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Mesh independent analysis of shell‐like structures

Mesh independent analysis is motivated by the desire to use accurate geometric models represented as equations rather than approximated by a mesh. The trial and test functions are approximated or interpolated on a background mesh that is independent of the geometry. This background mesh is easy to generate because it does not have to conform to the geometry. Essential boundary conditions can be applied using the implicit boundary method where the trial and test functions are constructed utilizing approximate step functions such that the boundary conditions are guaranteed to be satisfied. This approach has been demonstrated for two‐dimensional (2D) and three‐dimensional (3D) structural analysis and is extended in this paper to model shell‐like structures. The background mesh consists of 3D elements that use uniform B‐spline approximations, and the shell geometry is assumed to be defined as parametric surfaces to allow arbitrarily complex shell‐like structures to be modeled. Several benchmark problems are used to study the validity of these 3D B‐spline shell elements. Copyright © 2012 John Wiley & Sons, Ltd.