Finite difference solution for circular plates on elastic foundations

The large deflection on problem of circular plate on elastic foundation and in conjunction with linear elastic structure

A combined boundary-finite element procedure for dynamic analysis of plates with fluid and foundation interaction considering free surface effect

Nonlinear problems of circular plates with variable thickness under central concentrated load

Circular plates are important structural elements in modern engineering structures. In this paper a computationally efficient and accurate numerical model is presented for the study of free vibration and bending behavior of thick circular plates based on Mindlin plate theory. The approach developed is based on the discrete singular convolution method and the use of regularized Shannon's delta kernel. Frequency parameters, deflections and bending moments are obtained for different geometric parameters of the circular plate. Comparisons are made with existing numerical and analytical solutions in the literature. It is found that the DSC method yields accurate results for the free vibration and bending problems of thick circular plates. Copyright © 2008 John Wiley & Sons, Ltd.

Loaded contact pressure distribution prediction for spiral bevel gear

Presented herein are the exact axisymmetric buckling solutions of Reddy circular plates on the Pasternak foundation and subjected to a uniform radial load. The boundary conditions of the circular plates covered in this study are (1) simply supported edges; (2) clamped edges; and (3) simply supported edges with elastic rotational restraints. The Reddy buckling solutions are expressed in terms of the corresponding well-known Kirchhoff buckling solutions of circular plates without the elastic foundation. Sample buckling results of Reddy plates are also presented, which should be useful as benchmark solutions for testing numerical solutions and techniques.

On analytical-computerized method to solve nonlinear bending problem of circular plate under a concentrated load

In this paper, the complex variable reproducing kernel particle method (CVRKPM) for solving the bending problems of isotropic thin plates on elastic foundations is presented. In CVRKPM, one-dimensional basis function is used to obtain the shape function of a two-dimensional problem. CVRKPM is used to form the approximation function of the deflection of the thin plates resting on elastic foundation, the Galerkin weak form of thin plates on elastic foundation is employed to obtain the discretized system equations, the penalty method is used to apply the essential boundary conditions, and Winkler and Pasternak foundation models are used to consider the interface pressure between the plate and the foundation. Then the corresponding formulae of CVRKPM for thin plates on elastic foundations are presented in detail. Several numerical examples are given to discuss the efficiency and accuracy of CVRKPM in this paper, and the corresponding advantages of the present method are shown.

The general solution for axial symmetrical bending of nonhomogeneous circular plates resting on an elastic foundation

An analytical study is presented for the vibration characteristics of thin circular plates with rotational elastic edge support and resting on an elastic foundation. The Winkler model was used to describe this foundation. The exact analytical method is used to derive the frequency equation of the plate with elastic support and resting on this foundation. Parametric investigations of the vibration of circular plates with an restrained elastically edge against rotation and resting on an elastic foundation have been carried out with respect to various rotational stiffness parameters, foundation stiffness parameters, and boundary conditions. Twelve vibration modes are presented. The location of the stepped region with respect to rotational restraint changed very little and moved from the range of 0.014 26† [10.006 204 8‡]–1 134.227 [10.025 94] to 0.017 58 [14.001 133]–6 352.958 2 [14.658 356]. Here, † represents the rotational spring stiffness ratio, and ‡ represents the foundation stiffness ratio. Extensive data are tabulated so that pertinent conclusions can be arrived at on the influence of rotational edge restraint and the foundation parameters of a Winkler foundation on the natural frequencies of uniform thin isotropic circular plates.

On the conforming cubic triangular element for plate bending

In this study, the large deformation problem of a functionally-graded thin circular plate subjected to transversely uniformly-distributed load and with different moduli in tension and compression (bimodular property) is theoretically analyzed, in which the small-rotation-angle assumption, commonly used in the classical Föppl–von Kármán equations of large deflection problems, is abandoned. First, based on the mechanical model on the neutral layer, the bimodular functionally-graded property of materials is modeled as two different exponential functions in the tensile and compressive zones. Thus, the governing equations of the large deformation problem are established and improved, in which the equation of equilibrium is derived without the common small-rotation-angle assumption. Taking the central deflection as a perturbation parameter, the perturbation method is used to solve the governing equations, thus the perturbation solutions of deflection and stress are obtained under different boundary constraints and the regression of the solution is satisfied. Results indicate that the perturbation solutions presented in this study have higher computational accuracy in comparison with the existing perturbation solutions with small-rotation-angle assumption. Specially, the computational accuracies of external load and yield stress are improved by 17.22% and 28.79% at most, respectively, by the numerical examples. In addition, the small-rotation-angle assumption has a great influence on the yield stress at the center of the bimodular functionally-graded circular plate.

This paper presents the class of nonuniform beams and nonuniform axisymmetrical circular plates whose boundary value problems of free transverse vibrations and free transverse axisymmetrical vibrations, respectively, have been identified to be eigenvalue singular problems of orthogonal polynomials. Recent published results regarding a fourth order differential equation and eigenvalue singular problem of classical orthogonal polynomials allowed this study, which extends the class of nonuniform beams and circular nonuniform plates having exact solutions for the problem of free transverse vibrations. The geometry of the elements belonging to the class presented in this paper consists of beams convex parabolic thickness variation and polynomial width variation with the axial coordinate, and plates of convex parabolic thickness variation with the radius. Two boundary value problems of transverse vibrations of beams are reported: 1) complete beam (sharp at either end) with free-free boundary conditions, and 2) half-beam, i.e. a half of the symmetric complete beam, with the large end hinged and sharp end free. The boundary value problem of circular complete plate (zero thickness at zero and outer radii) with free-free boundary conditions has been also reported. For all these boundary value problems the exact mode shapes were Jacobi polynomials and the exact dimensionless natural frequencies were found from the eigenvalues of the eigenvalue singular problems of orthogonal polynomials.

Discontinuity solutions to plate and beam problems

The reliability of solid oxide fuel cell (SOFC) systems is closing the gap to meet the requirements for market implementation. Finite-element (FE) stack models, typically used for stack reliability analyses, commonly consider idealized components. In reality, dimensions and geometry of the produced stack components have statistical variations. The resulting variability in shape is expected to have an impact on the distribution of the contact pressure over the cell active area. In this study, the initial deformation of the metallic interconnect (MIC) is implemented in the stack model. The simulation starts with the simulation of the stack production and qualification. The results of this first calculation are used to simulate either thermal cycling or prolonged continuous operation. The distribution of the simulated contact pressure on the active area is found to evolve differently during thermal cycling and operation, if the initial deformation of the MIC is included in the stack model.