scholarly journals A New Form of the General Solution of the Elastic Space Axisymmetric Problem in Pavement Mechanics

2016 ◽  
Vol 2016 ◽  
pp. 1-6
Author(s):  
Jia Liang ◽  
Guo Jian ◽  
He Shikai
Keyword(s):  
General Solution ◽  
Axisymmetric Problem ◽  
Hankel Transform ◽  
Elastic Half Space ◽  
Displacement Function ◽  
Winkler Foundation ◽  
Elastic Space ◽  
Equilibrium Equations ◽  
Present Solution ◽  
New Form

In order to analyze the stress and displacement of pavement, a new form of the general solution of the elastic space axisymmetric problem is proposed by the method of mathematics reasoning. Depending on the displacement function put forward by Southwell, displacement function is derived based on Hankel transform and inverse Hankel transform. A new form of the general solution of the elastic space axisymmetric problem has been set up according to a few basic equations as the geometric equations, constitutive equations, and equilibrium equations. The present solution applies to elastic half-space foundation and Winkler foundation; the stress and displacement of pavement are obtained by mathematical deduction. The example results show that the proposed method is practically feasible.

scholarly journals Interior-stress fields produced by a general axisymmetric punch

Friction ◽  
2021 ◽  
Author(s):  
Longxiang Yang ◽  
Zhanjiang Wang ◽  
Weiji Liu ◽  
Guocheng Zhang ◽  
Bei Peng
Keyword(s):  
Hankel Transform ◽  
Elastic Half Space ◽  
Stress Fields ◽  
Dual Integral Equations ◽  
Total Load ◽  
Interior Stress ◽  
Von Mises ◽  
Von Mises Stresses ◽  
Relationship Of ◽  
Analytical Expressions

AbstractThis work is a supplement to the work of Sneddon on axisymmetric Boussinesq problem in 1965 in which the distributions of interior-stress fields are derived here for a punch with general profile. A novel set of mathematical procedures is introduced to process the basic elastic solutions (obtained by the method of Hankel transform, which was pioneered by Sneddon) and the solution of the dual integral equations. These processes then enable us to not only derive the general relationship of indentation depth D and total load P that acts on the punch but also explicitly obtain the general analytical expressions of the stress fields beneath the surface of an isotropic elastic half-space. The usually known cases of punch profiles are reconsidered according to the general formulas derived in this study, and the deduced results are verified by comparing them with the classical results. Finally, these general formulas are also applied to evaluate the von Mises stresses for several new punch profiles.

Contact Stress Analysis of a Layered Transversely Isotropic Half-Space

1992 ◽  
Vol 114 (2) ◽  
pp. 253-261 ◽  
Author(s):  
C. H. Kuo ◽  
L. M. Keer
Keyword(s):  
Half Space ◽  
Mixed Boundary ◽  
Contact Region ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Hankel Transform ◽  
Elastic Half Space ◽  
Contact Stresses ◽  
Stress Components ◽  
Contact Failure

The three-dimensional problem of contact between a spherical indenter and a multi-layered structure bonded to an elastic half-space is investigated. The layers and half-space are assumed to be composed of transversely isotropic materials. By the use of Hankel transforms, the mixed boundary value problem is reduced to an integral equation, which is solved numerically to determine the contact stresses and contact region. The interior displacement and stress fields in both the layer and half-space can be calculated from the inverse Hankel transform used with the solved contact stresses prescribed over the contact region. The stress components, which may be related to the contact failure of coatings, are discussed for various coating thicknesses.

A note on the infinitely deep dam with a Markovian input

1979 ◽  
Vol 16 (4) ◽  
pp. 917-922 ◽  
Author(s):  
R. M. Phatarfod
Keyword(s):  
Markov Chain ◽  
General Solution ◽  
Unit Disc ◽  
Linear Constraints ◽  
Equilibrium Equations ◽  
Ergodic Markov Chain

In this paper we consider an infinitely deep dam fed by inputs which form an ergodic Markov chain and whose release M is non-unit. The extension to non-unit release follows on lines similar to the independent inputs case. We show that P(θ) – θ MΙ where P(θ) = (pijθ i) has a maximum of N = M(M + l)/2 non-zero singularities in the unit disc, so that the general solution of the equilibrium equations has N unknown constants. We also show that these constants satisfy N linear constraints, so that the solution is fully determined.

Closed-Form Solutions of the Elastic Half Space due to a Line Heat Source

2014 ◽  
Vol 638-640 ◽  
pp. 2082-2091
Author(s):  
John C.C. Lu ◽  
Feng Tsai Lin
Keyword(s):  
Heat Source ◽  
Closed Form ◽  
Half Space ◽  
Hankel Transform ◽  
Elastic Half Space ◽  
Line Heat Source ◽  
Closed Form Solutions ◽  
Line Sink ◽  
Vertical Displacements ◽  
Thermoelastic Response

Thermoelastic response due to a line heat source is analog to poroelastic reaction caused by a fluid line sink. In this study, the strata are modeled as a thermoelastic or poroelastic half space bounded by horizontal surface in the mathematical model. Thermomechanics and poromechanics are applied on the formulation of basic governing equations, and an analogy is drawn to show the similarity. Using Hankel transform technique and approaching symbolic integral through Mathematica, the closed-form solutions of the horizontal and vertical displacements due to a fluid line sink are obtained. The displacements produced by the line heat source are described through analog quantities between thermoelasticity and poroelasticity. The solutions can be applied to dewater operations and build waste repository.

scholarly journals Axisymmetric Vibration for Micropolar Porous Thermoelastic Circular Plate

2017 ◽  
Vol 22 (3) ◽  
pp. 583-600 ◽  
Author(s):  
R. Kumar ◽  
P. Kaushal ◽  
R. Sharma
Keyword(s):  
Circular Plate ◽  
Axisymmetric Problem ◽  
Volume Fraction ◽  
Hankel Transform ◽  
Specific Model ◽  
Axisymmetric Vibration ◽  
Physical Domain ◽  
Special Cases ◽  
Eigen Value ◽  
Field Temperature

AbstractThe present investigation is concerned with a two dimensional axisymmetric problem in a homogeneous isotropic micropolar porous thermoelastic circular plate by using the eigen value approach. The Laplace and Hankel transform are used to solve the problem. The expression of displacements, microrotation, volume fraction field, temperature distribution and stresses are obtained in the transformed domain subjected to thermomechanical sources. A computer algorithm is developed for numerical computations. To obtain the resulting quantities in a physical domain, a numerical inversion technique is used. The resulting quantities are depicted graphically for a specific model. Some special cases are also deduced.

The Morley-Koiter Equations for Thin-Walled Circular Cylindrical Shells: Part 1—General Solution for Symmetrical Shells of Uniform Thickness

1973 ◽  
Vol 40 (4) ◽  
pp. 961-965 ◽  
Author(s):  
C. P. Mangelsdorf
Keyword(s):  
General Solution ◽  
Evaluation Procedure ◽  
Uniform Thickness ◽  
Equilibrium Equations ◽  
Line Load ◽  
Longitudinal Line ◽  
Symmetrical Loading ◽  
Circular Cylindrical Shells ◽  
Simple Supports ◽  
Thin Walled

Modified Donnell equilibrium equations are solved in Part 1 for the case of symmetrical loading and supports, using Fourier series. An evaluation procedure for simple, fixed, and relaxed simple conditions is suggested. In Part 2, an application of the general solution is made for a shell with small circumferential grooves (or ribs) subjected to a longitudinal line load after approximations to allow for such grooves are introduced. The solution is completed for the boundary conditions of classical simple supports and relaxed simple supports and the results compared with experimental data.

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