Bending of circular plates of hardening material

Popov, Egor P.; Khojasteh-Bakht, M.; Yaghmai, S.

doi:10.1016/0020-7683(67)90023-6

Cited by 19 publications

(4 citation statements)

References 9 publications

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“…done during plastic deformation. Thus substituting the flow rule (2) we have simply By equation (7) we now see that L disappears and we can write a strictly determinate form if explicit relationship between F and K is known. in which suffixes 1, 2, 3 refer to the normal stress components and 4, 5, 6 to shear stress components.…”

Section: Significance Of Parameter 'A'mentioning

confidence: 99%

Elasto‐plastic solutions of engineering problems ‘initial stress’, finite element approach

Zienkiewicz

Valliappan

King

1969

Numerical Meth Engineering

508

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SUMMARYThe paper presents first a general formulation of the elasto-plastic matrix for evaluating stress increments from those of stresses for any yield surface with an associated flow rule. A new 'initial stress' computational process is proposed which is shown (I) to yield more rapid convergence than alternative approaches (2) to permit large load increments without violating the yield criteria and thus simply to establish lower bound solutions. Several solutions showing stress distribution, strain developnient and growth of plastic enclaves are given both for the von Mises and for Coulomb (Drucker) type yield surfaces. Load reversal and thermoplastic behaviour are dealt with.

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Section: Significance Of Parameter 'A'mentioning

confidence: 99%

Elasto‐plastic solutions of engineering problems ‘initial stress’, finite element approach

Zienkiewicz

Valliappan

King

1969

Numerical Meth Engineering

508

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“…for any test function u * in an appropriate functional space. In order to solve the resulting nonlinear problem, various computational procedures have been proposed and extensively used, among them [15][16][17][18][19][20][21][22].…”

Section: Extension Of the Methods To Plasticitymentioning

confidence: 99%

On the coupling of local 3D solutions and global 2D shell theory in structural mechanics

Quaranta

Ziane

Daim

et al. 2019

Adv. Model. and Simul. in Eng. Sci.

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Most of mechanical systems and complex structures exhibit plate and shell components. Therefore, 2D simulation, based on plate and shell theory, appears as an appealing choice in structural analysis as it allows reducing the computational complexity. Nevertheless, this 2D framework fails for capturing rich physics compromising the usual hypotheses considered when deriving standard plate and shell theories. To circumvent, or at least alleviate this issue, authors proposed in their former works an in-plane-out-of-plane separated representation able to capture rich 3D behaviors while keeping the computational complexity of 2D simulations. However, that procedure it was revealed to be too intrusive for being introduced into existing commercial softwares. Moreover, experience indicated that such enriched descriptions are only compulsory locally, in some regions or structure components. In the present paper we propose an enrichment procedure able to address 3D local behaviors, preserving the direct minimally-invasive coupling with existing plate and shell discretizations. The proposed strategy will be extended to inelastic behaviors and structural dynamics.

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“…(24) in Eq. (19) leads to different formulations for the material law depending on the integer m.For m = 1 (Prandtl-Reuss [a], see Section 11):For m = 2 (Popov et al[9], see Section 11):…”

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confidence: 99%