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1
Content available Quaternions and Cauchy Classical Theory of Elasticity
Danielewski Marek, Sapa Lucjan
Advances in Manufacturing Science and Technology
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2020
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Vol. 44, nr 2
67--70
EN
Developed by French mathematician Augustin-Louis Cauchy, the classical theory of elasticity is the starting point to show the value and the physical reality of quaternions. The classical balance equations for the isotropic, elastic crystal, demonstrate the usefulness of quaternions. The family of wave equations and the diffusion equation are a straightforward consequence of the quaternion representation of the Cauchy model of the elastic solid. Using the quaternion algebra, we present the derivation of the quaternion form of the multiple wave equations. The fundamental consequences of all derived equations and relations for physics, chemistry, and future prospects are presented.
2
Meshless modelling of elastic solids
Lobovsky L, Kren J, Zemcik Z
Modelling and Optimization of Physical Systems
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2008
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z. 7
69--74
EN
The study is concerned about an application of the smoothed particle hydrodynamics (SPH) method in elastodynamics. A brief description of the SPH model for elastic materials and related stabilising terms are presented. The performance of the implemented SPH code is tested for elementary problems of linear elasticity as well as for a complex problem involving large deformations.
3
Content available remote Concentated Forces in Two-dimensional Nonlocal Elastic Solid
Povstenko J., Kubik I.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2003
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Vol. 9
81--85
4
Content available remote Duality method in limit analysis problem of non-linear elasticity
Brigadnov I. A.
Computer Assisted Mechanics and Engineering Sciences
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2003
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Vol. 10, No. 4
385-387
EN
The limit analysis problem (LAP) for estimation of mechanical durability for non-linear elastic solids is examined. The appropriate dual problem is formulated. After the standard piecewise linear continuous finite-element approximation, the dual LAP is transformed into the problem of mathematical programming with linear limitations as equalities. This finite dimensional problem is solved by the standard method of gradient projection.
5
Model zagadnienia dynamicznego kontaktu z wydzielaniem ciepła tarcia
Olesiak Z.
Zeszyty Naukowe Katedry Mechaniki Stosowanej / Politechnika Śląska
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1998
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z. 7
261--266
PL
Celem pracy jest skonstruowanie i zbadanie modelu ciała sprężystego z uwzględnieniem wydzielania ciepła tarcia , w ruchu o zmiennej prędkości. Ciało w postaci warstwy sprężystej porusza się pod działaniem siły, będącej funkcją czasu . Ciepło tarcia powoduje wzrost temperatury i przyrost objętości ciała i zaklinowywanie się między dwoma ścianami . Zmniejszenie prędkości powoduje zmniejszenie wydzielanego ciepła i ponowne zwiększeni e prędkości. Pełną wersję pracy czytelnik znajdzie w publikacj i [1] .
EN
The purpose of the paper is to construct an dinvestigate a model of an elastic solid with frictional heat generation in motion with varying velocity. The solid in the form of a layer moves between two rigid walls under the action of ateime dependent force . The frictional heat generates not onl y an increase of temperature, but also an increase of the solid volume . Then the gap between the walls and the solid decreases and in the result the motion slows down until the arrest . The full version of the paper has been discussed and presented in [1].
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