Analytical modeling of concentrated and localized loads of bars with a curvilinear plain axis. Part i. Modeling of concentrated load
Journal Title: Вісник Одеської державної академії будівництва та архітектури - Year 2018, Vol 1, Issue 73
Abstract
In applied mechanics, the common types of load are concentrated force, moment, and also distributed load localized in a certain part of the bar. 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 variety of gage sections of the bar, within which the load is a continuous function. However, in well-known scientific papers, this approach is developed only for rectilinear bars and partially for circular ones. This paper is devoted to the problem of modeling of concentrated (force, moment) and localized loads for bars with a curvilinear plain axis of an arbitrary shape in the natural coordinate system. The first part of the work deals with the mathematical background of analytical modeling of forces and moments concentrated at a point of a longitudinal cylindrical or end surface of a curvilinear bar in the natural curvilinear coordinate system. General analytical relations for modeling of concentrated force on longitudinal surfaces and ends of a curvilinear bar were obtained by limiting transition from a statically equivalent localized load to the boundary case of the load concentrated at a point using the elements of the theory of generalized functions. The mathematical background of the analytical modeling of concentrated moment has been developed on the basis of the relation for modeling of normal force by limiting transition for a couple of concentrated forces as the arm of couple tends to zero. The obtained relations are of a general nature and invariant to the coordinate system under consideration. Based on them, a number of relations have been obtained for modeling of concentrated loads in individual cases of circular, elliptical and parabolic bars in natural coordinate systems. The obtained results can be used to solve a wide range of applied problems of deformation of curvilinear bars.
Authors and Affiliations
S. , Kovalchuk, O. , Goryk
Keywords
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