Stress Distribution in a Uniformly Rotating Equilateral Triangular Shaft

1955 ◽  
Vol 22 (2) ◽  
pp. 255-259
Author(s):  
H. T. Johnson
Keyword(s):  
Approximate Solution ◽  
Stress Distribution ◽  
Boundary Conditions ◽  
Plane Strain ◽  
Cross Section ◽  
Plane Stress ◽  
Biharmonic Equation ◽  
Approximate Solutions ◽  
Distribution Of Stresses ◽  
General Method

Abstract An approximate solution for the distribution of stresses in a rotating prismatic shaft, of triangular cross section, is presented in this paper. A general method is employed which may be applied in obtaining approximate solutions for the stress distribution for rotating prismatic shapes, for the cases of either generalized plane stress or plane strain. Polynomials are used which exactly satisfy the biharmonic equation and the symmetry conditions, and which approximately satisfy the boundary conditions.

Analysis of Deep Beams

1951 ◽  
Vol 18 (2) ◽  
pp. 163-172
Author(s):  
H. D. Conway ◽  
L. Chow ◽  
G. W. Morgan
Keyword(s):  
Exact Solution ◽  
Approximate Solution ◽  
Stress Distribution ◽  
Finite Difference ◽  
Boundary Conditions ◽  
Normal Stress ◽  
Stress Function ◽  
Beam Theory ◽  
Deep Beam ◽  
Stress Functions

Abstract This paper presents a method of analyzing the stress distribution in a deep beam of finite length by superimposing two stress functions. The first stress function is chosen in the form of a trigonometric series which satisfies all but one of the boundary conditions—that of zero normal stress on the ends of the beam. The principle of least work is then used to obtain a second stress function giving the distribution of normal stress on the ends which is left by the first stress function. By superimposing the two solutions, all the boundary conditions are satisfied. Two particular cases of a given type of loading are solved in this way to investigate the stresses in a deep beam and their deviation from the ordinary beam theory. In addition, an approximate solution by the numerical method of finite difference is worked out for one of the two cases. Results from the two methods are compared and discussed. A method of obtaining an exact solution to the problem is given in an Appendix.

Damage and healing mechanics in plane stress, plane strain, and isotropic elasticity

2020 ◽  
Vol 29 (8) ◽  
pp. 1246-1270 ◽  
Author(s):  
George Z Voyiadjis ◽  
Chahmi Oucif ◽  
Peter I Kattan ◽  
Timon Rabczuk
Keyword(s):  
Plane Strain ◽  
Cross Section ◽  
Plane Stress ◽  
Elastic Energy ◽  
Elastic Stiffness ◽  
Self Healing ◽  
Theoretical Formulation ◽  
Stiffness Reduction ◽  
Energy Equivalence ◽  
Isotropic Elasticity

The present paper presents a theoretical formulation of different self-healing variables. Healing variables based on the recovery in elastic modulus, shear modulus, Poisson's ratio, and bulk modulus are defined. The formulation is presented in both scalar and tensorial cases. A new healing variable based on elastic stiffness recovery in proposed, which is consistent with the continuum damage-healing mechanics. The evolution of the healing variable calculated based on cross-section as function of the healing variable calculated based on elastic stiffness is presented in both hypotheses of elastic strain equivalence and elastic energy equivalence. The components of the fourth-rank healing tensor are also obtained in the case of isotropic elasticity, plane stress, and plane strain. It is found that the healing variable calculated based on elastic stiffness reduction is greater than the one calculated based on cross-section reduction in the case of the hypothesis of elastic energy equivalence. It is also shown that the healing tensor fits the boundary conditions of the healing variable in the case of scalar formulation.

Static Stability Behaviour of Plate Elements with Non-Uniform, in-Plane Stress Distribution

1979 ◽  
Vol 21 (5) ◽  
pp. 363-365
Author(s):  
P. K. Datta
Keyword(s):  
Stress Distribution ◽  
Boundary Conditions ◽  
Rectangular Plate ◽  
Plane Stress ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Static Stability ◽  
Buckling Loads ◽  
Plate Elements ◽  
Edge Loading

The results of analytically and experimentally determined buckling loads of a rectangular plate, subjected to partial edge loading and mixed boundary conditions, are presented.

scholarly journals WAVE TRANSMISSION THROUGH PERMEABLE BREAKWATERS

1972 ◽  
Vol 1 (13) ◽  
pp. 99 ◽  
Author(s):  
Charles K. Sollitt ◽  
Ralph H. Cross
Keyword(s):  
Approximate Solution ◽  
Boundary Conditions ◽  
Cross Section ◽  
Wave Breaking ◽  
Wave Reflection ◽  
Rectangular Cross Section ◽  
Wave Component ◽  
Additional Consideration ◽  
Reflection And Transmission ◽  
Theoretical Results

A theory is derived to predict ocean wave reflection and transmission at a permeable breakwater of rectangular cross section. The theory solves for a damped wave component within the breakwater and matches boundary conditions at the windward and leeward breakwater faces to predict the reflected and transmitted wave components. An approximate solution to conventional rubble mound breakwater designs is formulated in terms of an equivalent rectangular breakwater with an additional consideration for wave breaking. Experimental and theoretical results are compared and evaluated.

scholarly journals An Analytical Model for Predicting the Stress Distributions within Single-Lap Adhesively Bonded Beams

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Xiaocong He ◽  
Yuqi Wang
Keyword(s):  
Stress Distribution ◽  
Boundary Conditions ◽  
Plane Strain ◽  
Analytical Model ◽  
Longitudinal Direction ◽  
Plane Strain Condition ◽  
Strain Condition ◽  
Stress Distributions ◽  
Governing Equations ◽  
Adhesively Bonded

An analytical model for predicting the stress distributions within single-lap adhesively bonded beams under tension is presented in this paper. By combining the governing equations of each adherend with the joint kinematics, the overall system of governing equations can be obtained. Both the adherends and the adhesive are assumed to be under plane strain condition. With suitable boundary conditions, the stress distribution of the adhesive in the longitudinal direction is determined.

Studies on Plastic Flow of Anisotropic Metals

1956 ◽  
Vol 23 (3) ◽  
pp. 444-450
Author(s):  
L. W. Hu
Keyword(s):  
Stress Distribution ◽  
Internal Pressure ◽  
Strain Hardening ◽  
Plane Strain ◽  
Plastic Flow ◽  
Plane Stress ◽  
Biaxial Tension ◽  
Plastic Behavior ◽  
Theory Of Plastic Flow ◽  
Walled Cylinder

Abstract This investigation deals with a study of the plastic behavior of anisotropic metals. By extending Hill’s theory of plastic flow of anisotropic metals, plastic stress-strain relations for anisotropic materials with strain hardening are developed. Applications of these relations are also made to plane-stress and plane-strain problems with anisotropy. The effect of anisotropy on the stress distribution and on the pressure to produce yielding in a thick-walled cylinder under internal pressure is discussed. The influence of anisotropy on the interpretation of conventional biaxial tension-tension and tension-torsion tests is also considered in this study.

Collapse loads for thin cantilevers with rectangular holes along the centre-line

1976 ◽  
Vol 11 (2) ◽  
pp. 84-96 ◽  
Author(s):  
A S Ranshi ◽  
W Johnson ◽  
N R Chitkara
Keyword(s):  
Lower Bound ◽  
Plane Strain ◽  
Cross Section ◽  
Plane Stress ◽  
Slip Line ◽  
Rectangular Cross Section ◽  
Local Buckling ◽  
Experimental Results ◽  
Line Field ◽  
Theoretical Results

Plane stress slip-line field solutions, which provide the modes of yielding and the corresponding yield loads, are presented for the plastic bending of end-loaded thin cantilevers of rectangular cross-section containing rectangular holes. The theoretical results obtained from these solutions are compared with some experimental results and those obtained from plane strain slip-line fields and lower bound estimates, all presented previously by the authors (1)‡. It is observed that the correlation of the experimental results was much better with the plane stress solutions than with either the plane strain or lower bound results. The effect of adjacent holes and possible lateral or local buckling on the ultimate strength of the cantilevers is also examined.

Force Fits and Shrinkage Fits in Crank Webs and Locomotive Driving Wheels

1934 ◽  
Vol 127 (1) ◽  
pp. 249-275 ◽  
Author(s):  
E. G. Coker ◽  
Miss R. Levi
Keyword(s):  
Experimental Investigation ◽  
Stress Distribution ◽  
Plane Stress ◽  
Point Of View ◽  
Experimental Point ◽  
Engineering Practice ◽  
Stress Distributions ◽  
Balance Weight ◽  
Driving Wheel ◽  
General Method

This experimental investigation relates to a general method of measuring stress distribution when force fits and shrinkage fits of the plane stress type are employed in engineering practice. Important cases occur in the webs of built-up crankshafts for locomotives and Diesel engines. When the latter are of high power and short stroke, so that crankshaft and crankpins are large and relatively close together, the initial constructional stresses are shown to attain high values. More complicated cases, from an experimental point of view, occur in the driving wheels of locomotives with a tyre shrunk over a wheel centre having a crank and balance weight integral therewith, while the main axle and crankpin are forced or shrunk in. Such a case is examined with reference to a driving wheel of the London Midland and Scottish Railway locomotive Royal Scot, and the stress distributions measured in various parts of a model of it are described in detail.

Concentrated-Force Problems in Plane Strain, Plane Stress, and Transverse Bending of Plates

1946 ◽  
Vol 13 (3) ◽  
pp. A183-A197
Author(s):  
P. S. Symonds
Keyword(s):  
Boundary Conditions ◽  
Plane Stress ◽  
Biharmonic Equation ◽  
Infinite Plate ◽  
Outer Edge ◽  
Transverse Force ◽  
Concentrated Force ◽  
Transverse Bending ◽  
Complementary Function ◽  
Concentrated Forces

Abstract A general method is described for the solution of problems of transverse bending of thin plates acted on by concentrated normal forces, and of problems of plane stress or plane strain, in which concentrated forces are applied to the boundaries. The solution is taken in two parts: (a) The special functions which give the stresses or deflections in the neighborhood of the concentrated forces. (b) A complementary function, satisfying the appropriate biharmonic equation, such that the complete solution satisfies the boundary conditions of the problem. For certain types of boundaries, this complementary function can be determined by expanding the concentrated-force functions as infinite trigonometric series. Then by addition of general solutions of the appropriate biharmonic equation, the required boundary conditions may be satisfied. The method is first illustrated by solving the plate-bending problem, for which the solution is known, of a clamped circular disk loaded by a transverse force at any point. It is then applied to the problem of an infinite plate fixed at an inner circular boundary, with outer edge free, and loaded by a transverse force at any point. This solution is obtained in finite form, and typical curves of deflection, bending moments, and shear forces are given in Figs. 3 to 8, inclusive. Using this result, solutions are next obtained for ring-shaped plates of finite outer radius, with the force applied either at the outer edge or at any point between the inner clamped edge and the outer free edge. The former case was previously solved by H. Reissner. Curves comparing the maximum moments and shears in the infinite plate with those of the annular plate with force either at the outer edge, or inside the ring are given in Figs. 9 to 12, inclusive. Finally, a solution is given of the problem in plane stress of a large plate containing an elliptical hole, which is loaded by line forces at the ends of the minor axes of the ellipse. Curves showing results of this solution are given in Figs. 14 and 15.

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