scholarly journals STATIC ANALYSIS OF THIN ORTHOTROPIC DECKS ON WINKLER ELASTIC FOUNDATION

2021 ◽  
Vol 22 (1) ◽  
pp. 32-37
Author(s):  
M. Delyavskyi ◽  
K. Rosińskyi ◽  
Yu. Famuliak
Keyword(s):  
Static Analysis ◽  
Elastic Foundation ◽  
Winkler Elastic Foundation

Static Analysis for Exact Vibration Analysis of Clamped Plates

2015 ◽  
Vol 15 (08) ◽  
pp. 1540030 ◽  
Author(s):  
Moshe Eisenberger ◽  
Aharon Deutsch
Keyword(s):  
Static Analysis ◽  
Elastic Foundation ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Point Load ◽  
Vibration Frequencies ◽  
Concentrated Load ◽  
Simply Supported ◽  
Winkler Elastic Foundation ◽  
Isotropic Rectangular Plate

Presented herein is a new method for the analysis of plates with clamped edges. The solutions for the natural frequencies of the plates are found using static analysis. The starting are the equations of motion of an isotropic rectangular plate supported on Winkler elastic foundation, with a positive or negative value. In either case, one can solve the displacements of such a plate under a given concentrated load. This deflection will be infinite if the plate losses its stiffness, or in other words, the generalized foundation is causing the plate to be unstable. The solution for the vibration frequencies of the plate is equivalent to finding the values of the negative elastic foundation that will yield infinite deflection under a point load on the plate. The solution for a clamped plate is decomposed as the sum of three cases of plates resting on elastic foundation: simply supported plate with a concentrated load, and two cases of distributed moments along opposite edges. The solution for simply supported plates with elastic foundation is found using Navier's method. For zero force, the vibration frequencies are found up to the desired accuracy by careful calculations at the neighborhood of the roots.

Stability Analysis of Cylindrical Shells Resting on Winkler Elastic Foundation Using Semi-Analytical Quadrature Element Method

2019 ◽  
Vol 821 ◽  
pp. 459-464
Author(s):  
Qi Gao Hu ◽  
Xu Dong Hu ◽  
Zhi Qiang Shen ◽  
Liang Yun Tao ◽  
Ze Tan
Keyword(s):  
Elastic Foundation ◽  
Cylindrical Shells ◽  
Longitudinal Direction ◽  
External Pressure ◽  
Element Formulation ◽  
Quadrature Element Method ◽  
Advanced Composite Materials ◽  
Winkler Elastic Foundation ◽  
Parametric Studies ◽  
Element Method

The buried pipelines or vessels and other similar structures made of homogeneous or advanced composite materials are commonly used in civil engineering and biotechnology. The radial stability problem of these structures was widely studied using the cylindrical shell model over the past years. In this paper, the linear stability of cylindrical shells resting on Winkler elastic foundation under uniformly distributed external pressure was analyzed with semi-analytical quadrature element method (QEM). As for the longitudinal direction, the radial deflection of shell was approximated by the quadrature element formulation. While the analytic trigonometric function was adopted for description of radial deflection in circumferential direction. The Numerical results of critical buckling load were compared with the semi-analytical FEM. It is found that the semi-analytical QEM possesses higher computational efficiency and applicability than semi-analytical FEM. Then, the effects of the shell length, radius, and thickness on the critical buckling pressures are systematically investigated through the parametric studies.

scholarly journals REINFORCED CONCRETE COATING PLATES OF HIGHWAYS ON AN ELASTIC HALF-SPACE

2018 ◽  
Vol 14 (2) ◽  
pp. 149-157
Author(s):  
Slav D. Semeniuk ◽  
Roman V. Kumashov
Keyword(s):  
Reinforced Concrete ◽  
Static Analysis ◽  
Elastic Foundation ◽  
Strain State ◽  
Ritz Method ◽  
Elastic Half Space ◽  
Numerical Studies ◽  
Concrete Coating ◽  
Plate On Elastic Foundation ◽  
Made In

Static analysis of the stress-strain state of a plate on elastic foundation is made in two ways on the example of a reinforced concrete road plate 2PP30.18-30 series B3.503.1-1 intended for temporary roads. These plates are considered as a planar structure on an elastic foundation. The plates are calculated by the method of B.N. Zhemochkin using the Ritz method to determine plate deflections in the main system using the mathematical package «MathCad». Also the plates are calculated on the PC «LIRA». There are given the results of experimental and numerical studies in this article

Static and Dynamic Response of a Beam on a Winkler Elastic Foundation

2005 ◽  
Author(s):  
Timour M. A. Nusirat ◽  
M. N. Hamdan
Keyword(s):  
Elastic Foundation ◽  
Governing Equation ◽  
Initial Value Problem ◽  
Nonlinear Partial Differential Equation ◽  
Static Case ◽  
Initial Value ◽  
Characteristic Curves ◽  
System Parameters ◽  
Winkler Elastic Foundation ◽  
Dynamic Case

This paper is concerned with analysis of dynamic behavior of an Euler-Bernoulli beam resting on an elastic foundation. The beam is assumed to be subjected to a uniformly distributed lateral static load, have an initial quarter-sine shape deflection. At one end, the beam is assumed to be restrained by a pin, while at the other end, the beam is assumed to be restrained by a torsional and a translational linear spring. The beam is modeled by a nonlinear partial differential equation where the nonlinearity enters the governing equation through the beam axial force. In the static case, because of a unique feature of governing equation, the analysis was carried out using the theory of linear differential equations, but takes into account the effect of actual deflection on the induced axial thrust. In the dynamic case, stability analysis of the beam is carried out by calculating the nonlinear frequencies of free vibration of the beam about its static equilibrium configuration. The assumed mode method is used to discretize and find an equivalent nonlinear initial value problem. Then the harmonic balance is used to obtain an approximate solution to the nonlinear oscillator described by the equivalent initial value problem. The analyses of results were carried out for a selected range of values of the system parameters: foundation elastic stiffness, lateral load, and maximum beam edge deflection. In the static case the results are presented as characteristic curves showing the variation of the beam static deflection and associated bending moment distribution with each of the above system parameters. In the dynamic case, the presented characteristic curves show the variation of the nonlinear natural frequency corresponding to the first and the second modes over a range of each of the above system parameters.

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