Ellipsoidal load-domain shakedown analysis with von Mises yield criterion: A robust optimization approach

2016 ◽  
Vol 107 (13) ◽  
pp. 1136-1144 ◽  
Author(s):  
Takashi Yamaguchi ◽  
Yoshihiro Kanno
Keyword(s):  
Robust Optimization ◽  
Yield Criterion ◽  
Optimization Approach ◽  
Shakedown Analysis ◽  
Criterion A ◽  
Von Mises Yield Criterion ◽  
Von Mises

Design Equation for Minimum Required Thickness of a Cylindrical Shell Subject to Internal Pressure Based on Von Mises Criterion

2019 ◽  
Author(s):  
James Lu ◽  
Barry Millet ◽  
Kenneth Kirkpatrick ◽  
Bryan Mosher
Keyword(s):  
Cylindrical Shell ◽  
Internal Pressure ◽  
Yield Criterion ◽  
Design Equation ◽  
Shell Wall ◽  
Section Viii ◽  
Von Mises Yield Criterion ◽  
Von Mises ◽  
Division 2 ◽  
Shell Wall Thickness

Abstract Design equation (4.3.1) for the minimum required thickness of a cylindrical shell subjected to internal pressure in Part 4 “design by rule (DBR)” of the ASME Boiler and Pressure Vessel Code, Section VIII, Division 2 [1] is based on the Tresca Yield Criterion, while design by analysis (DBA) in Part 5 of the Division 2 Code is based on the von Mises Yield Criterion. According to ASME PTB-1 “ASME Section VIII – Division 2 Criteria and Commentary”, the difference in results is about 15% due to use of the two different criteria. Although the von Mises Yield Criterion will result in a shell wall thickness less than that from Tresca Yield Criterion, Part 4 (DBR) of ASME Division 2 adopts the latter for a more convenient design equation. To use the von Mises Criterion in lieu of Tresca to reduce shell wall thickness, one has to follow DBA rules in Part 5 of Division 2, which typically requires detailed numeric analysis performed by experienced stress analysts. This paper proposes a simple design equation for the minimum required thickness of a cylindrical shell subjected to internal pressure based on the von Mises Yield Criterion. The equation is suitable for both thin and thick cylindrical shells. Calculation results from the equation are validated by results from limit load analyses in accordance with Part 5 of ASME Division 2 Code.

Forming Limit Analysis of Sheet Metals Based on a Generalized Deformation Theory

2003 ◽  
Vol 125 (3) ◽  
pp. 260-265 ◽  
Author(s):  
C. L. Chow ◽  
M. Jie ◽  
S. J. Hu
Keyword(s):  
Strain Hardening ◽  
Deformation Theory ◽  
Yield Criterion ◽  
Strain Ratio ◽  
Yield Function ◽  
Forming Limit ◽  
Sheet Metals ◽  
Theory Of Plasticity ◽  
Von Mises Yield Criterion ◽  
Von Mises

This paper presents the development of a generalized method to predict forming limits of sheet metals. The vertex theory, which was developed by Sto¨ren and Rice (1975) and recently simplified by Zhu, Weinmann and Chandra (2001), is employed in the analysis to characterize the localized necking (or localized bifurcation) mechanism in elastoplastic materials. The plastic anisotropy of materials is considered. A generalized deformation theory of plasticity is proposed. The theory considers Hosford’s high-order yield criterion (1979), Hill’s quadratic yield criterion and the von Mises yield criterion. For the von Mises yield criterion, the generalized deformation theory reduces to the conventional deformation theory of plasticity, i.e., the J2-theory. Under proportional loading condition, the direction of localized band is known to vary with the loading path at the negative strain ratio region or the left hand side (LHS) of forming limit diagrams (FLDs). On the other hand, the localized band is assumed to be always perpendicular to the major strain at the positive strain ratio region or the right hand side (RHS) of FLDs. Analytical expressions for critical tangential modulus are derived for both LHS and RHS of FLDs. For a given strain hardening rule, the limit strains can be calculated and consequently the FLD is determined. Especially, when assuming power-law strain hardening, the limit strains can be explicitly given on both sides of FLD. Whatever form of a yield criterion is adopted, the LHS of the FLD always coincides with that given by Hill’s zero-extension criterion. However, at the RHS of FLD, the forming limit depends largely on the order of a chosen yield function. Typically, a higher order yield function leads to a lower limit strain. The theoretical result of this study is compared with those reported by earlier researchers for Al 2028 and Al 6111-T4 (Grafand Hosford, 1993; Chow et al., 1997).

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