Shape optimization of non-matching isogeometric shells with moving intersections

TL;DR

This paper introduces a shape optimization method for non-matching isogeometric shells with moving intersections, enabling flexible design adjustments while maintaining NURBS geometry, suitable for complex CAD models like aircraft wings.

Contribution

It develops a novel optimization approach that allows shell patches to move independently with intersection adjustments, using an implicit state function and analytical sensitivities.

Findings

Effective handling of large intersection movements in shell optimization.

Maintains NURBS geometry throughout optimization iterations.

Demonstrated applicability to aircraft wing stiffener design.

Abstract

While shape optimization using isogeometric shells exhibits appealing features by integrating design geometries and analysis models, challenges arise when addressing computer-aided design (CAD) geometries comprised of multiple non-uniform rational B-splines (NURBS) patches, which are common in practice. The intractability stems from surface intersections within these CAD models. In this paper, we develop an approach for shape optimization of non-matching isogeometric shells incorporating intersection movement. Separately parametrized NURBS surfaces are modeled using Kirchhoff--Love shell theory and coupled using a penalty-based formulation. The optimization scheme allows shell patches to move without preserving relative location with other members during the shape optimization. This flexibility is achieved through an implicit state function, and analytical sensitivities are derived for the relative movement of shell patches. The introduction of differentiable intersections expands the design space and overcomes challenges associated with large mesh distortion, particularly when optimal shapes involve significant movement of patch intersections in physical space. Throughout optimization iterations, all members within the shell structures maintain the NURBS geometry representation, enabling efficient integration of analysis and design models. The optimization approach leverages the multilevel design concept by selecting a refined model for accurate analysis from a coarse design model while maintaining the same geometry. We adopt several example problems to verify the effectiveness of the proposed scheme and demonstrate its applicability to the optimization of the internal stiffeners of an aircraft wing.