Surface effects on shape and topology optimization of nanostructures

We present a computational method for the optimization of nanostructures, where our specific interest is in capturing and elucidating surface stress and surface elastic effects on the optimal nanodesign. XFEM is used to solve the nanomechanical boundary value problem, which involves a discontinuity in the strain field and the presence of surface effects along the interface. The boundary of the nanostructure is implicitly represented by a level set function, which is considered as the design variable in the optimization process. Two objective functions, minimizing the total potential energy of a nanostructure subjected to a material volume constraint and minimizing the least square error compared to a target displacement, are chosen for the numerical examples. We present results of optimal topologies of a nanobeam subject to cantilever and fixed boundary conditions. The numerical examples demonstrate the importance of size and aspect ratio in determining how surface effects impact the optimized topology of nanobeams. B Harold S. Park [email protected] B Timon Rabczuk [email protected] S. S. Nanthakumar [email protected] Navid Valizadeh [email protected] 1 Institute of Structural Mechanics, Bauhaus-Universität Weimar, Marienstraße 15, 99423 Weimar, Germany 2 Department of Mechanical Engineering, Boston University, 730 Commonwealth Avenue, ENA 212, Boston, MA 02215, USA 3 School of Civil, Environmental and Architectural Engineering, Korea university, Seoul, Republic of Korea