Structural geometric model of associated sets of curves

   The paper is devoted to an iterative algorithm for constructing a one-parameter family of sets of mutually connected curves. Mutual connection means existence some one-to-one and continuous correspondence between the points of the curves. Each set of curves in the family satisfies its own set of boundary conditions that leave one parameter free for each curve of the set. This parameter allows us to organize an iterative process of approaching for each curve to the set of boundary conditions set for it. A special case of the described approach is considered in detail. The structural geometric model for predicting the shape of three-layer fabric package is proposed. Deformation of the package occurs through the action of an external force. The structural geometric model of normal cross-sectional image of such package is a one-parameter family of interconnected parabolas of higher degrees. Only one free parameter is connected functionally with the total stiffness of the package. The total stiffness of the package and its function can only be determined experimentally. In the paper, we consider this function as a linear one. One of the conditions for constructing one-parameter family is constancy of the lengths of arcs of mutually connected curves. Proposed approach may be applied to solving a number of theoretical and applied problems of engineering geometry in the field of designing multilayer fabric packages.

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