Optimum Thickness Variation in a Curved Strip under Pure Bending

1972 ◽  
Vol 23 (1) ◽  
pp. 77-86
Author(s):  
D R Blackeby ◽  
E H Mansfield
Keyword(s):  
Yield Criterion ◽  
Equivalent Stress ◽  
Thickness Variation ◽  
Curved Beam ◽  
Optimum Thickness ◽  
Pure Bending

SummaryThis paper determines the thickness variation in an annular strip (a curved beam) under pure bending to give a constant equivalent stress based on the Mises-Hencky yield criterion. The stresses due to an applied shear are also determined.

An Analysis of Filament Overwound Toroidal Pressure Vessels and Optimum Design of Such Structures

2002 ◽  
Vol 124 (2) ◽  
pp. 215-222 ◽  
Author(s):  
Shuguang Li ◽  
John Cook
Keyword(s):  
Optimum Design ◽  
Equivalent Stress ◽  
Mechanical Damage ◽  
Stress Rupture ◽  
Optimization Procedure ◽  
Pressure Vessels ◽  
Thickness Variation ◽  
Von Mises Equivalent Stress ◽  
Metal Liner ◽  
Von Mises

This paper is concerned with the membrane shell analysis of filament overwound toroidal pressure vessels and optimum design of such pressure vessels using the results of the analysis by means of mathematical nonlinear programming. The nature of the coupling between overwind and linear has been considered based on two extreme idealizations. In the first, the overwind is rigidly coupled with the liner, so that the two deform together in the meridional direction as the vessel dilates. In the second, the overwind is free to slide relative to the linear, but the overall elongations of the two around a meridian are identical. Optimized designs with the two idealizations show only minor differences, and it is concluded that either approximation is satisfactory for the purposes of vessel design. Aspects taken into account are the intrinsic overwind thickness variation arising from the winding process and the effects of fiber pre-tension. Pre-tension can be used not only to defer the onset of yielding, but also to achieve a favorable in-plane stress ratio which minimizes the von Mises equivalent stress in the metal liner. Aramid fibers are the most appropriate fibers to be used for the overwind in this type of application. The quantity of fiber required is determined by both its short-term strength and its long-term stress rupture characteristics. An optimization procedure for the design of such vessels, taking all these factors into account, has been established. The stress distributions in the vessels designed in this way have been examined and discussed through the examples. A design which gives due consideration of possible mechanical damage to the surface of the overwind has also been addressed.

Effect of the Constitutive Law on the Accuracy of Prediction of the Forming Limit Curves

2012 ◽  
Vol 504-506 ◽  
pp. 77-82 ◽  
Author(s):  
Liana Paraianu ◽  
Dan Sorin Comsa ◽  
Ioan Pavel Nicodim ◽  
Ioan Ciobanu ◽  
Dorel Banabic
Keyword(s):  
Sheet Metal ◽  
Mechanical Response ◽  
Yield Criterion ◽  
Plastic Anisotropy ◽  
Equivalent Stress ◽  
Point Of View ◽  
Constitutive Law ◽  
Forming Limit ◽  
Accuracy Of Prediction ◽  
Forming Limit Curves

The accuracy of the forming limit curves predicted by the Marciniak-Kuczynski model depends on the type and flexibility of the constitutive equations used to describe the mechanical response of the sheet metal. From this point of view, the yield criterion has the most significant influence. The paper presents a comparative analysis referring to the quality of the forming limit curves predicted by the Marciniak-Kuczynski model for the case when the plastic anisotropy of a DC04 sheet metal is described by the BBC2005 yield criterion. The coefficients included in the expression of the BBC2005 equivalent stress are evaluated using different identification strategies (with 4, 6, 7, and 8 mechanical parameters). The forming limit curves predicted by the Marciniak-Kuczynski model in each of the cases previously mentioned are compared with experimental data.

scholarly journals The generalized criterion of multiaxial random fatigue based on conception proposed by prof. Macha

2019 ◽  
Vol 300 ◽  
pp. 15001
Author(s):  
Tadeusz Łagoda ◽  
Marta Kurek ◽  
Karolina Łagoda
Keyword(s):  
Shear Stress ◽  
Complex Number ◽  
Mathematical Problem ◽  
Equivalent Stress ◽  
Complex Stress ◽  
Complex Numbers ◽  
Pure Bending ◽  
Pure Torsion ◽  
Special Cases ◽  
Random Fatigue

This criterion has been repeatedly verified, analyzed and special cases of this criterion reducing complex stress to equivalent uniaxial were taken into account. Since both normal and shear stress are vectors, we encounter the mathematical problem of adding these vectors, and the question arises how to understand the obtained equivalent stress, because two perpendicular vectors are added with weighting factors. Therefore, in this work it was proposed to adopt a system of complex numbers. Normal stress was defined as the real part and shear stress as imaginary part. As a result, on the basis of the defined complex number and basing on pure bending and pure torsion after transformations, the expression for equivalent stress was identical to the previously proposed criteria defined on the basis of the concept of prof. Macha.

Numerical Simulation of Sheet Metal Forming Processes Using a New Yield Criterion

2007 ◽  
Vol 344 ◽  
pp. 833-840 ◽  
Author(s):  
Dan Sorin Comsa ◽  
Dorel Banabic
Keyword(s):  
Yield Criterion ◽  
Plastic Anisotropy ◽  
Equivalent Stress ◽  
Constitutive Models ◽  
Cold Forming ◽  
Material Parameters ◽  
Numerical Tests ◽  
Hardening Law ◽  
Asymptotic Function ◽  
New Formulation

The paper is focused on the development of a new phenomenological yield criterion able to describe the inelastic response of sheet metals subjected to cold forming. The model consists in two components: the equivalent stress and the hardening law. The equivalent stress is a function incorporating 8 material parameters. Due to these parameters, the new formulation is able to describe four normalized yield stresses (y0, y45, y90, yb) and four coefficients of plastic anisotropy (r0, r45, r90, rb). The hardening law is defined as a linearly asymptotic function containing 4 material parameters. The numerical tests presented in the last section of the paper prove the capability of the elastoplastic constitutive models based on the new yield criterion to model the earing as well as the wrinkling phenomena accompanying the deep-drawing process.

Elastic-plastic stress distributions and limit angular velocities in rotating hyperbolic annular discs

2007 ◽  
Vol 221 (2) ◽  
pp. 137-142 ◽  
Author(s):  
N N Alexandrova ◽  
P M M Vila Real
Keyword(s):  
Rotational Speed ◽  
Yield Criterion ◽  
Circumferential Stress ◽  
Radial Pressure ◽  
Thickness Variation ◽  
Flow Rule ◽  
Stress Distributions ◽  
Elastic Plastic ◽  
Angular Velocities ◽  
Hyperbolic Form

Plastic analytical stress analysis of a rotating annular disc with its contours being free from the radial pressure and with specifically variable thickness is presented in terms of the Mises-yield criterion and its associated flow rule. The hyperbolic form of thickness variation is considered and optimized towards the maximum rotational speed and favourable stress combinations. Radial and circumferential stress distributions in the disc both in the intermediate elastic-plastic and in the limit plastic states are obtained. As a particular case, limit elastic angular velocity parameter is derived. The influences of rotational speed as well as the disc's thickness profile on the plastic solution and size of elastic-plastic zone are demonstrated and discussed. The results obtained may be used for the correct implementation of numerical codes and preliminary engineering design.

Limit Load Solutions of the Orthotropic Thick-Walled Pipe Subjected to Internal Pressure, Bending Moment and Torsion Moment

2019 ◽  
Author(s):  
Min Xu ◽  
Yujie Zhao ◽  
Binbin Zhou ◽  
Xiaohua He ◽  
Changyu Zhou
Keyword(s):  
Analytical Solution ◽  
Yield Strength ◽  
Internal Pressure ◽  
Yield Criterion ◽  
Bending Moment ◽  
Limit Load ◽  
Pure Bending ◽  
Pure Torsion ◽  
Torsion Moment ◽  
The Difference

Abstract Based on the Hill yield criterion, the analytical solutions of the limit load of orthotropic thick-walled pipes under pure internal pressure, bending moment and torsion are given respectively. The simplified Mises analytical solution and finite element results of limit load for isotropic thick-walled pipe are obtained. The solution verifies the reliability of the analytical solution. The paper discusses the difference of limit load of isotropic and orthotropic pipes under the conditions of pure internal pressure, pure bending moment and pure torsion moment. It is concluded that the influence of material anisotropy on the limit load is significant. The limit load of pipe under pure internal pressure is mainly determined by circumferential yield strength, pure bending is only related to axial yield strength and pure torsion moment is related to the yield strength in the 45° direction and radial yield strength.

scholarly journals A Limit Load Solution for Anisotropic Welded Cracked Plates in Pure Bending

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1764
Author(s):  
Sergei Alexandrov ◽  
Elena Lyamina ◽  
Alexander Pirumov ◽  
Dinh Kien Nguyen
Keyword(s):  
Numerical Method ◽  
Yield Criterion ◽  
Plastic Anisotropy ◽  
Bending Moment ◽  
Limit Load ◽  
Vertical Axis ◽  
Pure Bending ◽  
Cracked Plates ◽  
Base Materials ◽  
Assessment Procedures

The present paper’s main objective is to derive a simple upper bound solution for a welded plate in pure bending. The plate contains a crack located in the weld. Both the weld and base materials are orthotropic. Hill’s quadratic yield criterion is adopted. The solution is semi-analytic. A numerical method is only required for minimizing a function of two independent variables. Six independent dimensionless parameters classify the structure. Therefore, the complete parametric analysis of the solution is not feasible. However, for a given set of parameters, the numerical solution is straightforward, and the numerical method is fast. A numerical example emphasizes the effect of plastic anisotropy and the crack’s location on the bending moment at plastic collapse. In particular, the bending moment for the specimen having a vertical axis of symmetry is compared with that of the asymmetric specimen. It is shown that the latter is smaller for all considered cases. The solution found can be used in conjunction with flaw assessment procedures.

Limit Design of a Full Reinforcement for a Circular Cutout in a Uniform Slab

1952 ◽  
Vol 19 (3) ◽  
pp. 397-401
Author(s):  
H. J. Weiss ◽  
W. Prager ◽  
P. G. Hodge
Keyword(s):  
Upper Bound ◽  
Plastic Material ◽  
Yield Criterion ◽  
Curved Beam ◽  
Shearing Stress ◽  
Concentric Ring ◽  
Perfectly Plastic ◽  
Circular Cutout

Abstract A thin square slab with a central circular cutout reinforced by a concentric ring is subjected to uniform tensions Tx and Ty on the exterior edges. It is desired to determine the dimensions of the reinforcement if the slab is not to collapse under any load which could be supported by a similar slab without any cutout or reinforcement. It is assumed that the slab and reinforcement are made of a perfectly plastic material which satisfies the Tresca yield criterion of maximum shearing stress, and that the dimensions of the reinforcement are such that it may reasonably be approximated by a curved beam. Under these assumptions, an upper bound on the necessary thickness of the reinforcement for any given radius is obtained. Certain practical limitations of the theory are discussed.

A Semi-Analytical 3-D Solution for Bending Under Tension

2012 ◽  
Vol 586 ◽  
pp. 302-305
Author(s):  
Sergei Alexandrov ◽  
Elena Lyamina ◽  
Li Hui Lang
Keyword(s):  
Yield Criterion ◽  
Equivalent Stress ◽  
Three Dimensional ◽  
Equivalent Strain ◽  
Large Strains ◽  
Flow Rule ◽  
Viscoplastic Material ◽  
Equivalent Strain Rate ◽  
Bending Under Tension ◽  
Associated Flow Rule

The paper concerns with three-dimensional analysis of the process of bending under tension for incompressible, rigid viscoplastic material at large strains. The constitutive equations consist of the Mises-type yield criterion and its associated flow rule. No restriction is imposed on the dependence of the equivalent stress on the equivalent strain rate. The problem is reduced to evaluating ordinary integrals and solving transcendental equations.

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