The embedded isogeometric Kirchhoff–Love shell: From design to shape optimization of non-conforming stiffened multipatch structures

Abstract

Isogeometric shape optimization uses a unique model for the geometric description and for the analysis. The benefits are multiple: in particular, it avoids tedious procedures related to mesh updates. However, although the analysis of complex multipatch structures now becomes tractable with advanced numerical tools, isogeometric shape optimization has not yet been proven to be applicable for designing such structures. Based on the initial concept of integrating design and analysis, we develop a new approach that deals with the shape optimization of non-conforming multipatch structures. The model is built by employing the Free-Form Deformation principle. Introducing NURBS composition drastically simplifies the imposition of the shape updates in case of a non-conforming multipatch configuration. In the case of stiffened structures, the use of embedded surfaces enables to tackle the geometric constraint of connecting interfaces between the panel and the stiffeners during shape modifications. For the analysis, we introduce the embedded Kirchhoff–Love shell formulation. The NURBS composition defines the geometry of the shell while the displacement field is approximated using the same spline functions as for the embedded surface. We also formulate a new mortar method to couple non-conforming Kirchhoff–Love shells which intersect with any angle. We apply the developed method on different examples to demonstrate its efficiency and its potential to optimize complex industrial structures in a smooth manner.