Three-dimensional, elastic stress distribution in end-milled, keyed connections

1983 ◽  
Vol 18 (2) ◽  
pp. 143-149 ◽  
Author(s):  
H Fessler ◽  
M Eissa
Keyword(s):  
Elastic Stress ◽  
Three Dimensional ◽  
Empirical Equations ◽  
Two Dimensional ◽  
Stress Concentrations ◽  
Axial Distribution ◽  
Simple Method ◽  
Torque Transmission ◽  
Applied Torque ◽  
Stress Models

Three- and two-dimensional, photoelastic, frozen-stress models of Standard metric and inch keyed connections have been loaded in torsion. Results from models with three different key lengths are presented here and related to the axial distribution of torque transmission. Empirical equations for the elastic stress concentrations in the prismatic part of key and keyway at the positions of contact between key and shaft have been derived for any likely width, thickness, and length of key, keyway fillet size, and applied torque. A simple method of eliminating stress concentrations in the keyway end is described.

scholarly journals Two-Dimensional Visualization of the Three-Dimensional Planned Sacroiliac Screw Corridor with the Slice Fusion Method

2021 ◽  
Vol 10 (2) ◽  
pp. 184
Author(s):  
Maximilian Kerschbaum ◽  
Siegmund Lang ◽  
Florian Baumann ◽  
Volker Alt ◽  
Michael Worlicek
Keyword(s):  
Pelvic Ring ◽  
Three Dimensional ◽  
Fusion Method ◽  
Two Dimensional ◽  
Posterior Pelvic Ring ◽  
Simple Method ◽  
Sacroiliac Screw ◽  
Screw Insertion ◽  
Multiplanar Reconstructions ◽  
Screw Position

Insertion of sacro-iliac (SI) screws for stabilization of the posterior pelvic ring without intraoperative navigation or three-dimensional imaging can be challenging. The aim of this study was to develop a simple method to visualize the ideal SI screw corridor, on lateral two-dimensional images, corresponding to the lateral fluoroscopic view, used intraoperatively while screw insertion, to prevent neurovascular injury. We used multiplanar reconstructions of pre- and postoperative computed tomography scans (CT) to determine the position of the SI corridor. Then, we processed the dataset into a lateral two-dimensional slice fusion image (SFI) matching head and tip of the screw. Comparison of the preoperative SFI planning and the screw position in the postoperative SFI showed reproducible results. In conclusion, the slice fusion method is a simple technique for translation of three-dimensional planned SI screw positioning into a two-dimensional strict lateral fluoroscopic-like view.

A Sequel to Technical Note 13: The Curved Tetrahedronal and Triangular Elements TEC and TRIC for the Matrix Displacement Method

1969 ◽  
Vol 73 (697) ◽  
pp. 55-65 ◽  
Author(s):  
J. H. Argyris ◽  
D. W. Scharpf
Keyword(s):  
Computational Analysis ◽  
Three Dimensional ◽  
Technical Note ◽  
Radius Of Curvature ◽  
Two Dimensional ◽  
Displacement Method ◽  
Stress Concentrations ◽  
The Past ◽  
The Matrix ◽  
Triangular Elements

It is by now well established that the computational analysis of significant problems in structural and continuum mechanics by the matrix displacement method often requires elements of higher sophistication than used in the past. This refers, in particular, to regions of steep stress gradients, which are frequently associated with marked changes in geometry, involving rapid variations of the radius of curvature. The philosophy underlying the idealisation of such configurations into finite elements was discussed in broad terms in ref. 1. It was emphasised that the so successful, constant strain, two-dimensional TRIM 3 and three-dimensional TET 4 elements do not, in general, prove the best choice. For this reason elements with a linear variation of strain like TRIM 6 and TET 10 were originally evolved and followed up with the quadratic strain elements TRIM 15, TRIA 4 (two-dimensional) and TET 20, TEA 8 (three-dimensional) of ref. 2. However, all these elements are characterised by straight edges and necessitate a polygonisation or polyhedrisation in the idealisation process. This may not be critical in many problems, but is sometimes of doubtful validity in the immediate neighbourhood of a curved boundary, where stress concentrations are most pronounced. To overcome this difficulty with a significant (local) increase of elements does not always yield the most economical and technically satisfactory solution. Moreover, there arises another inevitable shortcoming when dealing with TRIM and TET elements with a linear or quadratic variation of strain. Indeed, while TRIM 3 and TET 4 elements permit a very elegant extension into the realm of large displacements, this is not possible for the higher order TRIM and TET elements. This is simply due to the fact that TRIM 3 and TET 4 elements, by virtue of their specification, always remain straight under any magnitude of strain, but this is not so for the triangular and tetrahedron elements of higher sophistication.

scholarly journals Extrinsic Calibration of Multiple Two-Dimensional Laser Rangefinders Based on a Trihedron

Sensors ◽  
2020 ◽  
Vol 20 (7) ◽  
pp. 1837 ◽  
Author(s):  
Fei Zhu ◽  
Yuchun Huang ◽  
Zizhu Tian ◽  
Yaowei Ma
Keyword(s):  
Autonomous Vehicles ◽  
Laser Scanning ◽  
Mobile Robotics ◽  
Three Dimensional ◽  
Point Problem ◽  
Two Dimensional ◽  
Simple Method ◽  
Extrinsic Calibration ◽  
Dimensional Reconstruction ◽  
Special Pattern

Multiple two-dimensional laser rangefinders (LRFs) are applied in many applications like mobile robotics, autonomous vehicles, and three-dimensional reconstruction. The extrinsic calibration between LRFs is the first step to perform data fusion and practical application. In this paper, we proposed a simple method to calibrate LRFs based on a corner composed of three mutually perpendicular planes. In contrast to other methods that require a special pattern or assistance from other sensors, the trihedron corner needed in this method is common in daily environments. In practice, we can adjust the position of the LRFs to observe the corner until the laser scanning plane intersects with three planes of the corner. Then, we formed a Perspective-Three-Point problem to solve the position and orientation of each LRF at the common corner coordinate system. The method was validated with synthetic and real experiments, showing better performance than existing methods.

Stresses at offset-oblique holes in thick-walled cylinders subjected to torsional loading

1980 ◽  
Vol 15 (4) ◽  
pp. 175-182 ◽  
Author(s):  
P Stanley ◽  
B V Day
Keyword(s):  
Shear Stress ◽  
Maximum Stress ◽  
Elastic Stress ◽  
Three Dimensional ◽  
Outer Edge ◽  
Torsional Loading ◽  
Stress Concentrations ◽  
Wide Range ◽  
Photoelastic Analysis ◽  
Geometric Variables

The paper describes a three-dimensional photoelastic analysis of a series of Araldite models, each containing five or six different offset-oblique holes positioned in such a way that there were no ‘interaction’ effects between neighbouring holes. The geometric parameters defining a hole were varied systematically and the elastic stress distribution around the outer edge of each hole was obtained. The stress data are presented in non-dimensional form in terms of the shear stress in a plain cylinder. The dependence of the maximum stress on the geometric variables is discussed and it is shown that the stress concentrations for a wide range of hole/cylinder parameters can be reasonably well predicted from flat plate data. In some cases the predictions are unconservative.

A method for the derivation of load effect envelopes based on statistical considerations

1993 ◽  
Vol 20 (2) ◽  
pp. 201-209
Author(s):  
Eugene J. O'Brien ◽  
Robert E. Loov
Keyword(s):  
Structural Analysis ◽  
Three Dimensional ◽  
Elastic Analysis ◽  
Two Dimensional ◽  
Statistical Parameters ◽  
Simple Method ◽  
Load Effect ◽  
Linear Elastic ◽  
Derived Design ◽  
Usual Process

A simple method is proposed as a substitute for the usual process of factoring loads, performing a linear elastic analysis, and determining an envelope of the results. The method is based on statistical principles, but only a minimum knowledge of statistics is required for its use. It involves conventional structural analysis followed by some processing of the results which could readily be incorporated into existing computer programs.The practice of performing two-dimensional analyses on parts of three-dimensional structures is possible with the proposed approach. The implications are clarified and the necessary statistical parameters are derived.Deterministically derived design envelopes represent all the extremes of loading that can reasonably be considered. The envelopes found by the new method not only reflect loading variations but also consider their relative probabilities of occurrence so that excursions beyond the envelope are expected to be equally infrequent along the entire length of the structure. Inconsistencies inherent in the conventional approach are highlighted by comparison with the proposed method for a number of examples. Key words: probabilistic, safety, load, imposed load, load effect envelope, building.

Stress Concentrations from Single-Filament Failures in Composite Materials

1969 ◽  
Vol 39 (7) ◽  
pp. 618-626 ◽  
Author(s):  
Peter Van Dyke ◽  
John M. Hedgepeth
Keyword(s):  
Matrix Material ◽  
Three Dimensional ◽  
Plastic Behavior ◽  
Two Dimensional ◽  
Failure Model ◽  
Stress Concentrations ◽  
Bond Failure ◽  
Single Filament ◽  
Concentration Problem ◽  
The Matrix

The solution of the two-dimensional, elastic, multiple-filament-failure stress concentration problem led to the treatment of three-dimensional, elastic failure models and a two-dimensional, plastic failure model where an ideally plastic behavior of the matrix material adjacent to a broken filament was assumed. Another plastic behavior is proposed wherein the bond between the broken filament and the adjacent matrix material fails completely after reaching a prescribed stress level. This failure formulation is applied to five- and seven-element-width models as well as to the infinite element case. Both the bond failure and matrix yield models are then extended to the three-dimensional cases with both square and hexagonal element configurations.

An Improved Fracture Criterion for Three-Dimensional Stress States

1976 ◽  
Vol 98 (2) ◽  
pp. 159-163 ◽  
Author(s):  
B. Paul ◽  
L. Mirandy
Keyword(s):  
Applied Stress ◽  
Stress Fracture ◽  
Fracture Criterion ◽  
Three Dimensional ◽  
Brittle Materials ◽  
Two Dimensional ◽  
Stress Concentrations ◽  
State Of Stress ◽  
Stress States ◽  
Free Material

A theory is developed to predict the onset of fracture in isotropic, brittle materials when subjected to three dimensional states of applied stress. It is assumed that fracture is precipitated by stress concentrations emanating from material flaws. The flaw model which has been adopted consists of randomly oriented, microscopic, flat triaxial ellipsoidal voids imbedded in an otherwise defect-free material. It is shown that the ensuing fracture criterion may be expressed as a parabolic Mohr’s envelope. These results are qualitatively similar to Paul’s earlier three-dimensional generalization of Griffith’s two-dimensional stress fracture criterion. To handle three-dimensional states of applied stress, Paul used an approximation based on two-dimensional elasticity to obtain the state of stress around a flat spheroid. Newly developed results for flat ellipsoidal cavaties are utilized herein to analyze the three-dimensional cavity. Pertinent effects due to Poisson’s ratio and ellipsoid geometry are reported.

A Simple Method of Elastic Contact Simulation

1994 ◽  
Vol 208 (4) ◽  
pp. 291-293 ◽  
Author(s):  
R W Snidle ◽  
H P Evans
Keyword(s):  
Contact Pressure ◽  
Iterative Algorithm ◽  
Three Dimensional ◽  
Elastic Contact ◽  
Two Dimensional ◽  
Simple Method

The note describes an iterative algorithm for calculating contact pressure and areas of contact in nonconforming, two-dimensional, non-Hertzian contacts. In principle the method can be easily extended to three-dimensional problems.

Stress Transmission in Polycrystals With Frictionless Grain Boundaries

1995 ◽  
Vol 62 (1) ◽  
pp. 1-6 ◽  
Author(s):  
G. J. Rodin
Keyword(s):  
Grain Boundaries ◽  
Three Dimensional ◽  
Maximum Tensile Stress ◽  
Two Dimensional ◽  
Normal Stresses ◽  
Simple Method ◽  
Periodic Arrays ◽  
Stress Transmission ◽  
Rhombic Dodecahedra ◽  
Applied Stresses

A simple method of analysis of stress transmission in polycrystals with frictionless grain boundaries is presented. This method applies to a large class of two-dimensional and three-dimensional polycrystals which can be modeled as either periodic or disordered arrays of polyhedra. Calculations are performed for the periodic arrays of rhombic dodecahedra and truncated octahedra, and for arrays generated by the Voronoy tessellation of disordered point lattices. Results of these calculations show that normal stresses transmitted by frictionless grain boundaries are significantly different from applied stresses. In particular, it is predicted that, in disordered polycrystals subjected to uniaxial compression, 45 percent of grain boundaries are in tension and the maximum tensile stress is one half of the applied stress.

A Simple Method for the Design of Supersonic Nozzles of Arbitrary Cross Section Shape

2020 ◽  
Author(s):  
N. Boughazi ◽  
A. Haddad
Keyword(s):  
Cross Section ◽  
Axisymmetric Flow ◽  
Three Dimensional ◽  
Arbitrary Cross Section ◽  
Geometrical Parameters ◽  
Two Dimensional ◽  
Cross Sectional ◽  
Simple Method ◽  
Supersonic Nozzles ◽  
De Laval Nozzle

Abstract A simple approach for the design of supersonic nozzles of complex 3D shapes is presented. The Method of characteristics is primarily applied to compute the axisymmetric flow field of the supersonic section of the de-Laval nozzle. Two-dimensional simulations are performed for the axisymmetric flow fields. The 3D configuration is then generated from the desired exit axisymmetric cross-sectional shape chosen through tracing its geometrical parameters back.to the throat. Elliptical, corrugated and two-dimensional wedge nozzles were designed using this approach. Preliminary results show a smooth geometrical transition from the throat to the exit cross section. Further three-dimensional analyses of the obtained geometries along with cold flow testing constitute the next steps to be performed.

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