Hierarchic Large Rotation Shell Model with Warping: Isogeometric Formulation and Modeling of Alternating Stiff/Soft Laminates

Abstract

This paper presents a hierarchic large rotation Kirchho-Love shell model with warping. Two unknowns are introduced for each through-the-thickness function warping, rep resenting its amplitudes in two directions tangent to the shell surface. NURBS are used to approximate reference surface displacement and warping amplitudes in the weak form. The transverse shear strains depend only on the warping parameters linearly and are free from lock ing. A patch-wise reduced integration avoids membrane locking and improves e ciency. Focus is given to composites made up of multiple sti layers coupled with soft interlayers. The alternat ing layup with high sti ness ratios induces a signi cant sectional warping with transverse shear strains concentrated in the soft layers. Two warping models are investigated: WI) all sti layers maintain the same director orthogonal to the deformed surface with independent transverse shear deformations of the soft layers; WZ) a single zigzag function linking these deformations. The numerical tests con rm the great accuracy of the hierarchic shell model in reproducing the solid solution with a small number of discrete parameters, provided that the correct warping model is chosen. WI is reliable for all alternating layups. WZ reduces the unknowns to ve per surface point, regardless of the number of layers, and is accurate for uniform soft layers

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