Analysis Of Elastic Plates Research Articles

Dimension reduction analysis of a three-dimensional thin elastic plate reinforced with fractal ribbons

AbstractThe aim of this paper is to study the dimension reduction analysis of an elastic plate with small thickness reinforced with increasing number of thin ribbons developing fractal geometry. We prove the$\Gamma $-convergence of the energy functionals to a two-dimensional effective energy including singular terms supported within the Sierpinski carpet.

Refined models for free vibration analysis of elastic plates with part-through surface cracks

In this paper, two refined models are proposed for the vibration analysis of isotropic and orthotropic thin plates with part-through surface cracks. The governing equations of cracked plates are formulated via the refined models. Like in the conventional model, crack terms are incorporated in the governing equations. All-over and finite-length cracks (i.e., central and edge cracks) can be directly handled by the new models and their modified forms, respectively. The matched interface and boundary method is then applied to formulate eigenvalue equations. A series of parametric studies for investigating the effects of crack depth and crack length are presented. Numerical results of the proposed models are compared with the existing and finite element solutions to validate their performance and accuracy. The salient feature of the refined models is to complement the deficiency of the conventional model for the analysis of crack depth problems. Several illustrative examples are provided to demonstrate the superior performance of the refined models over the conventional one. The present models are effective for predicting the natural frequencies of thin plates with part-through surface cracks.

Dynamic stability analysis of Mindlin viscoelastic plates subjected to constant and harmonic in-plane compressions based on free vibration analysis of elastic plates

Dynamic stability analysis of Mindlin viscoelastic plates subjected to constant and harmonic in-plane compressions based on free vibration analysis of elastic plates

Comparison of meshfree displacement and stress error recovery of finite element solutions using moving least squares interpolation

The moving least square (MLS) interpolation based the recovery procedures have been successfully applied to recover the finite element solution errors in the analysis of elastic plates and pipes problems and can be advantageously applied for large deformation and fracture problems. The study presents the displacement and stress error recovery characteristics in the error estimation analysis employing Moving Least Squares interpolation approach. The study considers quartic spline, cubic spline, and exponential weight function with three different order of basis function in Moving Least Squares interpolation based error recovery analysis. The displacement/stress errors in finite element solution are quantified in energy norm. The cylinder and plate benchmark examples using triangular and quadrilateral elements are analyzed to compare the convergence, effectivity and adaptively improved meshes obtained using the various displacement/stress recovery procedures. The study shows that cubic spline weight function and quadratic basis function found to perform better in MLS based meshfree recovery technique for stress as well as displacement errors recovery of finite element solution. It is observed from the study that increasing the order of basis function will enhance the error estimation quality that is, rate of convergence become faster with improved effectivity of the results. The increase in convergence rate with the increase of the order of basis function is more in displacement recovery technique as compared to stress recovery technique. It is observed in the analysis of benchmark example with linear triangular meshing that the error reduction using meshfree MLS interpolation based displacement and stress recovery is about 10% and 150% respectively for the displacement and stress recovery over the mesh dependent least square based displacement and stress recovery. The study concludes that the effectiveness and efficiency of meshfree displacement/stress error recovery technique strongly depends on the weight and basis functions of MLS method to recover the errors.

The Nodal Line Finite Difference Method with Iteration Procedure in the Analysis of Elastic Plates in Bending. (Dept. C)

The Nodal Line Finite Difference Method with Iteration Procedure in the Analysis of Elastic Plates in Bending. (Dept. C)

Free vibration analysis of viscoelastic plates with simultaneous calculation of natural frequency and viscous damping

This paper presents a new solution for the free vibration analysis of moderately thick viscoelastic plates with different shapes, based on free vibration analysis of elastic plates. The advantage of this method is that all natural frequencies and viscous damping can be easily calculated with low computational cost and high precision. Also, critical damped natural frequencies of Mindlin viscoelastic plates are calculated. The constitutive equation is written utilizing the Boltzmann integral law with constant bulk modulus. The Laplace transformation is used to convert equations from the time domain to the Laplace domain. The displacement vector is approximated using the separation of variables method. Besides, the effects of material and geometrical properties on the natural frequency, viscous damping, and critical damped natural frequency of viscoelastic Mindlin plates are investigated.

High-order free vibration analysis of elastic plates with multiple cutouts

This paper aims to conduct the free vibration analysis of single-layer and laminated composite plates with multiple cutouts based on the scaled boundary finite element method (SBFEM) incorporated with the precise integration method (PIM) and the technique of the degree of freedom transform. It is applicable to a variety of shaped plates containing cordiform, circular and other complicated cutouts. The key equations are formulated built on the two-dimensional model, and the discretization is carried out in terms of only three translational displacement components as the basic unknowns. The high-order spectral elements are applied in the proposed technique to accurately simulate the arc boundaries of cutouts. Characterized by the important semi-analytical feature of the SBFEM, responses of the transverse free vibration are accurately explored. The derivation of governing equations strictly follows the 3D theory of elasticity without introducing any assumptions. The general solution of the SBFEM key equation is in the form of the matrix exponent, which is calculated by the PIM. As a type of highly precise approach, the PIM is introduced to create the global stiffness matrix from the analytical exponential matrix, which can make sure the eigensolutions with enough accuracy. Aided by the methodology of the kinetic energy formula, the global mass matrix of the perforated plate structure is constructed. According to the thin plates, the degree of freedom transform is employed to lower the dimensions of eigenvalue equation and thus improve the computational efficiency. Numerical examples of flexible square and circular plates with various cutouts reveal that excellent agreement is achieved between the natural frequencies predicted by the developed method and those from other methods and exact solutions. Furthermore, the effect of boundary conditions, skew angles, thickness-to-length ratios and sizes of cutouts on distributions of vibration frequencies is discussed.

Free Vibration Analysis of Elastic Plates in Contact with an Inviscid Fluid Medium

In the present study, a finite element formulation is presented to investigate vibration response of elastic plates in contact with a fluid medium. The fluid is assumed to be incompressible and inviscid, and the impermeability condition of the plate is taken into account. The classical plate theory (CPT), first-order shear deformation plate theory (FSDT), and Reddy third-order shear deformation plate theory (RSDT) are considered for the kinematic description of the solid medium and the simplified Navier–Stokes equations are used as the governing equations for the fluid medium. For each plate theory, a coupled set of finite element equations is derived. The effect of the fluid pressure is considered as an added mass and its effect on natural frequencies and mode shapes is investigated through several numerical simulations by varying the boundary conditions.

Stability Analysis of Elastic Plate in Axial Subsonic Flow

The stability and dynamics of the two-dimensional elastic plate with simply supported boundary conditions in uniform axial subsonic flow were studied. The governing equations of coupled elastic plate in axial flow were derived based on the potential theory. The finite difference method was employed to discrete the governing equation and the flow potential function. The governing equation can be expressed as the function of structural transverse vibration displacement by the matrix operations. The eigenvalue method was used to analyze the stability of the elastic plate, the results of which show that the models with simply supported boundary conditions undergo divergent instability when flow velocity reaches the critical value, the critical divergence velocity is in close agreement with theoretical result using other analytical approaches.

The Decontaminating Device in Steel Wire Rope Automatic Cleaning, Detection and Maintenance Integration System

In order to improve the service life of wire rope used n tensile stringing, an automatic cleaning, detection and maintenance integration system was designed. Through the simulation analysis of elastic plates that fix the fixed brushes and the design of the rotating brushes driving system, a wire rope decontamination device assembled fixed brushes and rotating brushes was developed according to the demand of steel wire decontamination. The brush head adopts the design concept of elastic device, which makes the wire rope pressing force adjustable, ensures the wire connectors passable and makes the axial dirt sweeping of different diameter wire rope possible. The overall rotation mechanism with multiple brushes can circumferentially sweep the dirt in the wire rope gap. Then, the wire ropes were comprehensively sweeped with no dead cleanup. The device has been actually used, and the results showed that the decontamination effect is good.

Analysis of Stratified Rock under Vertical Load in Pile Foundation of Wind Turbine Using Circular Foundation Analysis Method with Equivalent Effective Width

In the design of pile foundation on the rock layer in the stratified structure with sedimentary and rock layers, the structural analysis of the stratified rock layer is required to determine the failure modes (flexural failure, punching shear failure or end bearing failure) and the bearing capacity of the rock layer. However, the existing usable Elastic Plate Analysis Method (EPAM) suggested by ACI committee 436 and Korean Code Requirements for Structural Foundation Design is very complex, and engineers have many difficulties in using it. Therefore, in this research, we proposed the relatively simple Circular Foundation Analysis Method (CFAM) with the concept and the equation of the equivalent effective width (radius) instead of the complex EPM, and the related equations of bending moment and shear force to be equal to the analysis results of EPAM. As a result, the proposed CFAM using the equivalent effective width (radius) is simple and convenient to use, and the analysis results of it are very good in their accuracies comparing those of EPAM and Finite Element Method.

Asymptotic analysis of laminated plates and shallow shells

It was noted long ago [1] that the material strength theory develops both by improving computational methods and by widening the physical foundations. In the present paper, we develop a computational technique based on asymptotic methods, first of all, on the homogenization method [2, 3]. A modification of the homogenization method for plates periodic in the horizontal projection was proposed in [4], where the bending of a homogeneous plate with periodically repeating inhomogeneities on its surface was studied. A more detailed asymptotic analysis of elastic plates periodic in the horizontal projection can be found, e.g., in [5, 6]. In [6], three asymptotic approximations were considered, local problems on the periodicity cell were obtained for them, and the solvability of these problems was proved. In [7], it was shown that the techniques developed for plates periodic in the horizontal projection can also be used for laminated plates. In [7], this was illustrated by an example of asymptotic analysis of an isotropic plate symmetric with respect to the midplane.

Book Review: J. N. Reddy, Theory and Analysis of Elastic Plates and Shells

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und MechanikVolume 88, Issue 10 p. 827-827 Book Review Book Review: J. N. Reddy, Theory and Analysis of Elastic Plates and Shells Holm Altenbach, Holm Altenbach Halle (Saale)Search for more papers by this author Holm Altenbach, Holm Altenbach Halle (Saale)Search for more papers by this author First published: 25 September 2008 https://doi.org/10.1002/zamm.200890020Citations: 6AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat No abstract is available for this article.Citing Literature Volume88, Issue10October 2008Pages 827-827 RelatedInformation

A BEM-BASED MESHLESS METHOD FOR ELASTIC BUCKLING ANALYSIS OF PLATES

In this paper, a BEM-based meshless method is developed for buckling analysis of elastic plates with various boundary conditions that include elastic supports and restraints. The proposed method is based on the concept of the Analog Equation Method (AEM) of Katsikadelis. According to this method, the original eigenvalue problem for a governing differential equation of buckling is replaced by an equivalent plate bending problem subjected to an appropriate fictitious load under the same boundary conditions. The fictitious load is established using a technique based on BEM and approximated by using the radial basis functions. The eigenmodes of the actual problem are obtained from the known integral representation of the solution for the classical plate bending problem, which is derived using the fundamental solution of the biharmonic equation. Thus, the kernels of the boundary integral equations are conveniently established and evaluated. The method has all the advantages of the pure BEM. To validate its effectiveness, accuracy as well as applicability of the proposed method, numerical results of various problems are presented.

A Comparison of X-Ray Microdiffraction and Coherent Gradient Sensing in Measuring Discontinuous Curvatures in Thin Film: Substrate Systems

The coherent gradient sensor (CGS) is a shearing interferometer which has been proposed for the rapid, full-field measurement of deformation states (slopes and curvatures) in thin film-wafer substrate systems, and for the subsequent inference of stresses in the thin films. This approach needs to be verified using a more well-established but time-consuming grain orientation and stress measurement tool, X-ray microdiffraction (XRD). Both CGS and XRD are used to measure the deformation state of the same W film/Si wafer at room temperature. CGS provides a global, wafer-level measurement of slopes while XRD provides a local micromeasurement of lattice rotations. An extreme case of a circular Si wafer with a circular W film island in its center is used because of the presence of discontinuous system curvatures across the wafer. The results are also compared with a theoretical model based on elastic plate analysis of the axisymmetric biomaterial film-substrate system. Slope and curvature measurements by XRD and by CGS compare very well with each other and with theory. The favorable comparison demonstrates that wafer-level CGS metrology provides a quick and accurate alternative to other measurements. It also demonstrates the accuracy of plate theory in modeling thin film-substrate systems, even in the presence of curvature discontinuities

Experimental Study on Added Mass of Elastic Plate on Water

A plate structural system has great possibilities for construction of oceanic structures, especially, floating structures on the sea, which can be applied to a floating artificial base so as to construct floating airport, floating city, IT industrial base, etc.The purpose of this study is to propose an easy calculation method for natural frequency analysis of elastic plate as coupled vibration of plate and water. In the dynamic analysis of floating plate, most of research subjects were on wave response related until now, and papers focused on natural frequency analysis corresponding to response function are hardly found. In addition, experimental approaches by the model testing can't be found. The fluid analysis requires special knowledge with complicated procedure of calculation. It is known that added mass depends on frequency, and in case of vibration problem, it depends on both shape of vibration mode and frequency.Using nine testing models of plate existing on water, modal experiment was carried out as plate-water coupled vibration. The feature of added mass distribution were grasped by identifying natural frequency corresponding to vibration mode order, and through the study a practical estimation method of added mass which can be combined to structural mass, is presented. The validity of this method has been verified by the demonstration through comparisons.

Dynamic analysis of elastic plates reinforced with beams of doubly-symmetrical cross section

In this paper a solution to the dynamic problem of elastic plates reinforced with beams of doubly – symmetrical cross section is presented. The adopted model takes into account the resulting inplane forces and deformations of the plate as well as the axial forces and deformations of the beam, due to combined response of the system. The analysis consists in isolating the beams from the plate by sections parallel to the lower outer surface of the plate. The method of analysis is based on the capability to establish a flexibility matrix with respect to a set of nodal mass points using the Analog Equation Method (AEM) for the static plate problem. A lumped mass matrix is constructed from the tributary mass areas to the nodal mass points. Both free and forced transverse vibrations are considered and numerical examples with great practical interest are presented. The discrepancy in the obtained eigenfrequencies using the presented analysis, which approximates better the actual response of the plate-beams system, and the corresponding ones ignoring the inplane forces and deformations justify the analysis based on the proposed model.

Buckling analysis of elastic plates by boundary element method

This study developed a more general boundary element formulation, which allowed for wide variety of boundary conditions and arbitrary planar shapes, to the investigation of the onset of instability of elastic plate. The formulation of the problem was strictly in terms of boundary integrals so as to eliminate any discretization of domain integrals. This proposed approach placed no restrictions on the nature of the distribution of the in-plane forces within the plate. In this study, the boundary integral formulation was just in terms of the three displacements of the plate's middle surface. This eliminated the need to introduce a stress function to handle the general distributive and variable nature of the in-plane forces so as to keep the introduction of loading to just in-plane known forces or displacements acting on boundaries of the plate system.

A simplified analysis of elastic plates with edge beams

This paper presents a simplified analytical method for rectangular plates with edge beams, such as building slabs, under the validity of the Kirchhoff–Love hypotheses. The accuracy of the Galerkin method depends on the shape functions used. However, it is difficult to find out the suitable shape functions satisfying the boundary conditions of plates with edge beams. So, the plate supported with edge beams is replaced with the plate supported with edges elastically restrained against translation and rotation. From relationships between these different boundary conditions, the shape functions in the current plate use the shape functions of beams supported with equivalent translational stiffness and torsional stiffness. Approximate but accurate solutions for static and dynamic problems of a rectangular plate with edge beams are proposed by the use of the Galerkin method. The numerical results obtained from the proposed theory for an isotropic plate with edge beams show good agreement with results obtained from the finite element method (FEM) using FEM code MSC/NASTRAN.

Justification of the asymptotic analysis of elastic plates, I. The linear case

Justification of the asymptotic analysis of elastic plates, I. The linear case