The study of natural fiber–based composites, which are being seen as a potential eco‐friendly alternative to popular synthetic fiber–reinforced composites, has, of late, gained considerable momentum. Replacing the latter composites is, however, an uphill task especially for advanced mechanical and structural engineering applications, which often require assessment of behaviors of materials and components numerically till failure. An implied scenario, for example, would be to design automotive body components using natural fiber–reinforced composites of sufficient strength for meeting crashworthiness requirements. In the current study, bi‐directionally woven jute fabric, due to its established supply base and consistent quality, has been chosen along with a general purpose polyester resin for fabrication of laminates of high fiber volume fraction obtained by combining the hand layup method with compression molding. A detailed and comprehensive mechanical characterization includes, for the first time, determination of tensile, compressive, shear, and flexural behaviors of jute–polyester laminates in a single unified study. The consistency of the generated mechanical properties, including deployment of secant moduli instead of conventional initial tangent moduli, in a finite element constitutive model is established by predicting the test‐based stress–strain or load–displacement behaviors and failure modes using a commercially available explicit nonlinear dynamic analysis code viz. LS‐DYNA.
The goal of this paper is to compute the generating series of a closed-loop system when the plant is described in terms of a Chen-Fliess series and an additive static output feedback is applied. The first step is to consider the so called Wiener-Fliess connection consisting of a Chen-Fliess series followed by a memoryless function. Of particular importance will be the contractive nature of this map, which is needed to show that the closed-loop system has a Chen-Fliess series representation. To explicitly compute the generating series, two Hopf algebras are needed, the existing output feedback Hopf algebra used to describe dynamic output feedback, and the Hopf algebra of the shuffle group. These two combinatorial structures are combined to compute what will be called the Wiener-Fliess feedback product. It will be shown that this product has a natural interpretation as a transformation group acting on the plant and preserves the relative degree of the plant. The convergence of the Wiener-Fliess composition product and the additive static feedback product are completely characterized.
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