Structural Optimization of a Longitudinally Moving Layered Web Based on a Multi-Criteria Approach

The longitudinal motion at a constant speed of a thin continuous elastic web through a system of roller bearings under the action of a given constant tension is considered. One span between adjacent supports is considered. The web is modeled by a thin layered plate hinged on two opposite edges, the remaining two sides of the plate are free. It is assumed that the plate in the process of longitudinal movement can perform small transverse vibrations. The layers of the plate from a given set of materials are arranged symmetrically to the middle surface and fit tightly to each other. The total thickness of all layers is given and is small compared to the span length and plate width. Analytical expressions are derived for the effective characteristics of the plate, as a result of which the initial composite structure can be considered as an isotropic homogeneous plate, for which the known equations for calculating the critical velocity are applied. Within the framework of multi-criteria Pareto optimization, using a numerical method of non-local optimization, the order of the layers and their thickness are determined in order to satisfy a number of selected criteria: the maximum critical divergence rate, the maximum flexural stiffness, and the minimum unit weight of the layered web. An example of the found optimal structure of the plate and the constructed Pareto front for a given set of defining parameters of the problem are given.