Mechanics |
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2005, No. 3
Y.N. Radayev
ĐThe problem of determining independent variables for the system of partial differential equations of axially-symmetric perfect plasticity in order to obtain its simplest Cauchy’s normal form is considered. The system is originally represented by the isostatic co-ordinate net and belongs to a strongly non-linear type. The principle of maximum simplicity of Cauchy’s normal form is formulated and is shown be appropriate for the classification technique. By the aid of this principle the pair of independent variables whereby the original system can be transformed into its simplest normal form is obtained. The principle is shown be stronger than the t-hyperbolic condition. The original system is found belong to t-hyperbolic type with respect to the both isostatic co-ordinates thus allowing to correctly formulate the Cauchy problems on the both isostatic lines ensuring the existence, uniqueness and stability of the solutions.
Y.N. Radayev, V.A. Gudkov
ON t-HYPERBOLIC PROPERTY OF THREE-DIMENSIONAL EQUATIONS OF PERFECT PLASTICITY
The problem of transformation of three-dimensional equations of the perfect plasticity into their simplest Cauchy’s normal form by changing independent variables is considered. The original system of partial differential equations is represented by isostatic co-ordinates and appears as essentially non-linear. The maximum simplicity principle for Cauchy’s normal forms is formulated whereby the independent variables which afford one of the simplest normal forms for 3-dimensional equations of the perfect plasticity are found. The principle is shown be stronger than the t-hyperbolic condition. The original system is found belong to t-hyperbolic type with respect to the third canonical isostatic co-ordinate thus allowing to correctly formulate the Cauchy problems on layers normal to directions of the maximum (or minimum) principal stresses ensuring the existence, uniqueness and stability of the solutions.
Y.I. Rudaev, D.A. Kitaeva
KINETIC EQUATIONS FOR A DYNAMIC SUPERPLASTICITY MODEL
A problem of formulating kinetic equations in the framework of model suitable for the description of materials deformation in wide temperatures and rates of deformation ranges (including interval of superplasticity) is considered.
V.S. Feoktistov
Computational techniques for stress distribution in cylindrical solids under thermo-elastic martensitic phase transition are proposed in the case of arbitrary thermo-elastic response. Applicability of the mentioned techniques to establish steady-state conditions for a power-drive made of a shape memory alloy is demonstrated by examples of highly effective small equipment and instruments.