Abstract
Based on the Independent Continuous Mapping method (ICM), a topological optimization model with continuous topological variables is built by introducing three filter functions for element weight, element allowable stress and element stiffness, which transform the 0-1 type discrete topological variables into continuous topological variables between 0 and 1. Two methods for the filter functions are adopted to avoid the structural singularity and recover falsely deleted elements: the weak material element method and the tiny section element method. Three criteria (no structural singularity, no violated constraints and no change of structural weight) are introduced to judge iteration convergence. These criteria allow finding an appropriate threshold by adjusting a discount factor in the iteration procedure. To improve the efficiency, the original optimization model is transformed into a dual problem according to the dual theory and solved in its dual space. By using MSC/Nastran as the structural solver and MSC/Patran as the developing platform, a topological optimization software of frame structures is accomplished. Numerical examples show that the ICM method is very efficient for the topological optimization of frame structures.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Michell G.M. (1904) The limits of economy of materials in frame structures. Philos. Mag. Ser. 6 8(47): 589–597
Dorn W., Gomory R., Greenberg H. (1964) Automatic design of optimal structures. J. Mech. 3(1): 25–52
Ringertz U. (1985) On topology optimization of trusses. Eng. Opt. 9(3): 209–218
Kirsch U. (1989) Optimal topologies of truss structures. Comp. Meth. Appl. Mech. Eng. 72(1): 15–28
Cheng G.D., Jiang Z. (1992) Study on topology optimization with stress constraints. Eng. Opt. 20, 29–148
Cheng G.D., Guo X. (1997) \(\varepsilon \)-Relaxed approach in structural topology optimization. Struct. Opt. 13(4): 258–266
Bechers M., Fleury C. (1997) A primal-dual approach in truss topology optimization. Comput. Struct. 64(1–4): 77–88
Cheng G.D.(2000) On singular optima of structural topology optimization of trusses. J. Dalian Univ. Technol. 40(4): 379–383, (in Chinese)
Sui Y.K. Modelling, Transformation and Optimization – New Developments of Structural Synthesis Method. Dalian University of Technology Press. China (1996) (in Chinese)
Sui Y.K., Yang D.Q. (1998) A new method for structural topological optimization based on the concept of independent continuous variables and smooth model. Acta Mech. Sin. 18(2): 179–185
Sui Y.K.: ICM Method of Topological Optimization for Truss, Frame and Continuum Structure. WCSMO-4, June 4–8 (2001) Dalian
Sui Y.K., Long L.C., Ren X.C.: Topological optimization of frame structures with stress and displacement constraints under multi-loading cases. WCSMO-4, June 4–8 (2001) Dalian
Sui Y.K., Ren X.C., Long L.C. (2001) Topological optimization of frame structures. Acta Mech. Solida Sin. Spec.(22): 95–100, (in Chinese)
Sui Y.K., Ren X.C., Long L.C., Ye B.R. (2003) Topological optimization of frame based on ICM method. Chin. J. Comput. Mech. 20(3): 286–289, (in Chinese)
Author information
Authors and Affiliations
Corresponding author
Additional information
The project supported by the National Natural Science Foundation of China (10472003) and Beijing Natural Science Foundation (3042002) The English text was polished by Yunming Chen.
Rights and permissions
About this article
Cite this article
Sui, Y., Du, J. & Guo, Y. Independent continuous mapping for topological optimization of frame structures. Acta Mech Sin 22, 611–619 (2006). https://doi.org/10.1007/s10409-006-0031-8
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10409-006-0031-8