Аналітичне моделювання зосереджених та локалізованих навантажень брусів із криво-лінійною плоскою віссю. Частина 1. Моделювання зосереджених у точці навантажень

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dc.contributor.authorКовальчук, Станіслав Богданович
dc.contributor.authorГорик, Олексій Володимирович
dc.date.accessioned2019-02-20T14:50:46Z
dc.date.available2019-02-20T14:50:46Z
dc.date.issued2018-12
dc.description.abstractIn applied mechanics, the common types of load are concentrated force, moment, and also distributed load localized in a certain part of the beam. An effective approach to the analytical modeling of such loads is the use of generalized functions, with the help of which it is possible to avoid considering the many design sections of the beam, within which the load is a continuous function. However, in well-known scientific papers, this approach is developed only for rectilinear rods and partially for circular ones. This paper is devoted to the problem of modeling concentrated loads (force, moment) and loads localized on a surface for bars with a curvilinear plane axis of arbitrary shape in a natural coordinate system. In the first part, the mathematical substantiation of analytical modeling of forces and moments concentrated at a point of a longitudinal cylindrical or end surface of a curvilinear bar in a natural curvilinear coordinate system is illuminated. By limiting the transition from a statically equivalent local load to the boundary case of a load concentrated at a point on the surface of the beam, using the elements of the theory of generalized functions, we obtained general analytical relations for modeling the concentrated force. On the basis of the ratio obtained, by passing to the limit for a pair of concentrated forces as the pair’s arm tends to zero, a mathematical rationale for analytical modeling of the concentrated moment is constructed. The relations obtained are of a general nature and are invariant with respect to the coordinate system under consideration. Based on them, a number of relations have been obtained for modeling concentrated loads in individual cases of circular, elliptical and parabolic bars in natural coordinate systems. The results obtained can be used to solve a wide range of applied problems of deforming curvilinear bars.uk_UA
dc.identifier.issn2415-377Х
dc.identifier.urihttps://dspace.pdau.edu.ua/handle/123456789/2988
dc.language.isouk_UAuk_UA
dc.publisherОдеська державна академія будівництва та архітектуриuk_UA
dc.relation.ispartofseriesВісник Одеської державної академії будівництва та архітектури;Випус 73
dc.subjectкриволінійний брусuk_UA
dc.subjectзосереджена силаuk_UA
dc.subjectзосереджений моментuk_UA
dc.subjectприродна система координатuk_UA
dc.subjectузагальнена функціяuk_UA
dc.subjectкриволинейный брусuk_UA
dc.subjectсосредоточенная силаuk_UA
dc.subjectсосредоточенный моментuk_UA
dc.subjectестественная система координатuk_UA
dc.subjectобобщенная функцияuk_UA
dc.subjectcurvilinear baruk_UA
dc.subjectconcentrated forceuk_UA
dc.subjectconcentrated momentuk_UA
dc.subjectlocal loaduk_UA
dc.subjectnatural coordinate systemuk_UA
dc.subjectgeneralized functionuk_UA
dc.titleАналітичне моделювання зосереджених та локалізованих навантажень брусів із криво-лінійною плоскою віссю. Частина 1. Моделювання зосереджених у точці навантаженьuk_UA
dc.title.alternativeAnalytical modeling of concentrated and localized loads of bars with a curvilinear flat axis. Part 1. Modeling of concentrated loadsuk_UA
dc.title.alternativeАналитическое моделирование сосредоточенных и локализованных нагрузок брусьев с криволинейной плоской осью. Часть 1. Моделирование сосредоточенных нагрузокuk_UA
dc.typeArticleuk_UA
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