Showing papers in "Applications of Mathematics in 1982"
TL;DR: In this article, the tetrahedral stress element is introduced and two different types of finite piecewise linear approximation of the dual elasticity problem are investigated on a polyhedral domain Fot both types a priori error estimates $O(h^2)$ in $L_2$-norm and O(h^{1/2})$ in O(L_\infty$)-norm are established, provided the solution is smooth enough
Abstract: The tetrahedral stress element is introduced and two different types of a finite piecewise linear approximation of the dual elasticity problem are investigated on a polyhedral domain Fot both types a priori error estimates $O(h^2)$ in $L_2$-norm and $O(h^{1/2})$ in $L_\infty$-norm are established, provided the solution is smooth enough These estimates are based on the fact that for any polyhedron there exists a strongly regular family of decomprositions into tetrahedra, which is proved in the paper, too
35 citations
TL;DR: In this paper, the homogenization problem for linear elasticity equation is studied in terms of displacements and stresses and the results compared with the results obtained by the multiple-scale method, and the convergence of displacment vector, stress tensor and local energy is proved by a simplified local energy method.
Abstract: The homogenization problem (i.e. the approximation of the material with periodic structure by a homogeneous one) for linear elasticity equation is studied. Both formulations in terms of displacements and in terms of stresses are considered and the results compared. The homogenized equations are derived by the multiple-scale method. Various formulae, properties of the homogenized coefficients and correctors are introduced. The convergence of displacment vector, stress tensor and local energy is proved by a simplified local energy method.
25 citations
TL;DR: In this paper, the Haar-Karman principle is extended to the case of a unilateral contact between two bodies without friction, and approximate approximations are proposed by means of piecewise constant triangular finite elements.
Abstract: If the material of the bodies is elastic perfectly plastic, obeying the Hencky's law, the formulation in terms of stresses is more suitable than that in displacements. The Haar-Karman principle is first extended to the case of a unilateral contact between two bodies without friction. Approximations are proposed by means of piecewise constant triangular finite elements. Convergence of the method is proved for any regular family of triangulations.
19 citations
TL;DR: In this paper, convergence and rate-of-convergence results are established for two well-known quadrature rules for numerical evaluation of Cauchy type principal value integrals along a finite interval.
Abstract: New convergence and rate-of-convergence results are established for two well-known quadrature rules for the numerical evaluation of Cauchy type principal value integrals along a finite interval, namely the Gauss quadrature rule and a similar interpolatory quadrature rule where the same nodes as in the Gauss rule are used. The main result concerns the convergence of the interpolatory rule for functions satisfying the Holder condition with exponent less or equal to $\frac12$. The results obtained here supplement a series of previous results on the convergence of the aforementioned quadrature rules.
15 citations
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TL;DR: In this article, the adaptive Runge-Kutta method with rational coefficients is presented. But the adaptive R. K. method is not a generalization of the R.K. formula.
Abstract: In the article containing the algorithm of explicit generalized Runge-Kutta formulas of arbitrary order with rational parameters two problems occuring in the solution of ordinary differential equaitions are investigated, namely the determination of rational coefficients and the derivation of the adaptive Runge-Kutta method. By introducing suitable substitutions into the nonlinear system of condition equations one obtains a system of linear equations, which has rational roots. The introduction of suitable symbols enables the authors to generalize the Runge-Kutta formulas. The starting point for the construction of adaptive R. K. method was the consistent $s$-stage R. K. formula. Finally, the S-stability of the ARK method is investigated.
3 citations
TL;DR: A non-Markovian queueing system with Poisson input is studied under a modified operating rule called "control operating policy" in which the server begins "start-up" only when the queue length reaches a fixed number.
Abstract: A non-Markovian queueing system with Poisson input is studied under a modified operating rule called "control operating policy" in which the server begins "start-up" only when the queue length reaches a fixed number $n(\geq 1)$. By using the supplementary variable technique, the distribution of the queue length (excluding those being served) in the form of a generating function is obtained. As a special case, a Markovian queueing system with exponential start-up is discussed in detail to analyse the economic behaviour of the system.
TL;DR: In this paper, a system of definitions and theorems for fuzzy sets is introduced, aimed at an adequate expression of the point of view of the objective property of fuzzy sets.
Abstract: Fuzzy sets establish a mapping from the interval of values of a criterial function onto a system of subsets of a basic set. In the paper, a system of definitions and theorems is introduced, which is aimed at an adequate expression of this point of view. The criterial function, with an arbitrary interval of values, serves for expressing the really existing objective property, forming the basis for defining a fuzzy set.