Studies on large deflection of geometrically nonlinear corrugated structures
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O R I G I NA L PA P E R
Deepak Kumar · Shaikh Faruque Ali · A. Arockiarajan
Studies on large deflection of geometrically nonlinear corrugated structures
Received: 12 January 2020 / Revised: 2 August 2020 / Accepted: 15 October 2020 © Springer-Verlag GmbH Austria, part of Springer Nature 2020
Abstract This manuscript proposes an iterative scheme for geometrically large deflection analysis of corrugated structures using the nonlinear shooting method. The corrugated structure is modeled by discretizing it in several corrugated units. The solution of each unit is obtained assuming it to be consistering of several beam elements. Finally, the deflection of a corrugated structure is calculated assembling the deflection of each of the corrugated units. The formulation has been extended to various boundary conditions (fixed–fixed and fixed–hinged) and loading conditions (point loads and uniformly distributed load). This shows the versatility of the methods in solving various problems. Furthermore, two prototypes of the corrugated structure are fabricated using aluminum and carbon fiber reinforced polymer (CFRP) laminate, and a moment actuation test is performed. The deflections of these prototypes obtained using the proposed iterative scheme are compared with the numerical model and validated with experiments, and results are found to be in good agreement.
1 Introduction The term “corrugation” generally refers to a sequence of parallel crests and troughs. In engineering applications, any structure that has a corrugated surface, made either by folding, molding, or any other method of manufacturing, is called a corrugated structure [1]. The main feature of a corrugated structure is its anisotropic behavior, which means that it has relatively high stiffness along the corrugation direction and is compliant in the other directions that are perpendicular to the corrugation (see Fig. 1). Due to this property, these structures are widely used in industrial applications such as beams with corrugated web, corrugated roofs, corrugated pipes, corrugated boards, etc. [1]. Lately, corrugated structures are also used for advanced technological applications like morphing wings, marine structures and pyramidal lattice truss sandwich structures [2–4]. In recent years, studies on morphing wings have gained substantial attention, leading to research on corrugation for the potential applications as morphing structures [5–10]. As an essential requirement of the morphing wing, it should undergo large deflection in the chord direction and should be stiffer in the span direction [11]. Due to the low mass-to-stiffness (along corrugations) ratio, large deformations are possible along the chord direction with small actuation forces, while the out of plane stiffness can be large enough to carry aerodynamic loads. D. Kumar · S. F. Ali · A. Arockiarajan (B) Department of Applied Mechanics, Indian Institute of Technology Madras, Chennai 600 036, India E-mail: [email protected] D. Kumar E-mail: [email protected] S. F. Ali E-mail: [email protected]
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