Isogeometric analysis (IGA)

In the works below, an isogeometric analysis combined with adjoint sensitivity analysis is used for the design of mechancial metamaterials. A detailed introduction to isogeometric analysis (IGA), formulation and implementation of adjoint sensitivity analysis in the nonlinear regime for auxetics design is included in the thesis and papers below. The work presents a holistic physics-based approach for structural shape optimization using IGA. Kindly cite the work if you find useful. 

Publications:

Graphical Abstract (from Publication 2 below):

Abstract:

Abstract

This paper presents a design methodology based on a combination of isogeometric analysis (IGA),

level set and point wise density mapping techniques for topology optimization of piezoelectric /

flexoelectric materials. The fourth order partial differential equations (PDEs) of flexoelectricity,

which require at least C 1 continuous approximations, are discretized using Non-Uniform Rational

B-spline (NURBS). The point wise density mapping technique with consistent derivatives is