Authors D. V. Tymoshenko, G. V. Kupovykh, A. A. Ilyukhin
Month, Year 05, 2018 @en
Index UDC 531.38, 575
Abstract In this paper we present the fundamentals of the method for analyzing the geometric configurations of elastic one-dimensional objects (flexible rods) made of composite materials with a multi-layered internal structure. Interest in studying the deformation processes of rods is due to the fact that rods or objects close to them in terms of properties are constructive elements of a large number of technical systems. Examples include mobile, connecting and damping devices and structures in transport and engineering facilities. In addition, the flexible rod model finds its application in the study of the behavior and properties of biological polymers molecules and, in particular, DNA. The need to develop new and existing methods for the qualitative and numerical analysis of the dynamics of elastic elements in engineering systems is explained by the high requirements for such studies, their applied nature. At the same time, the absence of strict continuity with simultaneous complication of the hierarchy of structures for composite materials in the case of significant deformations leads to fundamental difficulties in describing these phenomena using standard methods of the theory of elasticity. The recent development of microstructural research allows one to draw conclusions about the significant influence of the structural properties of matter on the dynamics of deformation processes. Expansion of the field of composite materials application makes it necessary to intensify studies of the relationships between the mechanical properties of composites and their structure, including from the standpoint of determining stable forms of equilibrium in deformed elastic elements. The method of transition from the structural characteristics of the material to the spatial geometry of the object described in this work is illustrated by the example of the state of the rod’s natural twist. Particular attention is paid to the study of the conditions for the formation of closed configurations, since they correspond to critical cases of the systems functioning.

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Keywords Elastic rods; continuum models; composite materials.
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