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1

Spira Mirabilis in the selected models of Bittner operational calculus

Wysocki H.

Zeszyty Naukowe Akademii Marynarki Wojennej

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2015

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R. 56 nr 4 (203)

65--96

EN

Parametric descriptions of spirals being analogues of the logarithmic spiral are determined using the concept of the exponential element in the non-classical Bittner operational calculus and applying the chosen models of it.

PL

Korzystając z pojęcia elementu wykładniczego w nieklasycznym rachunku operatorów Bittnera oraz stosując wybrane modele tego rachunku, wyznaczono opisy parametryczne spiral będących odpowiednikami spirali logarytmicznej.

2

Some remarks on Burzyński's failure criterion for anisotropic materials

Szeptyński P.

Engineering Transactions

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2011

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Vol. 59, iss. 2

119-136

EN

Some misstatements appearing in the final form of the failure criterion formulation, derived from Burzyński’s hypothesis of material effort for anisotropic bodies, which haven’t beennoticed in the literature as yet, are pointed out and discussed. Alternative interpretations of the results obtained by Burzyński are presented. Propositions of different formulation of the failure criterion, basing on original ideas of Burzyński, are given.

3

Model nieklasycznego rachunku operatorów Bittnera dla różnicy wstecznej

Wysocki H.

Zeszyty Naukowe Akademii Marynarki Wojennej

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2010

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R. 51 nr 2 (181)

37-48

PL

W pracy skonstruowano -model rachunku operatorów Bittnera dla różnicy wstecznej u (k) = u (k) - u (k-1) w przestrzeni ciągów dwustronnych, w którym wyprowadzono postać wzoru Taylora. Dokonano uogólnienia modelu, rozważając operację u (k) = u (k) - u (k-1).

EN

In this paper there is constructed the -model of the Bittner operational calculus for the backward difference u (k) = u (k) - u (k-1) in the space of two-sided sequences, in which a form of the Taylor’s formula is determined. Considering the operation of u (k) = u (k) - u (k-1) the -model is generalized.

4

Energy-based limit conditions for transversally isotropic solids

Kowalczyk K., Ostrowska-Maciejewska J.

Archives of Mechanics

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2002

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Vol. 54, nr 5-6

497-523

EN

Using an example of transversal isotropy, the limit condition having an energy interpretation for anisotropic bodies proposed by J. Rychlewski [11] has been illustrated. Transversal isotropy is characterized by the highest degree of symmetry, for which the spherical tensor is not any more the eigenstate of the compliance tensor C. In the case when the spectral decomposition of the compliance tensor C is taken as a main energy-orthogonal decomposition, the limit condition representing a generalization of the Maxwell-Huber-Mises condition is obtained. For a prescribed form of the limit tensor H, the Mises condition is presented in the form of a sum of elastic energies corresponding to uniquely defined energy-orthogonal parts of stress with certain weights, representing the limiting values of those energies. The effect of Burzyński's condition on the form of anisotropy and on the limit condition is discussed. Experimental tests are proposed which could be useful in determining the physical parameters describing the transversal isotropy.

5

The Gram-Schmidt Method in the Identification of a Generalized Control System

Wysocki H.

International Journal of Applied Mathematics and Computer Science

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2000

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Vol. 10, no 2

245-271

EN

This article discusses the identification of a generalized linear control system described in the Bittner operational calculus by an abstract linear differential equation with constant coefficients. The identification problem leads to that of the best approximation in the vector space l_m^2 and is solved by using the Gram-Schmidt orthonormalization method. The classical Strejc method and the Shinbrot modulating function method are generalized here.