A Numerical Procedure for Designing Profiled Rolling Elements

1976 ◽  
Vol 98 (4) ◽  
pp. 547-551 ◽  
Author(s):  
K. P. Oh ◽  
E. G. Trachman
Keyword(s):  
Closed Form Solution ◽  
Numerical Procedure ◽  
Potential Method ◽  
Form Solution ◽  
Geometric Constraints ◽  
Stress Distributions ◽  
Elastic Bodies ◽  
Rolling Elements ◽  
Quadratic Programming Method ◽  
Quadratic Surfaces

A numerical procedure is developed for studying the pressure and stress distributions resulting from the contact of two elastic bodies. The pressure distribution is obtained by a quadratic programming method such that the resulting displacements satisfy the geometric constraints of the contact problem, and the bodies are in a state of minimum potential energy. The potential method is used to calculate the subsurface stresses due to a constant pressure over a rectangular element. The stresses due to the contact pressure are then obtained by superposition of the contributions of all the elements in the contact area. A small number of elements (5 × 5) provides pressure and stress solutions within two percent of the closed-form solution for quadratic surfaces. For surfaces with abrupt changes in geometry, more elements are required. This procedure can be used to locate an optimum profile for rolling element bearings.

Design for Buckle-Free Shapes in Pressure Vessels

1985 ◽  
Vol 107 (4) ◽  
pp. 387-393 ◽  
Author(s):  
W. Szyszkowski ◽  
P. G. Glockner
Keyword(s):  
Pressure Vessel ◽  
Nonlinear Differential Equations ◽  
Closed Form Solution ◽  
Numerical Procedure ◽  
Pressure Vessels ◽  
Form Solution ◽  
Loading Conditions ◽  
Loading Case ◽  
Present Design ◽  
Axisymmetric Structures

There are many applications of thin-walled axisymmetric structures as pressure vessels in which buckle-free in-service behavior can only be guaranteed by reinforcements, such as stringers and girths, which not only raise the weight of the structure but also increase its cost. Buckle-free behavior, however, can also be assured by “correcting” the shape of the pressure vessel by a small amount in the area of impending instability. This paper proposes the use of the theory of inflatable membranes to obtain the shape of a pressure vessel subjected to tension only stress state, whereby the possibility of buckling is excluded. Such a shape will be referred to as the “buckle-free” shape. A set of nonlinear differential equations are derived which are valid for any axisymmetric pressure vessel subjected to axisymmetric loadings. The shape obtained from the solution of the equations is an “extremum” to possible stable shapes under the given loading conditions; i.e., there are other stable shapes, for which the circumferential compressive stiffness of the structure has to be relied upon. A closed-form solution for the set of equations was obtained for the constant pressure loading case. For hydrostatic pressure a numerical procedure is applied. Results on “buckle-free” shapes for typical pressure vessel strucures for these two loading conditions are presented. It is established that the deviation of such shapes from the shapes obtained by present design methods and code specifications is small so that this proposed method and the resulting “corrections’ leading to “buckle-free” inservice behavior should not present an aesthetic problem in design.

Exact Solution of the Elastica with Transverse Shear Effects

2014 ◽  
Vol 14 (08) ◽  
pp. 1440019
Author(s):  
Adrian Marcel Zalmanovici ◽  
Reyolando Manoel Lopes Rebello da Fonseca Brasil ◽  
José Manoel Balthazar
Keyword(s):  
Exact Solution ◽  
Transverse Shear ◽  
Closed Form Solution ◽  
Numerical Procedure ◽  
Form Solution ◽  
Total Potential ◽  
Euler’S Elastica ◽  
Shear Effects ◽  
Set Up ◽  
Transverse Shear Effects

A new derivation of Euler's Elastica with transverse shear effects included is presented. The elastic potential energy of bending and transverse shear is set up. The work of the axial compression force is determined. The equation of equilibrium is derived using the variation of the total potential. Using substitution of variables an exact solution is derived. The equation is transcendental and does not have a closed form solution. It is evaluated in a dimensionless form by using a numerical procedure. Finally, numerical examples of laminates made of composite material (fiber reinforced) and sandwich panels are provided.

scholarly journals HYBRID CAMERA POSE ESTIMATION COMBINING SQUARE FIDUCIALS LOCALIZATION TECHNIQUE AND ORTHOGONAL ITERATION ALGORITHM

2008 ◽  
Vol 08 (01) ◽  
pp. 169-188 ◽  
Author(s):  
JEAN-YVES DIDIER ◽  
FAKHR-EDDINE ABABSA ◽  
MALIK MALLEM
Keyword(s):  
Closed Form ◽  
Pose Estimation ◽  
Closed Form Solution ◽  
Form Solution ◽  
Geometric Constraints ◽  
Hybrid Technique ◽  
Localization Technique ◽  
Camera Pose Estimation ◽  
Camera Pose ◽  
Orthogonal Iteration

Camera pose estimation from video images is a fundamental problem in machine vision and Augmented Reality (AR) systems. Most developed solutions are either linear for both n points and n lines, or iterative depending on nonlinear optimization of some geometric constraints. In this paper, we first survey several existing methods and compare their performances in an AR context. Then, we present a new linear algorithm which is based on square fiducials localization technique to give a closed-form solution to the pose estimation problem, free of any initialization. We also propose an hybrid technique which combines an iterative method, in fact the orthogonal iteration (OI) algorithm, with our own closed form solution. An evaluation of the methods has shown that this hybrid pose estimation technique is accurate and robust. Numerical experiments from real data are given comparing the performances of our hybrid method with several iterative techniques, and demonstrating the efficiency of our approach.

The Effect of Compressibility on the Stress Distributions in Thin Elastomeric Blocks and Annular Bushings

1992 ◽  
Vol 59 (4) ◽  
pp. 902-908 ◽  
Author(s):  
Yeh-Hung Lai ◽  
D. A. Dillard ◽  
J. S. Thornton
Keyword(s):  
Finite Element Analysis ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Stress Distributions ◽  
Element Analysis ◽  
Shape Factors ◽  
Closed Form Solutions ◽  
Apparent Stiffness ◽  
Bulk Compressibility

The effect of the bulk compressibility of elastomers on the response of rubber blocks and bushings bonded to platens is in vestigated. Closed-form solutions for the stresses and deformations within the elastomer are presented for the case of rigid adherends. It is shown that even with relatively small shape factors, the compressibility can significantly affect the apparent stiffness. A finite element analysis shows that the closed-form solution accurately predicts the stress distribution for rigid adherends, but also reveals that platen deformations in realistic systems may significantly alter the distributions.

Stress Fields in a Continuous Fiber Composite With a Variable Interphase Under Thermo-Mechanical Loadings

1994 ◽  
Vol 116 (3) ◽  
pp. 367-377 ◽  
Author(s):  
Yozo Mikata
Keyword(s):  
Carbon Fiber ◽  
Stress Field ◽  
Fiber Composite ◽  
Closed Form Solution ◽  
Form Solution ◽  
Stress Fields ◽  
Circular Cylinders ◽  
Stress Distributions ◽  
Continuous Fiber ◽  
Al 6061

Stress fields in a continuous fiber composite with a variable interphase subjected to thermomechanical loadings are studied by using a four concentric circular cylinders model. An exact closed form solution is obtained for the stress field in the interphase in a series form using Frobenius method in a certain case. Numerical results are presented for FP fiber/Al 6061 composite with interphase, and carbon fiber/Al 6061 composite with interphase. It is found that the variableness of the thermoelastic constants in the interphase has significant effects on the stress distributions in the interphase. Therefore, this will, in turn, affect the initiation of cracks in the interphase.

Exact Solution for Pure Torsion of SMA Curved Bars With Application to Analyzing SMA Helical Springs

2011 ◽  
Author(s):  
Reza Mirzaeifar ◽  
Reginald DesRoches ◽  
Arash Yavari
Keyword(s):  
Cross Sections ◽  
Pure Shear ◽  
Three Dimensional ◽  
Closed Form Solution ◽  
Form Solution ◽  
Stress Distributions ◽  
Pure Torsion ◽  
Helical Springs ◽  
Torsional Response ◽  
The One

In this paper, the pure torsion of SMA curved bars with circular cross sections is studied analytically. First, a three-dimensional phenomenological macroscopic constitutive model for polycrystalline SMAs is reduced to the one-dimensional pure shear case and then a closed-form solution for torsional response of SMA curved bars in loading and unloading is obtained. The effect of a direct shear force in the cross section is also considered in the solution which enables the formulation for analyzing SMA helical springs. Several case studies are presented in order to investigate the accuracy of the proposed method in predicting the torsional response of SMA curved bars, the stress distributions, and analyzing SMA helical springs.

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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