Flexible Elastic Plate Research Articles

Nonlinear dynamical response of sinusoidal impulsive actuated piezoelectric/porous sandwich nanoharvesters via GM-based meshfree collocation formulations

In this paper a new effective computational approach based upon a meshless collocation formulation of the Gurtin-Murdoch (GM) continuum elasticity is described. The newly developed computational model for the third-order shear flexible elastic plates is then employed to analyze the nonlinear dynamical response of piezoelectric/porous sandwich nanoharvesters subjected to a sinusoidal impulsive actuation. The material properties relevant to the porous passive core having uniform or two graded through thickness porosity dispersions are estimated using the approach of Gaussian random field. The weak form of model conception is discretized and solved numerically via employing an incorporation of the polynomial and radial basis functions having the capability to remove any feasible singularity as well as taking more precise approximation into account within the GM-based meshfree collocation formulations. It is deduced that by contemplating the surface stress tensor via the established GM-based model, the achieved voltage from the sinusoidal impulsive actuated sandwich nanoharvesters reduces, especially for those possessing lower thickness. Also, it is deduced that for the fully simply supported impulsive actuated sandwich nanoharvester, by changing the porosity decoration of distribution from the uniform decoration to FGO and FGX graded ones, the significance of the role of surface stress tensor in the achieved voltage reduces from 12.45% to 12.28%, and enhances from 12.45% to 12.64%, respectively. For the fully clamped impulsive actuated sandwich nanoharvester, by changing the porosity decoration of distribution from the uniform decoration to FGO and FGX graded ones, the significance of the role of surface stress tensor in the achieved voltage reduces from 15.01% to 14.68%, and enhances from 15.01% to 15.37%, respectively.

EQUILIBRIUM OF A NORMALLY LOADED ELASTIC SHALLOW CYLINDRICAL SHELL WITH DISLOCATIONS AND DISCLINATIONS

We consider the problem of the equilibrium of a normally loaded elastic shallow rectangular circular cylindrical shell, which contains sources of internal stress in the form of fields of continuously distributed edge dislocations and wedge disclinations or other sources, for example, thermal ones. Based on the modified system of Karman equations for the equilibrium of an elastic plate with dislocations and disclinations, a system of nonlinear equilibrium equations for the shell was constructed. The resulting system of equations differs from the Karman system of equilibrium equations for an elastic shallow cylindrical shell under the action of a normal load by the presence on the right side of the continuity equation of a nonzero function, called the incompatibility function, which is expressed through the densities of edge dislocations and wedge disclinations. The edges of the shell are freely clamped or hinged. In the absence of internal stress sources, this system transforms into a system of equilibrium equations for a shallow shell, and in the case of an infinitely large radius of curvature (and the presence of internal stress sources) into a modified system of Karman equilibrium equations for a flexible elastic plate with dislocations and disclinations. To solve the system of nonlinear shell equilibrium equations, the Newton – Kantorovich method in combination with the difference method is proposed. For the case of small values of the normal load and small values of the incompatibility function, linearization is carried out with respect to the deflection and stress function. As a result, a linear boundary value problem was obtained in the form of a system of differential equations for the deflection and the stress function, which is solved by the difference method. The solution of the linearized system is used as an initial approximation in the implementation of the Newton – Kantorovich method. Examples of numerical calculations of deflection and stress function for given values of normal load and incompatibility function are given, and corresponding graphs are constructed.

On numerical approximations to fluid–structure interactions involving compressible fluids

In this paper we introduce a numerical scheme for fluid–structure interaction problems in two or three space dimensions. A flexible elastic plate is interacting with a viscous, compressible barotropic fluid. Hence the physical domain of definition (the domain of Eulerian coordinates) is changing in time. We introduce a fully discrete scheme that is stable, satisfies geometric conservation, mass conservation and the positivity of the density. We also prove that the scheme is consistent with the definition of continuous weak solutions.

Wave Interaction and Overwash with a Flexible Plate by Smoothed Particle Hydrodynamics

The motion of a flexible elastic plate under wave action is simulated, and the well–known phenomena of overwash is investigated. The fluid motion is modelled by smoothed particle hydrodynamics, a mesh-free solution method which, while computationally demanding, is flexible and able to simulate complex fluid flows. The freely floating plate is modelled using linear thin plate elasticity plus the nonlinear rigid body motions. This assumption limits the elastic plate motion to be small but is valid for many cases both in geophysics and in the laboratory. The principal conclusion is that the inclusion of flexural motion causes significantly less overwash than that which occurs for a rigid plate.

Development of composition and technology of children's dental films with anesthetic and anti-inflammatory activity

The work purpose . To develop composition and technology of children's dental films with anesthetic and anti-inflammatory activity. Materials and methods. Pharmaceutical substance of trimecaine, Chamomile flowers and excipients: sodium carboxymethylcellulose, gelatin, polyethylene oxide-600, purified water were used in the study. These were permitted for medical use and meet the requirements of the relevant regulatory documents. Aqueous extract from Chamomile flowers was obtained in laboratory conditions with method of remaceration in compliance with rules of technology for this method. The content of flavonoids in terms of rutin in flowers of Chamomile and the resulting aqueous extracts was determined with spectrophotometria by Pharmacopoeias method. Film-forming solutions were prepared in accordance with their physico-chemical properties and recommended technological modes of preparation. The dental films were obtained by the method of watering the film mass on a glass substrate, followed by drying. In order to select the optimal composition of dental films we investigated their adhesive properties, osmotic activity and biopharmaceutical performance. The adhesion activity of dental films was studied by the method, based on the determination of the strength of separation the glass plates from each other. The osmotic activity of dental films was determined by method of dialysis through a semipermeable membrane. The biopharmaceutical properties were evaluated by the method of diffusion in agar. Results . It was found that the most appropriate way to obtain an aqueous extract of Chamomile flowers is a three-stage remaceration of hot purified water, which allows to extract more than 70 % of the amount of flavonoids from the feedstock. To determine the rational combination of auxiliary components of film matrix several different compositions, comprising sodium carboxymethylcellulose, gelatin, polyethylene oxide-600, trimecaine, sodium benzoate, and aqueous extract of chamomile flowers were prepared. The resulting films were a flexible elastic plates light brown color with a pleasant characteristic odor and taste characteristic for organoleptic properties of Chamomile flowers. As a result of the comparative study of adhesive and osmotic activity and of biopharmaceutical properties of experimental films of samples, we found that the optimal composition of the dosage form comprises 0.2 g trimecaine; 2.0 g of sodium carboxymethylcellulose; 2.0 g of gelatin; 2.0 g of polyethylene oxide-600; 0.01 g of sodium benzoate and aqueous extract of Chamomile flowers to 100.0 g. Conclusions . Was developed the composition and technology of dental films with anesthetic and anti-inflammatory action, to be used in children, containing trimecaine and aqueous extract of Chamomile flowers.

Behavior of Thin-Film-Type Delamination of Layered Composite in Post-Buckling

A revision of the basic assumptions those are usually used in the analysis of stability of thin delaminated layer and delamination propagation in a compressed composite is presented in this paper. For this purpose, the theory of flexible elastic plates with large displacements was used. As a result the compressive force and the total longitudinal strain of sub-laminate are expressed in terms of complete elliptic integrals, which uniquely identify the buckled shape of sub-laminate, the effect of buckling on the compression strain and increment of the compressive force in the buckled state. Stress and strain, as well as the strength of the buckled sub-laminate in the dangerous cross-section were also analyzed. The results of the general analysis of delamination propagation and its compression-bending destruction in the buckled state allow to define the basic regularities of the damage behavior of compressed layered composite.

Crack-front instability in a confined elastic film

We study the undulatory instability of a straight crack front generated by peeling a flexible elastic plate from a thin elastomeric adhesive film. We show that there is a threshold for the onset of the instability that is dependent on the ratio of two length-scales that arise naturally in the problem: the thickness of the film and an elastic length defined by the stiffness of the plate and that of the film. A linear stability analysis predicts that the wavelength of the instability scales linearly with the film thickness. Our results are qualitatively and quantitatively consistent with recent experiments, and show how crack fronts may lose stability due to a competition between bulk and surface effects in the presence of multiple length scales.

Existence of Weak Solutions for the Unsteady Interaction of a Viscous Fluid with an Elastic Plate

The purpose of this work is to study the existence of solutions for an unsteady fluid-structure interaction problem. We consider a three-dimensional viscous incompressible fluid governed by the Navier–Stokes equations, interacting with a flexible elastic plate located on one part of the fluid boundary. The fluid domain evolves according to the structure’s displacement, itself resulting from the fluid force. We prove the existence of at least one weak solution as long as the structure does not touch the fixed part of the fluid boundary. The same result holds also for a two-dimensional fluid interacting with a one-dimensional membrane.

A simple non‐layered finite element for the elasto‐plastic analysis of shear flexible plates

AbstractA simple and accurate non‐layered plastic element which is capable of capturing the development of plastic curvatures across the thickness of the plates is presented in this paper. The influence of transverse shear forces on the plastic behaviour of plates is also investigated here. This non‐layered plastic element is based on: (i) the four‐node quadrilateral strain element for shear flexible elastic plates given by the authors; (ii) the plastic hinge formulation outlined by Shi and Atluri; and (iii) the modified Ilyushin's yield function which can account for both the development of plastic deformations across the thickness of plates and the effect of transverse shear forces. The numerical examples given here demonstrate that the present non‐layered plastic element can achieve the results obtained by the layered element model and the transverse shear forces considerably affect the plastic behaviour of plates under certain load conditions.

The analysis of flexible raft-pile systems

An analysis has been developed to predict the behaviour of a raft-pile foundation system. The analysis considers the system as a flexible elastic plate supported on a group of compressible friction piles, and the supporting soil is represented as an elastic homoeneous or non-homogeneous material. The ultimate load capacity of the piles is taken into account by a ‘load cut-off’ procedure. The analysis is used to establish the effectiveness of the pile group in reducing settlement of the raft and the effects of raft flexibility and size, and pile group parameters are considered. Two raft-pile systems, namely, the La Azteca building, Mexico City, and the Hyde Park Cavalry Barracks, London, are reanalysed. There is encouraging agreement between measured and predicted settlements and pile loads. Une méthode a été développeé afin de prévoir le comportement d'un système de fondation par radier général surpieux. L'analyse considère le système comme une plaque élastique flexible supportée par un groupe de pieux flottants compressibles, et le sol d'appui est répresenté comme un matériau élastique homogène ou non-homogène. On tient compte de la charge portante limite des pieux par un procédé de réduction de la charge. L'analyse est utilisée pour établir l'efficacité du groupe de pieux en réduisant le tassement du radier et les effets de la flexibilité et des dimensions du radier, et les caractéristiques du groupe de pieux, sont pris en compte. Deux exemples réels de radier surpieux le bâtiment ‘La Azteca’, à Mexico, et ‘Cavalry Barracks’, à Londres, sont analysés à nouveau. Il y a un accord encourageant entre les tassements mesurés et prévus et les charges des pieux.

Interactive adjustment of surfaces

The dilation or contraction of either a sub-region or the whole of an arbitrary, smooth, single v̇alued surface-patch defined in an X,Y plane by Monge's equation, Z = F(X,Y), is achieved by superposition of influence surfaces without loss of smoothness. The arbitrary surface is first transformed into a surface defined above the projection of its boundaries into a unit square in the x,y plane. The unit-square is next partitioned by an orthogonal rectangular grid and then, by a series of further transformations, approximately into a circle of unit radius. Within the circle of unit radius a second, influence surface is next postulated and its z values superimposed on the transformed arbitrary surface at corresponding nodes of the partitioning grid. This influence surface is defined as the shape assumed by a thin flexible elastic plate bounded by the circle and subjected to an eccentric, normal point-displacement at any desired grid-node. Displacements at other nodes are calculable by Michell's two-term closed solution for encastré boundaries or approximately by Föppl's or Clebsch's series solutions for semi-restrained boundaries. If an arbitrary surface is displayed as a net of profile-curves on a computer graphics terminal, the locations and amounts of desired displacements to effect shape-changes can be estimated. Influence surfaces “centred” at such nodes can then be specified and superimposed in the unit circle. Inverse transformation from unit circle to the original arbitrary surface then yields a modified surface for redisplay and reassessment. If a surface having a set of arbitrary Z values at particular grid-nodes is required, a set of influence surfaces, each appropriate to unit-displacement at each node of the set may be scaled and superimposed to yield a smooth corrective surface or to generate a surface, ab initio. In all cases the influence of corrective surfaces may be limited to sub-regions within the global boundaries of arbitrary surfaces.

New applications of the calculus of variations in the large to nonlinear elasticity

Global methods of the calculus of variations and the infinite dimensional critical point theories of Morse and Ljusternik are applied to investigate the structure of the equilibrium states of thin flexible elastic plates under general body forces. The arguments used are equally applicable to broad classes of physical systems governed by nonlinear elliptic partial differential equations.

On the theory of flexible elastic plates

On the theory of flexible elastic plates

Nonlinear Panel Response from a Turbulent Boundary Layer

The vibration of a flexible elastic plate is investigated by a Monte Carlo technique. The response analysis is performed in time domain by numerically simulating the resulting generalized forces. The nonlinear plate deflection and mutual interaction between the plate motion and external and/or internal airflow is included. The fluid perturbations due to the structural motion are described by linear aerodynamic theory. The boundary-layer pressure field is idealized as a homogeneous multidimensional Gaussian random process with mean zero. The plate differential equations of motion and boundary conditions are satisfied in a Galerkin sense by developing a modal solution. Illustrative examples are presented for subsonic and supersonic flow regions using shallow cavity and two plate mode approximations.