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History variational calculus
Höschl, Cyril
This paper present a short historical overview of evolution of infinitesimal and variotional calculus.Some of the classical variational problems ara formulated and described.
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Pitfalls in nonlinear elasticity
Höschl, Cyril
Assumed linear dependence of 2nd Piola-Kirchhoff stress tensor on Green-Lagrange strain tensor leads to a paradox even in simplest case of one-dimonsional compression. Such an extension of Hooke´s law to nonlinear elasticity is therefore dubious. The behavior of rubber and the theory of pure shear based on linear dependence of energetically conjugate Cauchy stress on logarithmic strain is shortly discussed, with the aim to avoid possible misunderstanding.
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Study of mechanics as a search for interrelations
Höschl, Cyril
Author presents examples of analogous problems from various fields of mechanics of elastic solids which are solved using an identical mathematical model. Paper deals also with discrepancies between solutions obteined either by analytical or numerical methods. By the use of functional analysis, an interrelation is found between methods of solution of discrete and continuum models. The limitations of the linear theory of elsticity are discussed.
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Loosening of press - fitted pivots
Dobiáš, Jiří ; Höschl, Cyril
If a press-fitted clamped-free pivot is exposed to alternating loading at its free end while the forces act normal to its central axis, a gradual global displacement of the pivot in the axial direction may occur under some circumstances.
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