Theoretical Solution for Thick Plate Resting on Pasternak Foundation by Symplectic Geometry Method

2013 ◽  
Vol 81 (3) ◽  
Author(s):  
Yang Zhong ◽  
Liu Heng
Keyword(s):  
Symplectic Geometry ◽  
Thick Plate ◽  
Solution Process ◽  
Theory Of Elasticity ◽  
Theoretical Solution ◽  
Rectangular Plates ◽  
Pasternak Foundation ◽  
Variable Separation ◽  
State Equations ◽  
Hamilton System

Based on the analogy of structural mechanics and optimal control, the theory of the Hamilton system can be applied in the analysis of problem solving 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 Pasternak foundation by the variable separation method. In this method, the governing equation of the 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.

Experiments on the Buckling of Simply-Supported Rectangular Plates

1969 ◽  
Vol 73 (703) ◽  
pp. 607-608 ◽  
Author(s):  
A. C. Mills
Keyword(s):  
Experimental Investigation ◽  
Theoretical Analysis ◽  
Boundary Conditions ◽  
Buckling Load ◽  
Theoretical Solution ◽  
Rectangular Plates ◽  
Uniform Load ◽  
Simply Supported

In ref. (1) Pope presents a theoretical analysis of the buckling of rectangular plates tapered in thickness under uniform load in the direction of taper. An experimental investigation into the end load buckling problem for a plate having simply-supported edges with the sides prevented from moving normally in the plane of the plate is described in ref. (2). For these boundary conditions the theoretical solution is exact. However, the compatability equation is not satisfied exactly when the sides are free to move in the plane of the plate. This experimental investigation demonstrates that the buckling load is nevertheless adequately predicted by the analysis in these circumstances.

Bending analysis of sandwich plates with composite face sheets and compliance functionally graded syntactic foam core

2016 ◽  
Vol 230 (20) ◽  
pp. 3606-3630 ◽  
Author(s):  
Mohammad Javad Lashkari ◽  
Omid Rahmani
Keyword(s):  
Plate Theory ◽  
Theory Of Elasticity ◽  
Functionally Graded ◽  
Shear Stresses ◽  
Rectangular Plates ◽  
Governing Equations ◽  
Positive Role ◽  
Virtual Displacement ◽  
The Core ◽  
Composite Face

In this paper, the problem of a rectangular plate with functionally graded soft core and composite face sheets is considered using high order sandwich plate theory. This theory applies no assumptions on the displacement and stress fields in the core. Face sheets were treated using classical theory and core was exposed to the theory of elasticity. Governing equations and boundary conditions are derived using principle of virtual displacement and the governing equations are based on eight primary variables including six displacements and two shear stresses. This solution is able to present localized displacements and stresses in places where concentrated loads are exerted to the structure since the displacements in the core can take a nonlinear form which could not be seen in the previous theories such as classical and higher order shear theories. This theory is suitable for rectangular plates under all types of loadings distributed or concentrated which can be different on upper and lower face sheets at the same point. The results were compared with the published literature using theory of elasticity and showed good agreement confirming the accuracy of the present theory. Subsequently, the solution for the core with functionally graded material is presented and effectively indicates positive role of functionally graded core.

Rectangular Thick Plate with Free Edges on Pasternak Foundation

1994 ◽  
Vol 120 (5) ◽  
pp. 971-988 ◽  
Author(s):  
X. P. Shi ◽  
S. A. Tan ◽  
T. F. Fwa
Keyword(s):  
Thick Plate ◽  
Pasternak Foundation ◽  
Free Edges

On the Applicability of New Symplectic Approach for Exact Bending Solutions of Moderately Thick Rectangular Plate

2011 ◽  
Vol 105-107 ◽  
pp. 611-614
Author(s):  
Bo Hu ◽  
Rui Li
Keyword(s):  
Eigenfunction Expansion ◽  
Symplectic Geometry ◽  
Rectangular Plates ◽  
State Variables ◽  
Simply Supported ◽  
Thick Rectangular Plate ◽  
Elasticity Equations ◽  
Basic Equations ◽  
Geometry Method ◽  
Basic Elasticity

The exact bending solutions of moderately thick rectangular plates with two opposite sides simply supported are derived based on the symplectic geometry method. The basic equations for the plates are transferred into Hamilton canonical equations. Then the whole state variables are separated. According to the method of eigenfunction expansion in the symplectic geometry, the exact bending solutions of the plates are obtained. Since only the basic elasticity equations of the plates are used and there is no need to select the deformation functions arbitrarily, the approach utilized is completely reasonable.

Transverse Vibration of Buried Pipelines Due to Internal Excitation at a Point

1993 ◽  
Vol 207 (1) ◽  
pp. 41-59 ◽  
Author(s):  
U G Köpke
Keyword(s):  
Theoretical Models ◽  
Element Model ◽  
Theory Of Elasticity ◽  
Pasternak Foundation ◽  
Buried Pipelines ◽  
Soil Response ◽  
Internal Excitation ◽  
Foundation Model ◽  
Support Conditions ◽  
Good Agreement

This paper is concerned with the dynamic response of buried pipelines due to excitation located inside the pipe. This work is important for application to techniques that employ vibration to investigate pipeline support conditions using a vibrating pipe inspection device. It also has application to the detection of spanning in off-shore pipelines. Three different theoretical models are developed and investigated. The first model employs the theory of elasticity, the second is a finite element model and the third is a beam-on-elastic Pasternak foundation. Good agreement between these models is demonstrated. The beam-on-elastic Pasternak foundation model is successfully used to predict ‘signatures’ of the pipe-soil response that characterize soil support features, such as hard and soft supports.

Solving the Deflection Equations of Thick Plate under Concentrated Load

2012 ◽  
Vol 594-597 ◽  
pp. 2659-2663
Author(s):  
Dan Zhang
Keyword(s):  
Rectangular Plate ◽  
Thick Plate ◽  
Numerical Results ◽  
Reciprocal Theorem ◽  
Rectangular Plates ◽  
Concentrated Load ◽  
Simply Supported ◽  
Thick Rectangular Plate ◽  
Reciprocal Theorem Method

According to reciprocal-theorem method (RTM), the deflection equations of thick rectangular plate with two edges simply supported and two edges free under concentrated load are obtained in this paper. Simultaneously through the programming computation, the numerical results with actual value are obtained, which further showed the accuracy and superiority of RTM to solve the bending of thick rectangular plates.

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