Expansion/contraction of a spherical elastic/plastic shell revisited

Alexandrov, Sergei; Pirumov, Alexander; Jeng, Yeau-Ren

doi:10.1007/s00161-014-0365-6

Cited by 9 publications

(4 citation statements)

References 14 publications

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“…Therefore, Equation (15) can be immediately integrated. This change of variables is useful for solving a class of elastic/plastic boundary value problems [39][40][41]. Paper [38] presented the solution for bending under tension.…”

Section: T Tmentioning

confidence: 99%

Plastic Bending at Large Strain: A Review

2021

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Finite plastic bending attracts researchers’ attention due to its importance for identifying material properties and frequent occurrence in sheet metal forming processes. The present review contains theoretical and experimental parts. The theoretical part is restricted to analytic and semi-analytic solutions for pure bending and bending under tension. The experimental part mainly focuses on four-point bending, though other bending tests and processes are also outlined.

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Section: T Tmentioning

confidence: 99%

Plastic Bending at Large Strain: A Review

2021

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“…Этому способствует замена радиальной координаты некоторой другой переменной. Такие замены успешно применялись при решении сферически симметричных краевых задач [15][16][17]. Решение получено в условиях плосконапряженного состояния.…”

Section: Introductionunclassified

Design of equi-strength rotating disk

Lyamina

Novozhilova

2023

Modern Transportation Systems and Technologies

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Background: Rotating disks, such as flywheels, are an important machine part of engines, which requires the development of the theoretical methods of their analysis and design. Aim: Determination of the profile of equi-strength rotating disks. Materials and Methods: Methods of the mathematical theory of elasticity and plasticity Results: Methodology for determining the profile of equi-strength rotating disks obeying the von Mises yield criterion and its application Conclusion: The methodology developed can be used to design equi-strength rotating disks subject to various combinations of internal and external pressures. It can be extended to more general yield criteria.

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“…For strain-hardening materials, a method to find semi-analytic solutions at large strains for a fully plastic sphere was proposed in [2]. A different method that allows for determining the elastic/plastic boundary was developed in [3]. Both methods take advantage of the dependence of the equivalent stress on a single quantity, namely, the equivalent strain.…”

Section: Introductionmentioning

confidence: 99%

“…However, if the process is isothermal, then the equivalent stress is only a function of the equivalent strain and the equivalent strain rate. In this case, the methods proposed in [2,3] cannot be used directly. A modification of these methods for finding a semi-analytic solution for an infinite rigid/plastic hollow cylinder loaded by inner pressure is developed in the present paper.…”

Section: Introductionmentioning

confidence: 99%

An Analytic Solution for an Expanding/Contracting Strain-Hardening Viscoplastic Hollow Cylinder at Large Strains and Its Application to Tube Hydroforming Design

2021

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This paper presents a semi-analytic rigid/plastic solution for the expansion/contraction of a hollow cylinder at large strains. The constitutive equations comprise the yield criterion and its associated flow rule. The yield criterion is pressure-independent. The yield stress depends on the equivalent strain rate and the equivalent strain. No restriction is imposed on this dependence. The solution is facilitated using the equivalent strain rate as an independent variable instead of the polar radius. As a result, it reduces to ordinary integrals. In the course of deriving the solution above, the transformation between Eulerian and Lagrangian coordinates is used. A numerical example illustrates the solution for a material model available in the literature. A practical aspect of the solution is that it readily applies to the preliminary design of tube hydroforming processes.

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Expansion/contraction of a spherical elastic/plastic shell revisited

Cited by 9 publications

References 14 publications

Plastic Bending at Large Strain: A Review

Plastic Bending at Large Strain: A Review

Design of equi-strength rotating disk

An Analytic Solution for an Expanding/Contracting Strain-Hardening Viscoplastic Hollow Cylinder at Large Strains and Its Application to Tube Hydroforming Design

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