Analysis of Laminated and Sandwich Composite Structures Using Solid-like Shell Elements
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Analysis of Laminated and Sandwich Composite Structures Using Solid-like Shell Elements Y. W. Kwon
Published online: 17 June 2012 # Springer Science+Business Media B.V. (outside the USA) 2012
Abstract A new solid-like shell element was formulated which is suitable for analysis of laminated and sandwich composite structures. Then, a multiscale analysis technique was implemented to the shell element formulation so that micro-level stresses and strains (i.e. stresses and strains in reinforcing fibers and the binding matrix) in those structures can be computed. The shell element has three displacement degrees of freedom per node like a 3-D solid element. Therefore, the shell elements can be stacked easily on top of one another like 3-D solid elements in order to represent multiple layers through the thickness of laminated and sandwich structures. The effect of a thin resin or adhesive layer in laminated and sandwich composite structures was investigated on both static and the dynamic responses of the structures using the developed shell elements. The study showed an apparent effect of the resin/adhesive layer even though it is very thin. As a result, the present shell element can be used effectively to include those thin layers in finite element analysis models of laminated and sandwich composite structures. Keywords Solid-like shell element . Laminated and sandwich composite . Adhesive layer . Resin layer . Multiscale analysis 1 Introduction Plates and shells support transverse loads effectively through fiber directional stresses. As a result, the finite element analysis method has been applied to the design and analysis of plates and shell structures. Initially, plate/shell finite elements were developed based on their classical theories [1–3]. However, the rigorous relationship between the transverse displacement and slopes was not easy to be satisfied at the interfaces of the finite elements. As a result, the relationship was relaxed by introducing the transverse shear energy as included in the Resissner-Mindlin theory [4, 5]. One of
Y. W. Kwon (*) Department of Mechanical & Aerospace Engineering, Naval Postgraduate School, Monterey, CA 93943, USA e-mail: [email protected]
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Appl Compos Mater (2013) 20:355–373
the drawbacks of the latter formulation was so called “shear locking”. As the plate/shell thickness becomes smaller, the shear energy begins to dominate over the bending energy, which should be the opposite in physics. In order to overcome the problem, many different techniques have been developed and proposed [6, 7]. Furthermore, the shell element formulations were started from the 3-D solid geometry by reducing the thickness dimension and assuming the inplane displacements vary linearly through the thickness direction [8–11]. This was achieved by introducing the inplane displacements at a reference plate/shell plane (mostly at the midplane along the thickness) and rotations (or called slopes) of the reference plane. Naturally, the plate/shell elements have both displacements and rotations as nodal degre
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