A spiral model for bending of non-linearly pretwisted helicoidal structures with lateral loading |
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| Institution: | 1. Experimental Continuum Mechanics Group, IMES, ETH Zürich, Institute for Mechanical Systems, 8092 Zürich, Switzerland;2. Laboratory of Composite Materials and Adaptive Structures, Department of Mechanical and Process Engineering, ETH Zürich, Laboratory of Composite Materials and Adaptive Structures, 8092 Zurich, Switzerland;1. Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong;2. Sorbonne Universités, Université Pierre-et-Marie-Curie, Laboratoire Jacques-Louis-Lions, 75005 Paris, France;1. Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong;2. Sorbonne Université, CNRS, Laboratoire Jacques-Louis-Lions, LJLL, 75005 Paris, France;1. Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong;2. Sorbonne Université, CNRS, laboratoire Jacques-Louis-Lions, LJLL, F-75005 Paris, France;1. Lab of Information Optics and Optoelectronic Technology, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, P.O. Box 800-211, Shanghai 201800, China;2. School of Physics and Optoelectronic Engineering, Ludong University, Yantai 264025, Shandong, China |
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| Abstract: | The paper presents a new approach in the bending analysis of helicoidal structures with a large non-linear pretwist and an external lateral loading. It also addresses the issue as to what extent the linearized twisting curvature is applicable in the analysis of pretwisted plates. Employing a non-linear helicoidal model and a natural orthogonal coordinate system, the large non-linear pretwist is formulated and the energy stored in a distorted helicoid subjected to an external pressure normal to the helicoid axis is derived. By integrating the internal strain energy and external pressure work over the helicoidal domain, a non-homogeneous system of equations is presented and numerical solutions are obtained. Significant structural responses such as deformation components and resultant, the effects of width and thickness of helicoid on bending are analyzed and discussed. The analysis can be extended to other areas of interest such as turbomachinery blades, drilling structures, motors in micro-electro-mechanical systems and also DNA biomechanics. |
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