In density-based topological design, one expects that the final result consists of elements either black (solid material) or white (void), without any grey areas. Moreover, one also expects that the optimal topology can be obtained by starting from any initial topology configuration. An improved structural topological optimization method for multi- displacement constraints is proposed in this paper. In the proposed method, the whole optimization process is divided into two optimization adjustment phases and a phase transferring step. Firstly, an optimization model is built to deal with the varied displacement limits, design space adjustments, and reasonable relations between the element stiffness matrix and mass and its element topology variable. Secondly, a procedure is proposed to solve the optimization problem formulated in the first optimization adjustment phase, by starting with a small design space and advancing to a larger deign space. The design space adjustments are automatic when the design domain needs expansions, in which the convergence of the proposed method will not be affected. The final topology obtained by the proposed procedure in the first optimization phase, can approach to the vicinity of the optimum topology. Then, a heuristic algorithm is given to improve the efficiency and make the designed structural topology black/white in both the phase transferring step and the second optimization adjustment phase. And the optimum topology can finally be obtained by the second phase optimization adjustments. Two examples are presented to show that the topologies obtained by the proposed method are of very good 0/1 design distribution property, and the computational efficiency is enhanced by reducing the element number of the design structural finite model during two optimization adjustment phases. And the examples also show that this method is robust and practicable.
[1]
Yang Deqing,et al.
A new method for structural topological optimization based on the concept of independent continuous variables and smooth model
,
1998
.
[2]
Y. Xie,et al.
A simple evolutionary procedure for structural optimization
,
1993
.
[3]
V. Kobelev,et al.
Bubble method for topology and shape optimization of structures
,
1994
.
[4]
Niels Olhoff,et al.
Topology optimization of continuum structures: A review*
,
2001
.
[5]
M. Fuchs,et al.
The SRV constraint for 0/1 topological design
,
2005
.
[6]
K. Svanberg,et al.
An alternative interpolation scheme for minimum compliance topology optimization
,
2001
.
[7]
Byung Man Kwak,et al.
Design space optimization using a numerical design continuation method
,
2002
.
[8]
Yun-Kang Sui,et al.
The ICM method with objective function transformed by variable discrete condition for continuum structure
,
2006
.
[9]
Martin P. Bendsøe,et al.
Optimization of Structural Topology, Shape, And Material
,
1995
.
[10]
J. Sethian,et al.
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
,
1988
.
[11]
B. Kwak,et al.
Design space optimization using design space adjustment and refinement
,
2007
.
[12]
George I. N. Rozvany,et al.
A critical review of established methods of structural topology optimization
,
2009
.
[13]
Xiaoming Wang,et al.
A level set method for structural topology optimization
,
2003
.