Structural Design Optimization Using Isogeometric Analysis: A Comprehensive Review

Isogeometric analysis(IGA),an approach that integrates CAE into conventional CAD design tools,has been used in structural optimization for 10 years,with plenty of excellent research results.This paper provides a comprehensive review on isogeometric shape and topology optimization,with a brief coverage of size optimization.For isogeometric shape optimization,attention is focused on the parametrization methods,mesh updating schemes and shape sensitivity analyses.Some interesting observations,e.g.the popularity of using direct(differential)method for shape sensitivity analysis and the possibility of developing a large scale,seamlessly integrated analysis-design platform,are discussed in the framework of isogeometric shape optimization.For isogeometric topology optimization(ITO),we discuss different types of ITOs,e.g.ITO using SIMP(Solid Isotropic Material with Penalization)method,ITO using level set method,ITO using moving morphable com-ponents(MMC),ITO with phase field model,etc.,their technical details and applications such as the spline filter,multi-resolution approach,multi-material problems and stress con-strained problems.In addition to the review in the last 10 years,the current developmental trend of isogeometric structural optimization is discussed.

Data-Driven Structural Design Optimization for Petal-Shaped Auxetics Using Isogeometric Analysis

Focusing on the structural optimization of auxetic materials using data-driven methods,a back-propagation neural network(BPNN)based design framework is developed for petal-shaped auxetics using isogeometric analysis.Adopting a NURBSbased parametric modelling scheme with a small number of design variables,the highly nonlinear relation between the input geometry variables and the effective material properties is obtained using BPNN-based fitting method,and demonstrated in this work to give high accuracy and efficiency.Such BPNN-based fitting functions also enable an easy analytical sensitivity analysis,in contrast to the generally complex procedures of typical shape and size sensitivity approaches.

Introduction to the Special Issue on Recent Developments of Isogeometric Analysis and Its Applications in Structural Optimization

Isogeometric analysis(IGA),which aims at integrating CAD and CAE models,is one of the most active research topics in both computational mechanics and computer-aided geometric design.The rapidly growing interests in IGA has led to profound developments of relevant theories and applications,one of which being structural optimization.With the rapid growth of researches in IGA,this special issue contributes to highlight recent developments,challenges and opportunities of IGA and IGA-based structural design optimization,with focuses on theory development,numerical implementations and potential applications.