Topology optimization for the design of periodic structures based on high-frequency homogenization method for the Helmholtz equation

2017 ◽  
Vol 2017.30 (0) ◽  
pp. 124
Author(s):  
Yuki NOGUCHI ◽  
Takayuki YAMADA ◽  
Kazuhiro IZUI ◽  
Shinji NISHIWAKI
Keyword(s):  
Topology Optimization ◽  
Helmholtz Equation ◽  
High Frequency ◽  
Periodic Structures ◽  
Homogenization Method

On the efficient evaluation of modal density and damping of one-dimensional periodic structures using a dynamic homogenization method

2021 ◽  
pp. 107754632110052
Author(s):  
Yongbin Ma ◽  
Zichen Deng
Keyword(s):  
Explicit Expression ◽  
High Frequency ◽  
Periodic Structures ◽  
Longitudinal Vibration ◽  
Perturbation Expansion ◽  
Analytical Form ◽  
Homogenization Method ◽  
Wave Number ◽  
One Dimensional ◽  
Modal Density

Modal density and damping are key parameters for structural vibration analysis. However, the current methods for calculating these properties of periodic structures in high-frequency environment are still insufficient in accuracy and efficiency. In this article, a semi-analytical form for the modal density and damping of longitudinal vibration of one-dimensional periodic structures is proposed based on a dynamic homogenization method. By virtue of asymptotic perturbation expansion, explicit expression is obtained for the dispersion relation. And then, the modal density is obtained in terms of the semi-analytical form by differentiating frequency with respect to wave number. By noting that the high-frequency homogenization method is valid only in the neighborhood of the standing wave frequencies, a weighted technique is introduced to compensate this deficiency. Based on the mode strain energy method, the damping loss factor is also obtained using the high-frequency homogenization results. Because explicit expression can be obtained analytically, the shortage of low computational efficiency and accuracy faced by traditional analysis is significantly made up by the proposed method, which is confirmed by numerical examples.

Modeling of a high frequency ultrasonic transducer using periodic structures

2007 ◽  
Author(s):  
P. Maréchal ◽  
L. Haumesser ◽  
G. Feuillard ◽  
L.P. Tran-Huu-Hue ◽  
J. Holc ◽  
...  
Keyword(s):  
High Frequency ◽  
Periodic Structures ◽  
Ultrasonic Transducer

Topology Optimization Algorithm for Plates and Shells Subjected to Plastic Deformations

1998 ◽  
Author(s):  
Kohei Yuge ◽  
Nobuhiro Iwai ◽  
Noboru Kikuchi
Keyword(s):  
Topology Optimization ◽  
Optimization Method ◽  
Homogenization Method ◽  
Finite Deformations ◽  
Thin Shells ◽  
Plastic Deformations ◽  
Material Tensor ◽  
Design Variables ◽  
Interpolation Technique ◽  
Plates And Shells

Abstract A topology optimization method for plates and shells subjected to plastic deformations is presented. The algorithms is based on the generalized layout optimization method invented by Bendsϕe and Kikuchi (1988), where an admissible design domain is assumed to be composed of microstructures with periodic cavities. The sizes of the cavities and the rotational angles of the microstructures are design variables which are optimized so as to minimize the applied work. The macroscopic material tensor for the porous material is numerically calculated by the homogenization method for the sensitivity analysis. In this paper, the method is applied to two-dimensional elasto-plastic problems. A database of the material tensor and its interpolation technique are presented. The algorithm is expanded into thin shells subjected to finite deformations. Several numerical examples are shown to demonstrate the effectiveness of these algorithms.

Sign in / Sign up

Export Citation Format

Share Document