Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 3

Winkler foundation Related Abstracts

3 Solution for Thick Plate Resting on Winkler Foundation by Symplectic Geometry Method

Authors: Mei-Jie Xu, Yang Zhong


Based on the symplectic geometry method, the theory of Hamilton system can be applied in the analysis of problem solved using the theory of elasticity and in the solution of elliptic partial differential equations. With this technique, this paper derives the theoretical solution for a thick rectangular plate with four free edges supported on a Winkler foundation by variable separation method. In this method, the governing equation of thick plate was first transformed into state equations in the Hamilton space. The theoretical solution of this problem was next obtained by applying the method of variable separation based on the Hamilton system. Compared with traditional theoretical solutions for rectangular plates, this method has the advantage of not having to assume the form of deflection functions in the solution process. Numerical examples are presented to verify the validity of the proposed solution method.

Keywords: symplectic geometry method, Winkler foundation, thick rectangular plate, variable separation method, Hamilton system

Procedia PDF Downloads 135
2 Nonlinear Analysis of Shear Deformable Deep Beam Resting on Nonlinear Two-Parameter Random Soil

Authors: M. Seguini, D. Nedjar


In this paper, the nonlinear analysis of Timoshenko beam undergoing moderate large deflections and resting on nonlinear two-parameter random foundation is presented, taking into account the effects of shear deformation, beam’s properties variation and the spatial variability of soil characteristics. The finite element probabilistic analysis has been performed by using Timoshenko beam theory with the Von Kàrmàn nonlinear strain-displacement relationships combined to Vanmarcke theory and Monte Carlo simulations, which is implemented in a Matlab program. Numerical examples of the newly developed model is conducted to confirm the efficiency and accuracy of this later and the importance of accounting for the foundation second parameter (Winkler-Pasternak). Thus, the results obtained from the developed model are presented and compared with those available in the literature to examine how the consideration of the shear and spatial variability of soil’s characteristics affects the response of the system.

Keywords: Nonlinear Analysis, Soil-Structure Interaction, timoshenko beam, Winkler foundation, spatial variability, Pasternak foundation, Euler-Bernoulli beam, large deflection

Procedia PDF Downloads 169
1 C Vibration Analysis of a Beam on Elastic Foundation with Elastically Restrained Ends Using Spectral Element Method

Authors: Hamioud Saida, Khalfallah Salah


In this study, a spectral element method is employed to predict the free vibration of a Euler-Bernoulli beam resting on a Winkler foundation with elastically restrained ends. The formulation of the dynamic stiffness matrix has been established by solving the differential equation of motion, which was transformed to frequency domain. Non-dimensional natural frequencies and shape modes are obtained by solving the partial differential equations, numerically. Numerical comparisons and examples are performed to show the effectiveness of the SEM and to investigate the effects of various parameters, such as the springs at the boundaries and the elastic foundation parameter on the vibration frequencies. The obtained results demonstrate that the present method can also be applied to solve the more general problem of the dynamic analysis of structures with higher order precision.

Keywords: Winkler foundation, elastically supported Euler-Bernoulli beam, free-vibration, spectral element method

Procedia PDF Downloads 6