1,354,356 research outputs found
'Homotopy' of prandtl and nadai solutions
No full textIn the present paper we provide two families of exact solutions for the system of plane ideal plasticity using the concept of homotopy of two functions. These functions are the well-known exact solutions of Nadai (for the flow of plastic material through the wedge-shaped converging channel and for the plastic zone around a circular cavity) and solution of Prandtl. The analysis of the envelopes of corresponding characteristic curves permits to determine the boundaries for obtained solutions, which give the description of the stresses for the blocks and cavities of specific forms. © 2010 Elsevier Ltd. All rights reserved
Decomposing diversity patterns of a soft-bottom macroinvertebrate community in the tropical eastern Pacific
No full textThe hyperbolic system of plane ideal plasticity equations under the Saint-Venant-Mises' yield criterion is considered. Its' characteristics curves are deformed by the action of admitted group of point transformations, that permits to construct a new analytical solution. The mechanical sense of obtained characteristic fields is discussed. The general algorithm of the relation of solutions of quasilinear hyperbolic system of two homogeneous equations of two independent variables is proposed. " 2009 Elsevier Ltd. All rights reserved.",,,,,,"10.1016/j.na.2009.01.161",,,"http://hdl.handle.net/20.500.12104/40505","http://www.scopus.com/inward/record.url?eid=2-s2.0-72149121546&partnerID=40&md5=8de203f29b83be3231bd87d42e928ab6",,,,,,"12",,"Nonlinear Analysis, Theory, Methods and Applications",,"e127
Deformation of characteristic curves of the plane ideal plasticity equations by point symmetries
No full textThe hyperbolic system of plane ideal plasticity equations under the Saint-Venant-Mises' yield criterion is considered. Its' characteristics curves are deformed by the action of admitted group of point transformations, that permits to construct a new analytical solution. The mechanical sense of obtained characteristic fields is discussed. The general algorithm of the relation of solutions of quasilinear hyperbolic system of two homogeneous equations of two independent variables is proposed. © 2009 Elsevier Ltd. All rights reserved
Some symmetry group aspects of a perfect plane plasticity system
No full textIn this paper, all the known classical solutions of a plane perfect plasticity system under the Saint Venant-Tresca-von Mises yield criterion are associated with some group of point symmetries. The equations of slip-line families for all solutions are constructed, which allows one to explicitly determine the boundaries of the plastic areas. It is shown how one can determine the compatible velocity solution for known stresses by considering symmetries. Some invariant solutions of velocities for Prandtl stresses are constructed. The mechanical sense of the obtained velocity fields is discussed. To the blessed memory of our teacher D D Ivlev © 2013 IOP Publishing Ltd
Conservation Laws, Hodograph Transformation and Boundary Value Problems of Plane Plasticity
No full textFor the hyperbolic system of quasilinear first-order partial differential equations, linearizable by hodograph transformation, the conservation laws are used to solve the Cauchy problem. The equivalence of the initial problem for quasilinear system and the problem for conservation laws system permits to construct the characteristic lines in domains, where Jacobian of hodograph transformations is equal to zero. Moreover, the conservation laws give all solutions of the linearized system. Some examples from the gas dynamics and theory of plasticity are considered
Lie - Backlund symmetries of homogeneous system of bi-dimensional equations
No full textThe framework of generalized (Lie-Backlund) symmetries is used to analyze a general homogeneous hyperbolic system of bi-dimensional quasilinear equations. The symmetries of the first order are constructed and the theorem of the existence of the generalized symmetries is formulated. As example, we consider the spatially one-dimensional time dependent system of equations, which describes the gravity-driven free surface flow of granular avalanches
Lie - Backlund symmetries of homogeneous system of bi-dimensional equations
No full textThe framework of generalized (Lie-Backlund) symmetries is used to analyze a general homogeneous hyperbolic system of bi-dimensional quasilinear equations. The symmetries of the first order are constructed and the theorem of the existence of the generalized symmetries is formulated. As example, we consider the spatially one-dimensional time dependent system of equations, which describes the gravity-driven free surface flow of granular avalanches
Reproduction of solutions of bidimensional ideal plasticity
No full textThe symmetries of a system of differential equations allowed the transformation of its solutions to a solution of this system. New analytical exact solutions of a system of two-dimensional ideal plasticity equations were constructed from two well-known solutions, that for a circular cavity stressed by normal pressure, and Prandtl's solution for a block compressed between perfectly rough plates, for the case where the thickness of the block was rather small. A mechanical sense of new solutions was discussed. � 2007 Elsevier Ltd. All rights reserved
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