Three-Dimensional Dynamic Topology Optimization with Frequency Constraints Using Composite Exponential Function and ICM Method

• Published in: Mathematical problems in engineering Vol. 2015; no. 2015; pp. 1 - 10
• Main Authors: Jun, Tie, Yun-kang, Sui, Chen, Ning, Ye, Hongling
• Format: Journal Article
• Language: English
• Published: Cairo, Egypt Hindawi Publishing Corporation 01.01.2015; John Wiley & Sons, Inc
• Subjects: Algorithms; Boundary conditions; Constraints; Continuity (mathematics); Design optimization; Dynamics; Eigenvalues; Engineering; Exponential functions; Homogenization; Investigations; Mapping; Mathematical analysis; Mathematical models; Mathematical programming; Methods; Nastran; Optimization; Quadratic programming; Series expansion; Taylor series; Three dimensional; Three dimensional composites; Topology optimization; Variables; Beijing China; China
• ISSN: 1024-123X; 1563-5147
• DOI: 10.1155/2015/491084

The dynamic topology optimization of three-dimensional continuum structures subject to frequency constraints is investigated using Independent Continuous Mapping (ICM) design variable fields. The composite exponential function (CEF) is selected to be a filter function which recognizes the design variables and to implement the changing process of design variables from “discrete” to “continuous” and back to “discrete.” Explicit formulations of frequency constraints are given based on filter functions, first-order Taylor series expansion. And an improved optimal model is formulated using CEF and the explicit frequency constraints. Dual sequential quadratic programming (DSQP) algorithm is used to solve the optimal model. The program is developed on the platform of MSC Patran & Nastran. Finally, numerical examples are given to demonstrate the validity and applicability of the proposed method.