Isogeometric Shape Design Optimization of Continuum-Nanoscale Structures considering Size Effects

Abstract

Recently, in both academic and industrial environment including naval architecture and ocean engineering, atomistic level design and analysis is essential to overcome the limitations in conventional continuum based approach. Conventionally, molecular dynamics (MD) simulation is used to obtain the physical properties and behaviour of atomistic level structures. However, the applications of MD simulation are restricted by its excessive computational time. Especially the limitation of MD simulation is more obvious in shape design optimization field. It is difficult to apply continuum-based shape design sensitivity analysis which is essential for shape design optimization due to the discrete nature of shape variations at the atomic level of MD simulation. Shape design optimization scheme requires repeated analysis process, which requires tremendous computational cost. In the thesis, an isogeometric shape design optimization method considering size effects in nanoscale structures is developed. We introduced continuum based model considering size effects for the analysis of nanoscale structures. Surface elasticity incorporating surface effects developed by Gurtin and Murdoch (1975) and nonlocal theory developed by Eringen (1983) are introduced, respectively. For experimental validation of developed method, three-point bending test of silver nanowires using atomic force microscope (AFM) are performed. Shape design optimization of curved structures is performed using continuum based Naghdi shell formulation in numerical examples. Isogeometric analysis (IGA) framework is used for numerical analysis method. A direct differentiation method is employed for the DSA and the design variables are selected as the control points defining the geometry for flexible modeling of free-form shell surfaces. Exact solutions derived from curved beam theory are presented to verify the numerical examples. It is shown that size effects affect the behaviour of the nanoscale structures and its optimal shape. The influence of surface effects in nanoscale is shown through three-point bending test of silver nanowires using AFM instruments. The behaviours of nanowires obtained from experimental results are compared with those obtained from theoretical calculation and good agreement is observed between them. Not only the behaviour of nanowires but the design sensitivity is validated through experimental results. The design sensitivity values obtained from fitting curve of experimental data are compared with those obtained by DSA based on continuum formulation considering surface effects, and it shows fairy good agreement. The isogeometric method has numerous advantages over the classical finite element analysis (FEA) due to its convenience of Non-Uniform Rational B-Spline (NURBS) basis functions. In the isogeometric method, the NURBS basis functions in CAD system are directly used in the response analysis, which enables an incorporation of exact geometry and higher continuity into the computational framework. Also, IGA provides more accurate design sensitivity for complex geometries including higher order geometric information such as normal vector and curvature. Especially for shell structures, exact geometry is more important issue and application of IGA gives more accurate computation results than FEA.