Limit Loads of Circular Plates Under Combined Loading

1973 ◽  
Vol 40 (3) ◽  
pp. 799-802 ◽  
Author(s):  
H. M. Haydl ◽  
A. N. Sherbourne
Keyword(s):  
Yield Criterion ◽  
Yield Condition ◽  
Combined Loading ◽  
Stress Fields ◽  
Collapse Load ◽  
Circular Plates ◽  
Limit Loads ◽  
Title Problem ◽  
Interaction Curves ◽  
Von Mises

Limit loads of circular plates under combined transverse and in-plane loading are given for the von Mises yield condition. Ivanov’s approximation to the Ilyushin yield surface is used. Collapse load interaction curves and stress fields are given for simply supported and clamped plates. The results are compared with existing solutions for the title problem based on the Tresca yield criterion.

Limit loads of variable-thickness circular plates accounting for transverse shear

1973 ◽  
Vol 8 (2) ◽  
pp. 108-112
Author(s):  
H M Haydl ◽  
A N Sherbourne
Keyword(s):  
Variable Thickness ◽  
Transverse Shear ◽  
Yield Condition ◽  
Collapse Load ◽  
Circular Plates ◽  
Limit Loads ◽  
Transverse Pressure ◽  
Von Mises

Limit loads of variable-thickness circular plates are given for the von Mises yield condition. The plates are loaded with a uniform transverse pressure and are hinge supported at the edge. The effect of transverse shear on the yield condition and the collapse load is examined. It is shown that the inclusion of transverse shear in the analysis leads to restrictions on the edge thickness of the plates.

scholarly journals Viscoplastic plates

2021 ◽  
Vol 477 (2254) ◽  
Author(s):  
Thomasina V. Ball ◽  
Neil J. Balmforth
Keyword(s):  
Yield Criterion ◽  
Yield Condition ◽  
Bending Moment ◽  
Constitutive Law ◽  
Viscoplastic Fluid ◽  
Asymptotic Model ◽  
Circular Plates ◽  
Viscous Stress ◽  
Flat Plates ◽  
Von Mises

An asymptotic model is constructed to describe the bending of thin sheets, or plates, of viscoplastic fluid described by the Herschel–Bulkley constitutive law, which incorporates the von Mises yield condition and a nonlinear viscous stress. The model reduces to a number of previous ones from plasticity theory and viscous fluid mechanics in various limits. It is characterized by a yield criterion proposed by Ilyushin which compactly combines the effect of the bending moment and in-plane stress tensors through three particular invariants. The model is used to explore the bending of loaded flat plates, the deflection of impulsively driven circular plates, and the tension-controlled deflection of loaded beams.

Overstraining of flush plain cross-bored cylinders

2004 ◽  
Vol 218 (2) ◽  
pp. 143-153 ◽  
Author(s):  
J M Kihiu ◽  
G O Rading ◽  
S M Mutuli
Keyword(s):  
Finite Element Method ◽  
Yield Criterion ◽  
Three Dimensional ◽  
Yield Condition ◽  
Solution Technique ◽  
Stress Distributions ◽  
Dimensional Finite Element ◽  
Von Mises ◽  
Three Dimensional Finite Element ◽  
Incremental Theory Of Plasticity

A three-dimensional finite element method computer program was developed to establish the elastic-plastic, residual and service stress distributions in thick-walled cylinders with flush and non-protruding plain cross bores under internal pressure. The displacement formulation and eight-noded brick isoparametric elements were used. The incremental theory of plasticity with a 5 per cent yield condition (an element is assumed to have yielded when the effective stress is within 5 per cent of the material yield stress) and von Mises yield criterion were assumed. The frontal solution technique was used. The incipient yield pressure and the pressure resulting in a 0.3 per cent overstrain ratio were established for various cylinder thickness ratios and cross bore-main bore radius ratios. For a thickness ratio of 2.25 and a cross bore-main bore radius ratio of 0.1, the stresses were determined for varying overstrain and an optimum overstrain ratio of 37 per cent was established. To find the accuracy of the results, the more stringent yield condition of 0.5 per cent was also considered. The benefits of autofrettage were presented and alternative autofrettage and yield condition procedures proposed.

The Biaxial Strengthening of Textured Titanium

1967 ◽  
Vol 89 (1) ◽  
pp. 13-18 ◽  
Author(s):  
H. W. Babel ◽  
D. A. Eitman ◽  
R. W. McIver
Keyword(s):  
Hoop Stress ◽  
Yield Criterion ◽  
Test Method ◽  
Stress Fields ◽  
Titanium Sheet ◽  
Homogeneous Stress ◽  
Stress States ◽  
Von Mises ◽  
Biaxial Behavior ◽  
Very High

The purpose of this investigation was to develop an understanding of the biaxial behavior of titanium sheet. An experimental test method was developed and found to provide homogeneous stress fields for obtaining biaxial data in a variety of stress states. Data were obtained using the same specimen geometry for 1-to-2 and 1-to-1 axial-to-hoop stress states. Significant increases in the biaxial yield strength were obtained over those predicted by von Mises’ yield criterion for isotropic materials. Very high biaxial burst strengths were also obtained; the maximum was 246 ksi for annealed Ti-5Al-2.5 Sn alloy in a 1-to-1 stress state. The data followed the general form predicted by Hill’s model for anisotropic materials.

The Determination of Safe Loads of Beams Subjected to Combined Twisting and Biaxial Bending Moments

1959 ◽  
Vol 26 (3) ◽  
pp. 442-447
Author(s):  
P. G. Hodge ◽  
R. Sankaranarayanan
Keyword(s):  
Yield Criterion ◽  
Piecewise Linear ◽  
Yield Condition ◽  
Bending Moments ◽  
Collapse Load ◽  
Biaxial Bending ◽  
Suitable Parameter ◽  
Bound Theorem ◽  
Safe Load

Abstract Using the lower-bound theorem of limit analysis, a yield criterion is obtained in terms of the stress resultants for a beam, subjected to combined twisting and biaxial bending moments. Based on a piecewise linear approximate yield condition, the “collapse load” is determined for a right-angle bent, subjected to a load in an arbitrary direction applied to the mid-point of one leg. Such a collapse load, which is a “safe load” for the beam, is plotted as a function of a suitable parameter.

Overstrain in flush optimal-chamfered cross-bored cylinders

2006 ◽  
Vol 220 (1) ◽  
pp. 15-25
Author(s):  
J M Kihiu ◽  
G O Rading ◽  
S M Mutuli
Keyword(s):  
Yield Criterion ◽  
Three Dimensional ◽  
Yield Condition ◽  
Meridional Plane ◽  
Stress Distributions ◽  
Dimensional Finite Element ◽  
Von Mises ◽  
Three Dimensional Finite Element ◽  
Stress Reversals ◽  
Incremental Theory Of Plasticity

A three-dimensional finite-element method computer program was developed to establish the elastic—plastic, residual, and service stress distributions in cylinders with flush and non-protruding optimal-chamfered cross-bores under internal pressure. Eight-noded brick and four-noded tetrahedral isoparametric elements and the displacement formulation were used. The incremental theory of plasticity with a 5 per cent yield condition and von Mises yield criterion were assumed. The incipient and 5 per cent overstrain (ov) pressures were established for various thickness ratios and cross-bore to main bore radius ratios. For the optimum chamfer angle geometrical configuration, the stresses were determined for varying ov. The maximum and minimum effective stresses were located 7.5° from the meridional and transverse planes, respectively. Meridional plane through thickness yielding occurred at an ov of 41 per cent. The service stress gradients at the cross-bore chamfer end increased with ov for ovs >30 per cent. Stress reversals were eliminated for overstrain >27 per cent. Alternative autofrettage and yield condition procedures were proposed.

Elastic-Plastic Tension-Torsion in a Circular Bar of Rate-Sensitive Material

1979 ◽  
Vol 46 (2) ◽  
pp. 311-316 ◽  
Author(s):  
S. A. Meguid ◽  
J. D. Campbell
Keyword(s):  
Yield Criterion ◽  
Effective Strain ◽  
Flow Rule ◽  
Viscoplastic Material ◽  
Sensitive Material ◽  
Linear Partial Differential Equations ◽  
Partial Pivoting ◽  
Interaction Curves ◽  
Circular Bar ◽  
Von Mises

A theoretical and numerical investigation is made of the behavior of a circular bar of elastic-viscoplastic material subjected to either proportional or nonproportional straining in tension and torsion. The tensile properties of the material are assumed to be adequately represented by the empirical formula of Bodner and Symonds, which is based on experimental results for mild steel. The analysis employs Perzyna’s generalization of von Mises’ yield criterion, and the associated plastic flow rule. Elastic compressibility is taken into account. The stresses, strains, and loading paths are determined for four prescribed straining paths; the results were obtained by solving numerically, using Crout’s method with partial pivoting, a system of six simultaneous quasi-linear partial differential equations of hyperbolic type. Closed-form analytical solutions are also obtained for the stresses, load, and torque corresponding to fully plastic conditions; interaction curves are plotted relating load and torque under these conditions, for quasi-static straining and for a range of finite effective strain rates.

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