Milan Batista

Integrability of the motion of a rolling disk of finite thickness on a rough plane

Abstract In this article an analytical solution of equations of motion of a rigid disk of finite thickness rolling on its edge on a perfectly rough horizontal plane under the action of gravity is given. The solution is given in terms of Gauss hypergeometric functions. The integrability results are used to construct various bifurcation diagrams of the steady motion of the disk. The bifurcations of the steady motion of a disk on a rough plane complements the authors bifurcation analysis of the steady motion of the disk on a smooth plane ( [M. Batista, Steady motion of a rigid disk of finite thickness on a horizontal plane, Int. J. Non-Linear Mech. 41 (4) (2006) 605–621]).

Steady Motion of a Rigid Disk of Finite Thickness on a Horizontal Plane

Abstract The article discusses the steady motion of a rigid disk of finite thickness rolling on its edge on a horizontal plane under the influence of gravity. The governing equations are presented and two cases allowing for a steady-state solution are considered: rolling on consistently rough ground and rolling on perfectly smooth ground. The conditions of steady motion are derived for both kinds of ground and it is shown that the possible steady motion of a disk is either on a straight line or in a circle. Oscillations about steady state are discussed and conditions for stable motion established. The bifurcations of steady motions on a smooth surface are also considered.

Large deflections of a beam subject to three-point bending

Abstract In this paper, a solution for the equilibrium configuration of an elastic beam subject to three-point bending is given in terms of Jacobi elliptical functions. General equations are derived, and the domain of the solution is established. Several examples that illustrate a use of the solution are discussed. The obtained numerical results are compared with the results of other authors. An approximation formula by which the beam load is given as a polynomial function of beam deflection is also derived. The range of applicability of the approximation is illustrated by numerical examples.

A cyclic block-tridiagonal solver

A simple algorithm for solving a cyclic block-tridiagonal system of equations is presented. Introducing a special form of a new variable, the system is split into two block-tridiagonal systems, which can be solved by known methods. Implementation details of the algorithm are discussed and numerical examples of diagonal and random generated systems are presented.

The use of the Sherman-Morrison-Woodbury formula to solve cyclic block tri-diagonal and cyclic block penta-diagonal linear systems of equations

The article presents a new theoretical viewpoint of Batistas algorithms for solving cyclic tri-diagonal (and penta-diagonal) linear systems. The theory is based on the Sherman-Morrison-Woodbury formula.

New analytical solution for bending problem of uniformly loaded rectangular plate supported on corner points

Presented herein is a new analytical solution for the bending problem of a uniformly loaded, thin rectangular elastic plate supported on corner points. The solution is given in the form of a trigonometric series where the coefficients of the series form a fully regular infinite system of linear equations. Accurate numerical values for deflection, moments and shear forces for various aspect ratios of the plate are given. The results are compared with those obtained by other researchers.

Identifying the key risk factors of traffic accident injury severity on Slovenian roads using a non-parametric classification tree

AbstractFrom both a practical and economic point of view, road transport meets almost all the requirements of modern life, but it is also a source of numerous negative effects, including traffic accidents. In order to design a safe transport system and achieve the ‘zero vision’ goal – no serious injuries or fatalities in traffic accidents – there is a growing need for a systematic approach to this problem. Prior to the assessment of any accident prevention measure it is necessary to identify the most important factors and significant patterns which affect the severity of accidents and injuries. In this study, the crash data from Slovenia pertaining to the period 2005–2009 were analysed with a Classification and Regression Tree (CART) algorithm, one of the most widely applied data mining technique when analysing a large amount of data with several independent quantitative or qualitative variables. Before building a non-parametric classification tree, the data were split into three totally separate subsets,...

Measurement and numerical analysis of surface residual stresses occurring under different quenching conditions

The paper presents the results of residual stresses modelling and experimental stress measurements after quenching of AISI 4140 heat-treatment steel specimens. In the research, cylindrical specimens of ? 40 ? 160 mm in size were used whereas in modelling specimens of the same diameter, i.e., ? 40 mm, but of infinite length were employed. One quenching agent was selected, i.e., a 15% polymer water solution. The influence of residual stresses due to martensitic transformation and temperature differences was investigated with different initial specimen temperatures above and under TAC1. Two different temperatures were chosen in order to reveal the nature and quantitative properties of temperature- and transformational-induced residual stresses. Analytical work was made by mathematical modelling of heat treatment which supposes that the rheological model of a continuum is thermo-elasto-plastic material. Austenitic-martensitic transformations are described with Koistinen-Marburger equation. Related experimenta...

Quantum cards and quantum rods

Quantum mechanical analysis of a rigid rod with one end fixed to a flat table is presented. Assuming that the rod is initally in the upright orientation, “the time of fall” is calculated using WKB wavefunctions representing energy eigenstates near the barrier summit.

A closed-form solution for Reissner planar finite-strain beam using Jacobi elliptic functions

Abstract In the paper, we introduce an analytical solution for a large-deflection, finite-strain, and planar Reissner beam that is subject to an end force and a bending moment. The solution is provided in terms of Jacobi elliptic functions. The obtained analytical solution is enhanced with numerical examples. The buckling and post-buckling behavior of a beam under an axial compressive load applied at its end and subject to various boundary conditions is also discussed in detail. In particular, the buckling factor is derived for all boundary conditions.