Thermal Shock on a Circular Surface of Exposure of an Elastic Half Space

1955 ◽  
Vol 22 (2) ◽  
pp. 177-182
Author(s):  
M. A. Sadowsky
Keyword(s):  
Thermal Shock ◽  
Half Space ◽  
Arbitrary Shape ◽  
Elastic Half Space ◽  
Circular Surface ◽  
Explicit Determination

Abstract The paper presents an explicit determination of displacements and stresses in a uniform circular thermal shock. In a generalization to nonuniform shocks on surfaces of arbitrary shape, it is shown that the protrusion arising at any place is proportional to the intensity of the shock at that place.

Response of an Elastic Half Space to Uniformly Moving Circular Surface Load

1970 ◽  
Vol 37 (1) ◽  
pp. 109-115 ◽  
Author(s):  
S. K. Singh ◽  
J. T. Kuo
Keyword(s):  
Half Space ◽  
Hypergeometric Functions ◽  
Integral Form ◽  
Elastic Half Space ◽  
Point Load ◽  
Surface Load ◽  
Static Part ◽  
Circular Load ◽  
Circular Surface ◽  
Velocity Effect

The problem of a uniformly moving circular surface load of a general orientation on an elastic half space for two types of load distribution, viz., “uniform” and “hemispherical,” is considered. The solutions have been obtained in integral form. The displacements on the surface of the half space, in the case in which the load velocity V is smaller than the transverse wave velocity of the medium CT are expressed in a closed form as a sum of two terms by using properties of Gauss’ hypergeometric functions. One of these terms gives the static part of the solution, whereas the other term represents the velocity effect part. At distances greater than about five radii from the center of the moving circular load, a moving point load is found to be a good approximation.

Accuracy of Stress Analysis Using Numerical Integration of Elastic Half-Space

2013 ◽  
Vol 300-301 ◽  
pp. 1127-1135 ◽  
Author(s):  
Radim Čajka
Keyword(s):  
Finite Element ◽  
Stress Analysis ◽  
Numerical Integration ◽  
Half Space ◽  
Elastic Half Space ◽  
Rigidity Matrix ◽  
Interaction Solutions ◽  
Proposed Model ◽  
Isoparametric Elements

In case of constructions placed on subsoil, it is necessary to create a rigidity matrix for the element subsoil. That rigidity matrix should be then added up in respective positions with the rigidity matrix of an element. To clarify the proposed model of the subsoil, a method is derived for determination of vertical subsoil stress analysis under any shape of a slab construction by means of numerical integration and theory of isoparametric elements using the Jacobian transformation. This approach is rather original and represents the key contribution of this work in interaction solutions. Using the proposed approach, the method can be employed for any shape of a finite element.

Wave propagation from extended, asymmetric surface sources in an elastic half-space

1979 ◽  
Vol 69 (3) ◽  
pp. 713-735
Author(s):  
N. C. Maiti ◽  
M. Mitra
Keyword(s):  
Wave Propagation ◽  
Half Space ◽  
Surface Displacement ◽  
Elastic Half Space ◽  
Stress Distributions ◽  
Surface Motion ◽  
Common Features ◽  
Exact Determination

abstract A procedure is given for the exact determination of the displacement produced in a half-space by arbitrary stresses acting on the surface. Solutions have been obtained for three different impulsive stress distributions acting on a circular portion of the surface and some common features of the solutions are examined. Numerical values of the surface displacement are exhibited graphically in the three cases showing that the pulses comprising the surface motion are oscillatory.

Dynamic Response of a Rigid Foundation Subjected to a Distance Blast

2012 ◽  
Author(s):  
Deji Ojetola ◽  
Hamid R. Hamidzadeh
Keyword(s):  
Dynamic Response ◽  
Half Space ◽  
Integral Transform ◽  
Numerical Technique ◽  
Formal Solution ◽  
Elastic Half Space ◽  
Numerical Results ◽  
Rigid Foundation ◽  
Transform Method

Blasts and explosions occur in many activities that are either man-made or nature induced. The effect of the blasts could have a residual or devastating effect on the buildings at some distance within the vicinity of the explosion. In this investigation, an analytical solution for the time response of a rigid foundation subjected to a distant blast is considered. The medium is considered to be an elastic half space. A formal solution to the wave propagations on the medium is obtained by the integral transform method. To achieve numerical results for this case, an effective numerical technique has been developed for calculation of the integrals represented in the inversion of the transformed relations. Time functions for the vertical and radial displacements of the surface of the elastic half space due to a distant blast load are determined. Mathematical procedures for determination of the dynamic response of the surface of an elastic half-space subjected to the blast along with numerical results for displacements of a rigid foundation are provided.

scholarly journals A coupled magneto-thermo-elastic problem in a perfectly conducting elastic half-space with thermal relaxation

1990 ◽  
Vol 13 (3) ◽  
pp. 567-578 ◽  
Author(s):  
S. K. Roy-Choudhuri ◽  
Gargi Chatterjee
Keyword(s):  
Relaxation Time ◽  
Elastic Wave ◽  
Thermal Shock ◽  
Half Space ◽  
Thermal Relaxation ◽  
Analytical Form ◽  
Elastic Half Space ◽  
Elastic Problem ◽  
Strain Fields ◽  
Thermal Fields

In the present paper we consider the magneto-thermo-elastic wave produced by a thermal shock in a perfectly conducting elastic half-space. Here the Lord-Shulman theory of thermoelasticity [1] is used to account for the interaction between the elastic and thermal fields. The solution obtained in analytical form reduces to those of Kaliski and Nowacki [2] when the coupling between the temperature and strain fields and the relaxation time are neglected. The results also agree with those of Massalas and DaLamangas [3] in absence of the thermal relaxation time.

Stresses in a Thin Piezoelectric Element Bonded to a Half-Space

1997 ◽  
Vol 50 (11S) ◽  
pp. S204-S209 ◽  
Author(s):  
Wolfgang E. Seemann
Keyword(s):  
Integral Equation ◽  
Shear Stress ◽  
Half Space ◽  
Piezoelectric Element ◽  
Elastic Half Space ◽  
Bonding Layer ◽  
Rigid Substrate ◽  
Stress Concentrations ◽  
Piezoceramic Element

In this paper, a thin piezoceramic element is considered which is bonded to an elastic or a rigid half-space. Such a model may be an approximation of the interaction between piezoceramic elements and elastic structures like beams and plates. For an elastic half-space, the determination of the shear stress in the bonding layer leads to a singular integral equation. A half-space which is very stiff may be modeled as a rigid substrate. For this case, displacement functions are introduced. Hamilton’s principle for electromechanical systems allows the use of Lagrange multipliers to incorporate the condition of a stress free upper surface of the piezoceramic element. The stresses in the bonding layer and in the piezoceramic element are estimated by this method and compared with Finite Element results. Though the singularity near the ends of the piezoceramic element cannot be modeled by both methods, stress concentrations can clearly be seen for the shear stress as well as for the normal stress. As infinite stresses due to the singularity do not occur in reality, the results allow an estimation of the bonding stresses except in the near vicinity of the edges. The knowledge of these stresses is important to prevent failure due to delamination.

Inclined Flat Punch of Arbitrary Shape on an Elastic Half-Space

1986 ◽  
Vol 53 (4) ◽  
pp. 798-806 ◽  
Author(s):  
V. I. Fabrikant
Keyword(s):  
Integral Representation ◽  
Half Space ◽  
Arbitrary Shape ◽  
Contact Problems ◽  
Elastic Half Space ◽  
Elastic Contact ◽  
Circular Sector ◽  
Flat Punch ◽  
Circular Segment ◽  
Arbitrary Planform

A new method is proposed for the analysis of elastic contact problems for a flat inclined punch of arbitrary planform under the action of a normal noncentrally applied force. The method is based on an integral representation for the reciprocal distance between two points obtained by the author earlier. Some simple yet accurate relationships are established between the tilting moments and the angles of inclination of an arbitrary flat punch. Specific formulae are derived for a punch whose planform has a shape of a polygon, a triangle, a rectangle, a rhombus, a circular sector and a circular segment. All the formulae are checked against the solutions known in the literature, and their accuracy is confirmed.

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