Shape and non-shape unified isogeometric optimal design for extremal band gaps

Mechanics Based Design of Structures and Machines, vol. 51, pp. 4813–4832

Abstract

A unified shape and non-shape design optimization for lattice structures is performed to obtain extremal band gaps in an isogeometric computational framework, which uses the same NURBS basis functions as used in CAD description. Using a precise numerical model in both response and shape sensitivity analyses, enhanced response and sensitivity can be obtained, which leads to a precise optimal design. A plane wave propagation in infinite periodic lattice is analyzed within a representative unit cell using the Bloch theory with periodic boundary conditions. The ligaments of lattice structures are modeled using geometrically exact beams whose cross-sectional area and configuration are regarded as design variables, which are parameterized by the NURBS basis functions. The design variables are controlled by a mathematical programming algorithm with efficient adjoint design sensitivity. The obtained optimal lattice structures of triangular, squared, hexagonal, and Kagomé structures are fabricated using a 3D printing machine to be validated by physical experiments. Through harmonic response analysis and physical experiment for the optimal and the original designs, the wave attenuation properties are compared to demonstrate the validity of the obtained optimal design.

Authors 6

1. Myung-Jin Choi Aachen Chair of Structural Analysis and Dynamics

   RWTH Aachen University · Seoul National University

   Affiliation as printed

   Chair of Structural Analysis and Dynamics, RWTH Aachen University, Aachen, Germany

   Department of Naval Architecture and Ocean Engineering, Seoul National University, Seoul, Republic of Korea

2. Min-Geun Kim corresponding

   Korea Institute of Machinery & Materials

   Affiliation as printed

   Department of Smart Industrial Machine Technology, Mechanical System Safety Research Division, Korea Institute of Machinery & Materials, Daejeon, Republic of Korea

   Department of Smart Industrial Machine Technology, Mechanical System Safety Research Division, Korea Institute of Machinery & Materials, Daejeon, Republic of Korea

3. Bonyong Koo

   Kunsan National University

   Affiliation as printed

   Department of Mechanical Engineering, Kunsan National University, Gunsan, Korea

4. Myung-Hoon Oh

   Seoul National University

   Affiliation as printed

   Department of Naval Architecture and Ocean Engineering, Seoul National University, Seoul, Republic of Korea

5. Hyunseok Kim

   Korea Research Institute of Ships and Ocean Engineering

   Affiliation as printed

   Alternative Fuels and Power System Research Division, KRISO, Daejeon, Korea

6. Seonho Cho corresponding

   Seoul National University

   Affiliation as printed

   Department of Naval Architecture and Ocean Engineering, Seoul National University, Seoul, Republic of Korea