Closed-form solutions of the nonlinear partial differential equations governing plane rigid perfect plasticity problems by ad hoc assumptions

Panayotounakos, D.E.; Andrianopoulos, N. P.; Boulougouris, V. C.

doi:10.1093/qjmam/hbi029

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The Prandtl' Problem Its Solution and Hypotheses1

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“…The perturbations of the Prandtl' solution by parameter corresponding to arbitrary weak nonhomogeneity are investigated in [17]. Also we should mention the recent works [18][19][20][21][22] dealing with subject being investigated here.…”

Section: The Prandtl' Problem Its Solution and Hypothesesmentioning

confidence: 99%

Asymptotic Analysis in the Prandtl’ Problem

Георгиевский¹,

Cabada²,

Liz³

et al. 2009

AIP Conference Proceedings

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On solvability of a three-point boundary value problem for second order nonlinear functional differential equations AIP Conf. Abstract.A long-standing question on possibility of construction of the PrandtF problem classic solution without some kind of kinematic or static hypotheses as well as on an existence of the other, "non-classic", solutions which the Prandtl' hypothesis is not correct for (and which cannot be verified in real experiment), is discussed and resolved. On the basis of asymptotic analysis with natural low geometric parameter, the exact solution (in sense of finite number of asymptotic terms) coinciding with the generaUzed PrandtF solution in case of arbitrary plate roughness coefficient, is obtained. A nonapplicabUity of this asymptotic near the middle cross-section of layer is precisely shown.

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Section: The Prandtl' Problem Its Solution and Hypothesesmentioning

confidence: 99%