Isogeometric Configuration Design Optimization of Three-dimensional Curved Beam Structures for Maximal Fundamental Frequency

TL;DR

This paper introduces an optimization method for 3D curved beam structures that maximizes fundamental frequency by simultaneously optimizing beam and surface design within an isogeometric framework.

Contribution

It develops a novel optimization approach for curved beam structures, including a design velocity computation and sensitivity analysis for repeated eigenvalues.

Findings

Effective maximization of fundamental frequency demonstrated

Simultaneous surface and beam design optimization achieved

Method validated through illustrative examples

Abstract

This paper presents a configuration design optimization method for three-dimensional curved beam built-up structures having maximized fundamental eigenfrequency. We develop the method of computation of design velocity field and optimal design of beam structures constrained on a curved surface, where both designs of the embedded beams and the curved surface are simultaneously varied during the optimal design process. A shear-deformable beam model is used in the response analyses of structural vibrations within an isogeometric framework using the NURBS basis functions. An analytical design sensitivity expression of repeated eigenvalues is derived. The developed method is demonstrated through several illustrative examples.