Isogeometric sizing and shape optimization of thin structures with a solid-shell approach

Abstract

This work explores the use of solid-shell elements in the the framework of isogeometric shape optimization of shells. The main difference of these elements with respect to pure shell ones is their volumetric nature which can provide recognized benefits to analyze, for example, structures with non-linear behaviors. From the design point of view, we show that this geometric representation of the thickness is also of great interest since it offers new possibilities: continuous sizing variations can be imposed by modifying the distance between the control points of the outer surfaces. In other words, shape and sizing optimization can be performed in an identical manner. Firstly, we carry out a range of numerical experiments in order to carefully compare the results with the commonly adopted technique based on the Kirchhoff-Love formulation. These studies reveal that both solid-shell and Kirchhoff-Love strategies lead to very similar optimal shapes. Then we apply a bi-step strategy to integrate shape and sizing optimization. We highlight the potential of the proposed approach on a stiffened cylinder where the cross-section along the stiffener is optimized leading to a final design with smooth thickness variations. Finally, we combine the benefits of both Kirchhoff-Love and solid-shell formulations by setting up a multi-model optimization process to efficiently design a roof.

Noninvasive multilevel geometric regularization of mesh‐based three‐dimensional shape measurement

“…In this paper, we developed a hybrid IG‐FE strategy for the regularization of the mesh‐based shape measurement occurring in FE‐SDIC. From a regularization point of view, the proposed strategy draws inspiration from the techniques developed recently in the IG shape optimization community, especially with the multilevel design concept . By making use of the advanced spline refinement procedures and of adequate Bézier‐based operators, the main idea here was to extract, from the initial FE subspace, smoother multilevel spline parametrizations of the geometry and to relate them with the multiscale images used for the initialization of shape measurement.…”

“…We notice that spline functions have already been successfully used in DIC given their high degree of regularity (eg, References ). In the context of shape measurement, their interest is expected to be even more important since these functions are particularly adapted to optimize free‐form surfaces …”

“…To answer this issue, one way to naturally proceed is to use the isogeometric analysis (IGA) framework which enables to discretize the structure with its intrinsic, spline‐based, CAD geometric definition. Isogeometric (IG) shape optimization has thus been successfully applied to a wide range of applications (see References among others). More precisely, it is based on a multilevel design concept offered by the spline technology in which one can refine the geometry without altering its initial shape and regularity .…”

An isogeometric numerical study of partially and fully implicit schemes for transient adjoint shape sensitivity analysis

“…[34][35][36][37]), shells (e.g., in Refs. [38,39]) and general curved structures (e.g., in Refs. [40][41][42][43][44][45]).…”

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

“…Thus, shape optimization is a great application of IsoGeometric Analysis since the latter integrates Computer-Aided Design and analysis [1,2]. As a result, isogeometric analysis optimization is an active research topic and it has been successfully applied in solid mechanics; see for example Wall et al [3], Qian [4], Nagy et al [5,6,7], Kiendl et al [8], Taheri and Hassani [9], Wang and Turteltaub [10], Fußeder et al [11], Kang and Youn [12], Lian et al [13], Wang et al [14], Choi and Cho [15], Lei et al [16], Hirschler et al [17], Ding et al [18], Weeger et al [19]. A general procedure, which has been improved over the years [20], is commonly adopted.…”