate frequency range.
Journal Article
An optimal control problem with respect to variable thicknesses for a vibrating elastic plate in a contact with a rigid obstacle
We deal with an optimal control problem governed by a hyperbolic variational inequality describing perpendicular vibrations of a simply supported anisotropic elastic plate against a rigid obstacle. A variable thickness of a plate plays the role of a control variable. The state problem is not uniquely solved. In order to overcome the problem of a priori estimates of states we restrict the admissible set to solutions obtained through a penalization method. We verify the existence of an optimal thickness function as a limit of the sequence of thicknesses solving the case of the penalized state problem.
Journal Article
Analytical Study of the Head-On Collision Process between Hydroelastic Solitary Waves in the Presence of a Uniform Current
The present study discusses an analytical simulation of the head-on collision between a pair of hydroelastic solitary waves propagating in the opposite directions in the presence of a uniform current. An infinite thin elastic plate is floating on the surface of water. The mathematical modeling of the thin elastic plate is based on the Euler–Bernoulli beam model. The resulting kinematic and dynamic boundary conditions are highly nonlinear, which are solved analytically with the help of a singular perturbation method. The Poincaré–Lighthill–Kuo method is applied to obtain the solution of the nonlinear partial differential equations. The resulting solutions are presented separately for the left- and right-going waves. The behavior of all the emerging parameters are presented mathematically and discussed graphically for the phase shift, maximum run-up amplitude, distortion profile, wave speed, and solitary wave profile. It is found that the presence of a current strongly affects the wavelength and wave speed of both solitary waves. A graphical comparison with pure-gravity waves is also presented as a particular case of our study.
Journal Article