Analytical solution to the elastic bending of long and rectangular thin plate resting on rubber foundation

2011 ◽  
Vol 226 (5) ◽  
pp. 1186-1197 ◽  
Author(s):  
M Mehrara ◽  
M J Nategh ◽  
H M Naeeni
Keyword(s):  
Mechanical Model ◽  
Contact Region ◽  
Closed Form Solution ◽  
Form Solution ◽  
Geometrical Parameters ◽  
Rectangular Thin Plate ◽  
Concentrated Load ◽  
Elastic Bending ◽  
System A ◽  
Numerical Analytical Method

In this study, the elastic bending of long and rectangular plate resting on unilateral rubber foundation under a concentrated load has been investigated. A new continuum model has been developed to study the rubber foundation reaction. A simplified one-parameter model could thus be obtained for the foundation reaction permitting the parameter to be directly determined without resorting to trial estimation. The governing differential equations have been derived for the plate–foundation system. A numerical–analytical method has been proposed for the exact and closed-form solution of the equations. Several examples have been presented in order to draw a comparison between the results of the proposed solution and the conventional numerical solution. The results have also been compared with the Winkler's mechanical model. Finally, the effect of various parameters on the behaviour of the plate–foundation system has been studied. The results indicate that the length of contact region between the plate and the foundation is influenced by the mechanical and geometrical parameters of the plate and also on the foundation modulus but does not depend on the loading.

Dynamic Analysis of an Elevated Water Tower Subjected to Wind Gust

1986 ◽  
Vol 10 (1) ◽  
pp. 47-51
Author(s):  
Salawu Sadiku ◽  
H.H.E. Leipholz
Keyword(s):  
Dynamic Load ◽  
Closed Form Solution ◽  
Form Solution ◽  
Wind Gust ◽  
Concentrated Mass ◽  
Differential Problem ◽  
System A ◽  
Elevated Water ◽  
The Green Function ◽  
Mass Distribution Function

The analysis of a column carrying a concentrated mass and subjected to a dynamic load is presented in its general form. The water tower is given as a specific example. Despite the singularity in the mass distribution function of the system, a closed form solution to the response problem is obtained. The Green function for the differential problem has been developed thus making the analysis applicable to any dynamic load.

REFINED BEAM THEORIES BASED ON A UNIFIED FORMULATION

2010 ◽  
Vol 02 (01) ◽  
pp. 117-143 ◽  
Author(s):  
ERASMO CARRERA ◽  
GAETANO GIUNTA
Keyword(s):  
Differential Equations ◽  
Cross Section ◽  
Cross Sections ◽  
Order Approximation ◽  
Three Dimensional ◽  
Closed Form Solution ◽  
Approximation Order ◽  
Form Solution ◽  
Geometrical Parameters ◽  
Beam Theories

This paper proposes several axiomatic refined theories for the linear static analysis of beams made of isotropic materials. A hierarchical scheme is obtained by extending plates and shells Carrera's Unified Formulation (CUF) to beam structures. An N-order approximation via Mac Laurin's polynomials is assumed on the cross-section for the displacement unknown variables. N is a free parameter of the formulation. Classical beam theories, such as Euler-Bernoulli's and Timoshenko's, are obtained as particular cases. According to CUF, the governing differential equations and the boundary conditions are derived in terms of a fundamental nucleo that does not depend upon the approximation order. The governing differential equations are solved via the Navier type, closed form solution. Rectangular and I-shaped cross-sections are accounted for. Beams undergo bending and torsional loadings. Several values of the span-to-height ratio are considered. Slender as well as deep beams are analysed. Comparisons with reference solutions and three-dimensional FEM models are given. The numerical investigation has shown that the proposed unified formulation yields the complete three-dimensional displacement and stress fields for each cross-section as long as the appropriate approximation order is considered. The accuracy of the solution depends upon the geometrical parameters of the beam and loading conditions.

A closed-form solution for the bending analysis of composite sandwich pipe with compliance core based on high-order sandwich theory

2018 ◽  
Vol 22 (6) ◽  
pp. 1786-1811 ◽  
Author(s):  
I Maleki ◽  
O Rahmani
Keyword(s):  
Closed Form ◽  
Shell Theory ◽  
Variational Principles ◽  
Closed Form Solution ◽  
Form Solution ◽  
High Order ◽  
Geometrical Parameters ◽  
Cross Sectional ◽  
Nonlinear Distortions ◽  
Flexible Core

In this paper, bending of cylindrical sandwich pipes based on the high-order theory of sandwich structures with flexible core is investigated. The cylindrical sandwich pipe is composed of a flexible core and two composite face sheets. Behavior of the cylindrical sandwich pipe is described by a high-order sandwich shell theory, which explains nonlinear distortions of cross-sectional plane of the flexible core as well as changes in its height. The theory based on variational principles and using an extremely thorough systematic closed-form approach is formulated. In this model, no assumption has been considered for displacement distribution of core components. In this study, stress and displacement of the flexible core are obtained through a three-dimensional elasticity solution and the face sheets are modeled using classical shell theory. Also, a comparison is made in order to verify high-order solution results between a closed-form solution, which is expanded for simply supported boundary conditions and results that are obtained from the commercial finite element method. Finally, influences of physical and geometrical parameters on behavior of the cylindrical sandwich pipe are investigated.

scholarly journals On the Design of Conical Antennas for Broadband Impedance Matching Performance

2017 ◽  
Vol 2017 ◽  
pp. 1-13
Author(s):  
Francisco Estêvão Simão Pereira ◽  
Maurício Henrique Costa Dias
Keyword(s):  
Input Impedance ◽  
Impedance Matching ◽  
Closed Form Solution ◽  
Form Solution ◽  
Geometrical Parameters ◽  
Performance Potential ◽  
Biconical Antenna ◽  
Matching Performance ◽  
Design Perspective ◽  
The Impact

In the scope of broadband radiators, the biconical antenna, or its monopole conical counterpart, is long known to be a proper choice. One common form of such radiator, the spherically capped conical antenna (SCCA), has closed-form solution to its input impedance, from which the broadband performance potential is easily verified. Nonetheless, from the design perspective, apart from a few clues inferred from existing solutions, little is found to accurately guide the choice of the main geometrical parameters of the antenna that will enable it to comply with a set of imposed bandwidth requirements. This paper proposes a simple 10-step sequence to derive conical or biconical antenna design charts. These charts provide straightforward information on the geometrical limits within which the required antenna impedance matching broadband performance is achieved. The method is assessed for the SCCA and the open conical antenna (OCA) using theoretical and simulated estimates of the input impedance. A discussion on the impact of the cap and the feed gap is included.

scholarly journals Extend Convergence-Confinement Method for deep tunnels in poroelastic anisotropic medium

2018 ◽  
Vol 251 ◽  
pp. 04051 ◽  
Author(s):  
Nam-Hung Tran ◽  
Thi-Thu-Nga Nguyen ◽  
Duc-Phi Do ◽  
Tri-Ta Nguyen ◽  
Chu-Quang Cao
Keyword(s):  
Anisotropic Medium ◽  
Mechanical Model ◽  
Strain State ◽  
Surrounding Medium ◽  
Closed Form Solution ◽  
Form Solution ◽  
Tunnel Face ◽  
Mechanical Coupling ◽  
Tunnel Design ◽  
Numerical Estimations

This paper is devoted to present a closed-form solution based on the approach of the conventional convergence-confinement method to study the effect of the movement of the tunnel face during the excavation on the stress-strain state of the surrounding medium and the interaction between the ground and the support for a deep tunnel in poroelastic anisotropic medium. In this study, a hydro-mechanical coupling behaviour of the ground at the steady-state of the groundwater flow will be taken into account. The obtained solution could be used as a quick tool to calibrate tunnels in elastic porous medium. Some numerical estimations indicate that, a hydro-mechanical model of the medium should be considered in tunnel design.

On a Closed-Form Solution of Prandtl's System of Equations

2013 ◽  
Vol 40 (2) ◽  
pp. 106-114
Author(s):  
J. Venetis ◽  
Aimilios (Preferred name Emilios) Sideridis
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Of Equations

Plane Wave Resonance in the Tire Air Cavity as a Vehicle Interior Noise Source

1995 ◽  
Vol 23 (1) ◽  
pp. 2-10 ◽  
Author(s):  
J. K. Thompson
Keyword(s):  
Closed Form Solution ◽  
Form Solution ◽  
Interior Noise ◽  
Cavity Resonance ◽  
Test Results ◽  
Vehicle Interior ◽  
Air Cavity ◽  
Vehicle Interior Noise ◽  
Wave Resonance ◽  
Resonance Frequencies

Abstract Vehicle interior noise is the result of numerous sources of excitation. One source involving tire pavement interaction is the tire air cavity resonance and the forcing it provides to the vehicle spindle: This paper applies fundamental principles combined with experimental verification to describe the tire cavity resonance. A closed form solution is developed to predict the resonance frequencies from geometric data. Tire test results are used to examine the accuracy of predictions of undeflected and deflected tire resonances. Errors in predicted and actual frequencies are shown to be less than 2%. The nature of the forcing this resonance as it applies to the vehicle spindle is also examined.

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