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.

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.

The Influence of Rotatory Inertia and Transverse Shear on the Dynamic Plastic Behavior of Beams

1979 ◽  
Vol 46 (2) ◽  
pp. 303-310 ◽  
Author(s):  
Norman Jones ◽  
J. Gomes de Oliveira
Keyword(s):  
Transverse Shear ◽  
Shear Force ◽  
Yield Criterion ◽  
Yield Condition ◽  
Bending Moment ◽  
Plastic Behavior ◽  
Plastic Response ◽  
Rotatory Inertia ◽  
Perfectly Plastic ◽  
Theoretical Procedure

The theoretical procedure presented herein examines the influence of retaining the transverse shear force in the yield criterion and rotatory inertia on the dynamic plastic response of beams. Exact theoretical rigid perfectly plastic solutions are presented for a long beam impacted by a mass and a simply supported beam loaded impulsively. It transpires that rotatory inertia might play a small, but not negligible, role on the response of these beams. The results in the various figures indicate that the greatest departure from an analysis which neglects rotatory inertia but retains the influence of the bending moment and transverse shear force in the yield condition is approximately 11 percent for the particular range of parameters considered.

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.

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.

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.

A theoretical and experimental study of projectile impact on clamped circular plates

1968 ◽  
Vol 306 (1487) ◽  
pp. 435-447 ◽  
Keyword(s):  
Experimental Study ◽  
Plastic Deformation ◽  
Mild Steel ◽  
Yield Condition ◽  
Flow Rule ◽  
Plastic Strains ◽  
Circular Plates ◽  
Projectile Impact ◽  
Von Mises ◽  
Associated Flow Rule

A method for the analysis of the plastic deformation of a circular plate subject to projectile impact is presented based on the assumption that the material is rigid viscoplastic, obeying a von Mises yield condition and associated flow rule. The predictions of the analysis are com­pared with the results of experiments in which projectiles of different masses are fired at various velocities at clamped plates of mild steel. The plates used in the experiments are such that substantial plastic strains can develop, while the maximum displacements are of the same order as the thickness. The analytical method presented predicts the behaviour of the plates to within the accuracy of the tests. The material constants which fit the results are in accord with those obtained from different tests.

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