Isogeometric configuration design optimization of built-up structures

Abstract

We derive the isogeometric configuration sensitivity of the Mindlin plates by using the material derivative and adjoint approaches. This is utilized in the shape design optimization that includes a variation of design components in its shape and orientation. By the isogeometric approach, the NURBS basis function in CAD system is directly utilized in the response analysis, which enables the seamless incorporation of higher continuity and exact geometry such as curvature and normal vector into the computational framework. The impact of exact curvature in the bending problem of Mindlin plates on the configuration design sensitivity is demonstrated through numerical examples. The obtained design sensitivity is further utilized in the shape design optimization of built-up structures. Due to the non-interpolatory property of the NURBS basis functions, a mismatch of patches in the built-up structures could occur during the isogeometric design optimization, which can be easily resolved using transformed basis functions.

Structural Design Optimization Using Isogeometric Analysis: A Comprehensive Review

“…In the context of isogeometric shape optimization, the exact geometric representation enables the computation of the boundary geometric parameters easily and seamlessly, hence, providing a natural platform to implement the continuum adjoint method. This has been intensively studied by Seonho Cho and his co-authors in Cho et al [Cho and Ha (2009)] for general discussions, in Ha et al [Ha, Choi and Cho (2010)] using T-spline based isogeometric method, in Ahn et al [Ahn and Cho (2010)] for level-set-based topology optimization of heat conduction problems, in Koo et al [Koo, Yoon and Cho (2013)] coping with Kronecker delta property, in Yoon et al [Yoon, Ha and Cho (2013); Yoon, Choi and Cho (2015)] for shape design optimization of heat conduction problems, in Choi et al [Choi and Cho (2014)] for stress intensity factors of curved crack problems, in Lee et al [Lee and Cho (2015)] for optimizing built-up structures, in Lee et al [Lee, Lee and Cho (2016)] for ferromagnetic materials in magnetic actuators, in Yoon et al [Yoon and Cho (2016)] for boundary integral equations, in Choi et al [Choi, Yoon and Cho (2016)] for designing curved Kirchhoff beams with finite deformations, in Lee et al [Lee, Yoon and Cho (2017)] for topological shape optimization using dual evolution with boundary integral equation and level sets, in Choi et al [Choi and Cho (2018a)] for designing lattice structures embedded on curve surfaces, in Choi et al [Choi and Cho (2018b)] for using curved beams to design auxetic structures and in Ahn et al [Ahn, Choi and Cho (2018); Ahn, Koo, Kim et al (2018)] for designing nanoscale structures. Wang and his co-authors implemented the continuum adjoint method in Wang et al [Wang and Turteltaub (2015)] for quasi-static problems considering discontinuities in the objective functions, in Wang et al ; Wang and Kumar (2017)] for transient heat conduction problems and in Wang et al [Wang, Poh, Dirrenberger et al (2017)] to design auxetic structures using numerical homogenization method.…”

Isogeometric configuration design sensitivity analysis of finite deformation curved beam structures using Jaumann strain formulation

“…Second, it significantly simplifies the design modification during the design optimization process without communicating with CAD systems. An isogeometric configuration DSA method was developed for Mindlin plate problems [31]. In the plate design component under the assumption of small design perturbations, the design variation is represented by the tangential design velocity for the shape variation and by the out-of-plane design velocity for the orientation variation.…”