Initial Studies in Three-Dimensional Dynamic Photoelasticity

1967 ◽  
Vol 34 (2) ◽  
pp. 405-410 ◽  
Author(s):  
J. W. Dally ◽  
W. F. Riley
Keyword(s):  
Shear Wave ◽  
Half Space ◽  
Three Dimensional ◽  
Point Load ◽  
Central Plane ◽  
Principal Stresses ◽  
Individual Values ◽  
Axis Of Symmetry ◽  
Thin Elements ◽  
Fringe Patterns

An initial study of stress waves propagating in a half space due to a point load on the surface has been accomplished by employing dynamic three-dimensional photoelasticity. The central plane of the half-space model was isolated for investigation by employing an embedded polariscope. Auxiliary experiments show that the thin elements of the polariscope do not significantly distort the stress wave as it propagates across the joints of the model containing the elements. Photographs of the dynamic fringe patterns were recorded with a Cranz-Schardin multiple spark gap camera operating at 400,000 fps. Three different waves were identified from the fringe patterns; namely, the incident dilatational and distortional waves and the reflected shear wave known as the von Schmidt wave. The data obtained for the shear wave in the form of isochromatic fringe orders were converted to individual values of the principal stresses along the axis of symmetry in the model. The method developed for separation of the principal stresses is only applicable when the distortional wave occurs alone along the axis of symmetry.

Three-dimensional analytical solutions for shakedown of cohesive-frictional materials under moving surface loads

2005 ◽  
Vol 461 (2059) ◽  
pp. 1951-1964 ◽  
Author(s):  
H.S Yu
Keyword(s):  
Lower Bound ◽  
Half Space ◽  
Analytical Solutions ◽  
Theoretical Basis ◽  
Yield Criterion ◽  
Three Dimensional ◽  
Yield Condition ◽  
Surface Load ◽  
Central Plane ◽  
Moving Surface

This paper develops analytical solutions for shakedown limits of a cohesive-frictional half-space under a three-dimensional moving surface load. Melan's lower-bound shakedown theorem has been adopted as the theoretical basis for deriving shakedown limits. Rigorous lower-bound solutions are obtained for shakedown limits by establishing a self-equilibrated residual stress field that, together with the applied elastic stress fields, lies within the Mohr–Coulomb yield criterion throughout the half-space. By searching through the half-space, this study shows that the most critical location for satisfying the yield condition lies on the central plane. The analytical solutions derived in the paper can be used to benchmark numerical shakedown results, as well as to serve as a theoretical basis for the development of an analytical design method for pavements under moving traffic loads.

A PHOTOELASTIC ANALYSIS OF STRESS WAVE PROPAGATION IN A LAYERED MODEL

Geophysics ◽  
1966 ◽  
Vol 31 (5) ◽  
pp. 881-899 ◽  
Author(s):  
W. F. Riley ◽  
J. W. Dally
Keyword(s):  
Wave Propagation ◽  
Dynamic State ◽  
Lead Azide ◽  
Stress Wave Propagation ◽  
Principal Stresses ◽  
Individual Values ◽  
Isochromatic Fringe ◽  
Fringe Patterns ◽  
The Individual ◽  
Explosive Detonation

Dynamic photoelasticity was used to study some fundamental aspects of wave propagation in layered media and to obtain information on the dynamic state of stress associated with the various waves generated by a point source explosion. Columbia Resin CR‐39 and aluminum were used to obtain a model with an acoustical impedance‐mismatch between layers of 6 to 1. A Cranz‐Schardin multiple spark camera, operating at approximately 200,000 frames per second, was used to record the dynamic isochromatic fringe patterns associated with the propagating stress waves. Small charges of lead azide were used to explosively load the models. Six different wave types were clearly identified. In the region near the explosive detonation, the predominant waves were the incident [Formula: see text] wave and the reflected [Formula: see text] waves from the interface and the free boundary. In regions away from the explosive detonation the headwaves ([Formula: see text], [Formula: see text], and [Formula: see text]) dominate since their rate of attenuation is much lower than the rate associated with the incident dilatational or the reflected shear waves. The data obtained in the form of isochromatic fringe patterns were converted to individual values of the principal stresses in several instances. The methods developed for this separation are applicable whenever the dilatational or distortional waves occur alone. The separation method requires no auxiliary data other than the isochromatic fringe orders and yields dynamic displacement data in addition to the individual values of the principal stresses.

scholarly journals The near-resonant regimes of a moving load in a three-dimensional problem for a coated elastic half-space

2016 ◽  
Vol 22 (1) ◽  
pp. 89-100 ◽  
Author(s):  
Bariş Erbaş ◽  
Julius Kaplunov ◽  
Danila A Prikazchikov ◽  
Onur Şahin
Keyword(s):  
Half Space ◽  
Moving Load ◽  
Three Dimensional ◽  
Elastic Half Space ◽  
Point Load ◽  
Phase Method ◽  
Stationary Phase Method ◽  
Dispersive Effect ◽  
Mach Cones ◽  
Integral Solutions

This paper deals with the three-dimensional analysis of the near-resonant regimes of a point load, moving steadily along the surface of a coated elastic half-space. The approach developed relies on a specialized hyperbolic–elliptic formulation for the wave field, established earlier by the authors. Straightforward integral solutions of the two-dimensional perturbed wave equation describing wave propagation along the surface are derived along with their far-field asymptotic expansions obtained using the uniform stationary phase method. Both sub-Rayleigh and super-Rayleigh cases are studied. It is shown that the singularities arising at the contour of the Mach cones typical of the super-Rayleigh case, are smoothed due to the dispersive effect of the coating.

Comparison of Conventional and Pontic Fixed Partial Dentures Over Implants Using the Finite Element Method: Three-Dimensional Analysis of Cortical and Medullary Bone Stress

2020 ◽  
Vol 46 (3) ◽  
pp. 175-181
Author(s):  
Marcelo Bighetti Toniollo ◽  
Mikaelly dos Santos Sá ◽  
Fernanda Pereira Silva ◽  
Giselle Rodrigues Reis ◽  
Ana Paula Macedo ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Three Dimensional ◽  
The Finite Element Method ◽  
Medullary Bone ◽  
Principal Stresses ◽  
Bone Stress ◽  
Bone Damage ◽  
Rehabilitation System ◽  
Minimum Requirements

Rehabilitation with implant prostheses in posterior areas requires the maximum number of possible implants due to the greater masticatory load of the region. However, the necessary minimum requirements are not always present in full. This project analyzed the minimum principal stresses (TMiP, representative of the compressive stress) to the friable structures, specifically the vestibular face of the cortical bone and the vestibular and internal/lingual face of the medullary bone. The experimental groups were as follows: the regular splinted group (GR), with a conventional infrastructure on 3 regular-length Morse taper implants (4 × 11 mm); and the regular pontic group (GP), with a pontic infrastructure on 2 regular-length Morse taper implants (4 × 11 mm). The results showed that the TMiP of the cortical and medullary bones were greater for the GP in regions surrounding the implants (especially in the cervical and apical areas of the same region) but they did not reach bone damage levels, at least under the loads applied in this study. It was concluded that greater stress observed in the GP demonstrates greater fragility with this modality of rehabilitation; this should draw the professional's attention to possible biomechanical implications. Whenever possible, professionals should give preference to use of a greater number of implants in the rehabilitation system, with a focus on preserving the supporting tissue with the generation of less intense stresses.

Guided Surface Waves on an Elastic Half Space

1971 ◽  
Vol 38 (4) ◽  
pp. 899-905 ◽  
Author(s):  
L. B. Freund
Keyword(s):  
Wave Propagation ◽  
Surface Wave ◽  
Surface Waves ◽  
Half Space ◽  
Body Wave ◽  
Three Dimensional ◽  
Elastic Half Space ◽  
Normal Displacement ◽  
Rigid Barrier ◽  
Wave Disturbances

Three-dimensional wave propagation in an elastic half space is considered. The half space is traction free on half its boundary, while the remaining part of the boundary is free of shear traction and is constrained against normal displacement by a smooth, rigid barrier. A time-harmonic surface wave, traveling on the traction free part of the surface, is obliquely incident on the edge of the barrier. The amplitude and the phase of the resulting reflected surface wave are determined by means of Laplace transform methods and the Wiener-Hopf technique. Wave propagation in an elastic half space in contact with two rigid, smooth barriers is then considered. The barriers are arranged so that a strip on the surface of uniform width is traction free, which forms a wave guide for surface waves. Results of the surface wave reflection problem are then used to geometrically construct dispersion relations for the propagation of unattenuated guided surface waves in the guiding structure. The rate of decay of body wave disturbances, localized near the edges of the guide, is discussed.

3D Profile Variety Measurement of Pectoral Fin in Fish Fast Start

2011 ◽  
Vol 83 ◽  
pp. 280-284
Author(s):  
Ming Jiang ◽  
Shu Zhang ◽  
Xiao Yuan He
Keyword(s):  
Fourier Transform ◽  
High Speed ◽  
Kinetic Characteristic ◽  
Three Dimensional ◽  
Pectoral Fin ◽  
Fourier Transform Profilometry ◽  
Fast Start ◽  
Fringe Patterns ◽  
3D Information ◽  
3D Profile

Fast-starts are brief, sudden accelerations used by fish during predator-prey encounters. In this paper, a three-dimensional (3D) test and analysis method is critical to understand the function of the pectoral fin during maneuvers. An experiment method based on Fourier Transform Profilometry for 3D pectoral fin profile variety during fish maneuvers is proposed. This method was used in a carp fast-start during prey. Projecting the moiré fringes onto a carp pectoral fin it will produce the deformed fringe patterns contain 3D information. A high speed camera captures these time-sequence images. By Fourier transform, filter, inverse Fourier transform and unwrap these phase maps in 3D phase space, the complex pectoral fin profile variety were really reconstructed. The present study provides a new method to quantify the analysis of kinetic characteristic of the pectoral fin during maneuvers.

scholarly journals Transient Excitation of an Elastic Half Space by a Point Load Traveling on the Surface

1969 ◽  
Vol 36 (3) ◽  
pp. 505-515 ◽  
Author(s):  
D. C. Gakenheimer ◽  
J. Miklowitz
Keyword(s):  
Exact Solution ◽  
Free Surface ◽  
Steady State ◽  
Wave Front ◽  
Half Space ◽  
Displacement Field ◽  
Elastic Half Space ◽  
Point Load ◽  
Limit Case ◽  
Transient Waves

The propagation of transient waves in a homogeneous, isotropic, linearly elastic half space excited by a traveling normal point load is investigated. The load is suddenly applied and then it moves rectilinearly at a constant speed along the free surface. The displacements are derived for the interior of the half space and for all load speeds. Wave-front expansions are obtained from the exact solution, in addition to results pertaining to the steady-state displacement field. The limit case of zero load speed is considered, yielding new results for Lamb’s point load problem.

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