6533b82efe1ef96bd1293b38

RESEARCH PRODUCT

Some Optimization Problems

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In this chapter, the problems of safety analysis and optimization of a moving elastic plate travelling between two rollers at a constant axial velocity are considered. We will use a model of a thin elastic plate subjected to bending and in-plane tension (distributed membrane forces). We will study transverse buckling (divergence) of the plate and its brittle and fatigue fracture caused by fatigue crack growth under cyclic in-plane tension (loading). Our aim is to find the safe ranges of velocities of an axially moving plate analytically under the constraints of longevity and stability. In the end of this chapter, the expressions for critical buckling velocity and the number of cycles before the fracture (longevity of the plate) as a function of in-plane tension and other problem parameters are used for formulation and we will study the case as an optimization problem. Our target is to find the optimal in-plane tension to maximize the performance function of paper production. This problem is solved analytically and the obtained results are presented as formulae and numerical tables.