Shear Buckling of a Clamped Infinitely Long Plate Reinforced by a Stiffener Mesh

1966 ◽  
Vol 17 (3) ◽  
pp. 302-309
Author(s):  
H. W. Parsons ◽  
I. T. Cook
Keyword(s):  
Shear Stress ◽  
Flexural Rigidity ◽  
Torsional Rigidity ◽  
Numerical Results ◽  
Theoretical Solution ◽  
The Other ◽  
Clamped Plate ◽  
Longitudinal Stiffeners ◽  
Shear Buckling ◽  
Special Case

SummaryA theoretical solution to the initial buckling under shear stress of a long clamped plate with parallel edges reinforced by a stiffener mesh is obtained. The mesh is formed by two families of stiffeners each evenly spaced. One family consists of longitudinal stiffeners parallel to the edges of the plate and the other consists of diagonal stiffeners inclined to the parallel edges. The flexural and torsional rigidity of the stiffeners are included in the analysis. Numerical results are given for the special case in which the longitudinal stiffeners are absent and the diagonal stiffeners have flexural rigidity only.

Shear Buckling of Clamped and Simply-Supported Infinitely Long Plates Reinforced by Transverse Stiffeners and a Central Longitudinal Stiffener

1962 ◽  
Vol 13 (2) ◽  
pp. 95-114 ◽  
Author(s):  
K. C. Rockey ◽  
I. T. Cook
Keyword(s):  
Shear Stress ◽  
Flexural Rigidity ◽  
Numerical Results ◽  
Simply Supported ◽  
Longitudinal Stiffener ◽  
Buckling Stress ◽  
Longitudinal Stiffeners ◽  
Edge Conditions ◽  
Shear Buckling ◽  
Clamped Edge

SummaryThe paper presents a solution to the buckling under shear stress of infinitely long plates which are reinforced by both transverse stiffeners and longitudinal stiffeners. Each family of stiffeners is assumed to consist of equally spaced stiffeners. Both simply-supported and clamped edge conditions are examined. Numerical results are obtained for the case of a plate with transverse stiffeners and a central longitudinal stiffener and relationships between the buckling stress and the flexural rigidity parameters of the stiffeners are provided for three different spacings of the transverse stiffeners.

Shear Buckling of Clamped and Simply-Supported Infinitely Long Plates Reinforced by Closed-Section Transverse Stiffeners

1962 ◽  
Vol 13 (3) ◽  
pp. 212-222 ◽  
Author(s):  
I. T. Cook ◽  
K. C. Rockey
Keyword(s):  
Circular Tube ◽  
Flexural Rigidity ◽  
Torsional Rigidity ◽  
Numerical Results ◽  
Rectangular Plates ◽  
Simply Supported ◽  
Shear Buckling ◽  
Thin Walled ◽  
The Individual

SummaryThe paper presents a solution to the buckling of infinitely long plates when they are reinforced by transverse stiffeners possessing both torsional and flexural rigidity. The cases of both edges being clamped and simply-supported are dealt with. Numerical results are presented for the ratio of torsional rigidity to flexural rigidity as obtained with a thin-walled circular tube. When the stiffeners are completely rigid, in which case the individual panels are clamped along the transverse edges, the results obtained are in agreement with existing solutions for isolated rectangular plates.

Shear Buckling of Orthogonally Stiffened, Infinitely Long Simply-Supported Plates–Stiffeners having Torsional and Flexural Rigidities

1969 ◽  
Vol 20 (1) ◽  
pp. 75-87
Author(s):  
K. C. Rockey ◽  
I. T. Cook
Keyword(s):  
Cross Section ◽  
Flexural Rigidity ◽  
Torsional Rigidity ◽  
List Type ◽  
Rectangular Plates ◽  
Simply Supported ◽  
Longitudinal Stiffener ◽  
Rigidity Parameter ◽  
Longitudinal Stiffeners ◽  
Shear Buckling

SummaryThe paper presents a solution to the buckling under shear stress of infinitely long plates orthogonally reinforced by stiffeners having both flexural and torsional rigidity. Each family of stiffeners is assumed to consist of equally spaced identical stiffeners. Numerical results are given for the case of a plate with transverse stiffeners and a central longitudinal stiffener for the following three cases: (i)Transverse and longitudinal stiffeners of closed tubular cross-section.(ii)Transverse stiffeners of closed tubular cross-section, longitudinal stiffeners possessing only flexural rigidity.(iii)Transverse stiffeners possessing only flexural rigidity, the longitudinal stiffeners being of closed tubular cross-section.Relationships between the buckling stress parameter K and the flexural rigidity parameter γ of the stiffeners are presented for each of the three cases when the identical transverse stiffeners are placed at spacings of d, 0·8d and 0·5d, where d is the depth of the webplate.Case (i) has provided values of the buckling coefficient K for finite rectangular plates clamped on three edges and simply-supported on the remaining edge.

Influence of the Torsional Rigidity of Transverse Stiffeners upon the Shear Buckling of Stiffened Plates

1964 ◽  
Vol 15 (2) ◽  
pp. 198-202 ◽  
Author(s):  
K. C. Rockey ◽  
I. T. Cook
Keyword(s):  
Flexural Rigidity ◽  
Torsional Rigidity ◽  
Stiffened Plates ◽  
Simply Supported ◽  
Rigidity Results ◽  
Buckling Resistance ◽  
Shear Buckling

SummaryThe paper provides relationships between the buckling resistance of simply-supported transversely stiffened plates and the flexural rigidity of the stiffeners for various values of the ratio of torsional rigidity to nexural rigidity. Results are presented for four different stiffener spacings.

Buckling of Axially Compressed Long Cylindrical Shell With Elastic Core

1962 ◽  
Vol 29 (2) ◽  
pp. 329-334 ◽  
Author(s):  
J. C. Yao
Keyword(s):  
Cylindrical Shell ◽  
Numerical Results ◽  
Theoretical Solution ◽  
Buckling Mode ◽  
Elastic Core ◽  
Long Cylindrical Shell ◽  
Special Case

This paper presents a theoretical solution to the problem of determining the buckling characteristics of an axially compressed, long, cylindrical shell which contains a solid or elastic core with a modulus lower than that of the shell. The buckling mode is assumed to be sinusoidal in both the axial and circumferential directions, with the bellows mode taken as a special case. Numerical results are obtained for the buckling characteristics of cylinders with solid cores. These results are found similar to those of P. Seide, who considered the bellows buckling mode.

Shear Buckling of Clamped Infinitely Long Plates—Influence of Torsional Rigidity of Transverse Stiffeners

1965 ◽  
Vol 16 (1) ◽  
pp. 92-95 ◽  
Author(s):  
K. C. Rockey ◽  
I. T. Cook
Keyword(s):  
Flexural Rigidity ◽  
Torsional Rigidity ◽  
Stiffened Plates ◽  
Rigidity Results ◽  
Buckling Resistance ◽  
Shear Buckling

SummaryThe paper provides relationships between the buckling resistance of clamped transversely stiffened plates and the flexural rigidity of the stiffeners for various values of the ratio of torsional rigidity to flexural rigidity. Results are presented for four different stiffener spacings.

Tire Treadwear — A Comprehensive Evaluation of the Factors: Generic Type, Aspect Ratio, Tread Pattern, and Tread Composition Part IV: Laboratory Measurement of Mechanical Properties and Mechanical Actions of Tires Relating to Treadwear

1986 ◽  
Vol 14 (4) ◽  
pp. 264-291
Author(s):  
K. L. Oblizajek ◽  
A. G. Veith
Keyword(s):  
Mechanical Properties ◽  
Shear Stress ◽  
Contact Zone ◽  
Flexural Rigidity ◽  
Comprehensive Evaluation ◽  
Shear Stiffness ◽  
Shear Stresses ◽  
Lateral Shear ◽  
Band Bending ◽  
Tread Rubber

Abstract Treadwear is explained by specific mechanical properties and actions of tires. Rubber shear stresses in the contact zone between the tire and the road become large at large slip angles. When normal stresses are insufficient to prevent sliding at the rear of the footprint, wear occurs at a rate that depends on test severity. Two experimental approaches are described to relate treadwear to tire characteristics. The first uses transducers imbedded in a simulated road surface to obtain direct measurements of contact stresses on the loaded, freely-rolling, steered tires. The second approach is developed with the aid of a simple carcass, tread-band, tread-rubber tire model. Various tire structural configurations; characterized by carcass spring rate, edgewise flexural band stiffness, and tread rubber shear stiffness; are simulated and lateral shear stress response in the contact zone is determined. Tires featuring high band stiffness and low carcass stiffness generate lower lateral shear stress levels. Furthermore, coupling of tread-rubber stiffness and band flexural rigidity are important in determining level of shear stresses. Laboratory measurements with the described apparatus produced values of tread-band bending and carcass lateral stiffness for several tire constructions. Good correlation is shown between treadwear and a broad range of tire stiffness and test course severities.

scholarly journals Onset of Convection in Two-Dimensional Porous Cavities with Open and Conducting Boundaries

2021 ◽  
Vol 136 (3) ◽  
pp. 791-812
Author(s):  
Peder A. Tyvand ◽  
Jonas Kristiansen Nøland
Keyword(s):  
Critical Rayleigh Number ◽  
Numerical Results ◽  
Temperature Perturbation ◽  
Two Dimensional ◽  
Onset Of Convection ◽  
Order Problem ◽  
Fourth Order Problem ◽  
Thermally Conducting ◽  
Perturbation Pressure ◽  
Special Case

AbstractThe onset of thermal convection in two-dimensional porous cavities heated from below is studied theoretically. An open (constant-pressure) boundary is assumed, with zero perturbation temperature (thermally conducting). The resulting eigenvalue problem is a full fourth-order problem without degeneracies. Numerical results are presented for rectangular and elliptical cavities, with the circle as a special case. The analytical solution for an upright rectangle confirms the numerical results. Streamlines penetrating the open cavities are plotted, together with the isotherms for the associated closed thermal cells. Isobars forming pressure cells are depicted for the perturbation pressure. The critical Rayleigh number is calculated as a function of geometric parameters, including the tilt angle of the rectangle and ellipse. An improved physical scaling of the Darcy–Bénard problem is suggested. Its significance is indicated by the ratio of maximal vertical velocity to maximal temperature perturbation.

scholarly journals The game of Double-Silver on intervals

2001 ◽  
Vol 26 (8) ◽  
pp. 485-496 ◽  
Author(s):  
Gerald A. Heuer
Keyword(s):  
Measure Zero ◽  
Optimal Strategies ◽  
The Other ◽  
Parameter Plane ◽  
Left Endpoint ◽  
Relative Placement ◽  
Special Case

Silverman's game on intervals was analyzed in a special case by Evans, and later more extensively by Heuer and Leopold-Wildburger, who found that optimal strategies exist (and gave them) quite generally when the intervals have no endpoints in common. They exist in about half the parameter plane when the intervals have a left endpoint or a right endpoint, but not both, in common, and (as Evans had earlier found) exist only on a set of measure zero in this plane if the intervals are identical. The game of Double-Silver, where each player has its own threshold and penalty, is examined. There are several combinations of conditions on relative placement of the intervals, the thresholds and penalties under which optimal strategies exist and are found. The indications are that in the other cases no optimal strategies exist.

Magnetocrystalline Anisotropy and Twinning Stress of 10M and 2M Martensites in Ni-Mn-Ga System

2006 ◽  
Vol 512 ◽  
pp. 195-200 ◽  
Author(s):  
Nariaki Okamoto ◽  
Takashi Fukuda ◽  
Tomoyuki Kakeshita ◽  
Tetsuya Takeuchi
Keyword(s):  
Magnetic Field ◽  
Shear Stress ◽  
Magnetocrystalline Anisotropy ◽  
Anisotropy Constant ◽  
The Other ◽  
Magnetic Shear ◽  
Maximum Value ◽  
Twinning Plane ◽  
Twinning Shear ◽  
The Difference

Ni2MnGa alloy with 10M martensite exhibits rearrangement of martensite variants (RMV) by magnetic field, but Ni2.14Mn0.92Ga0.94 with 2M martensite does not. In order to explain the difference, we measured uniaxial magnetocrystalline anisotropy constant Ku and the stress required for twinning plane movement τreq in these alloys. Concerning the former alloy, the maximum value of magnetic shear stress acting across twinning plane τmag, which is evaluated as |Ku| divided by twinning shear, becomes larger than τr eq. On the other hand, concerning the latter alloy, the maximum of τmag is only one-tenth of τreq at any temperature examined. Obviously, the relation, τmag> τr eq, is satisfied when RMV occurs by magnetic field and vice versa. In this martensite, the large twinning shear of 2M martensite is responsible for small τmag and large τreq.

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