A heuristic approach is presented to solve continuum topology optimization problems with specified constraints, e.g., structural volume constraint and/or displacement constraint(s). The essentials of the present approach are summarized as follows. First, the structure is regarded as a piece of bone and the topology optimization process is viewed as bone remodeling process. Second, a second-rank positive and definite fabric tensor is introduced to express the microstructure and anisotropy of a material point in the design domain. The eigenpairs of the fabric tensor are the design variables of the material point. Third, Wolff’s law, which states that bone microstructure and local stiffness tend to align with the stress principal directions to adapt to its mechanical environment, is used to renew the eigenvectors of the fabric tensor. To update the eigenvalues, an interval of reference strain, which is similar to the concept of dead zone in bone remodeling theory, is suggested. The idea is that, when any one of the absolute values of the principal strains of a material point is out of the current reference interval, the fabric tensor will be changed. On the contrary, if all of the absolute values of the principal strains are in the current reference interval, the fabric tensor remains constant and the material point is in a state of remodeling equilibrium. Finally, the update rule of the reference strain interval is established. When the length of the interval equals zero, the strain energy density in the final structure distributes uniformly. Simultaneously, the volume and the displacement field of the final structure are determined uniquely. Therefore, the update of the reference interval depends on the ratio(s) between the current constraint value(s) and their critical value(s). Parameters, e.g., finite element mesh the initial material and the increments of the eigenvalues of fabric tensors, are studied to reveal their influences on the convergent behavior. Numerical results demonstrate the validity of the method developed.
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e-mail: chenbs@dlut.edu.cn
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September 2008
Research Papers
Stiffness Design of Continuum Structures by a Bionics Topology Optimization Method
Kun Cai,
Kun Cai
State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics,
Dalian University of Technology
, Dalian 116024, P.R.C.
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Biao-song Chen,
Biao-song Chen
State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics,
e-mail: chenbs@dlut.edu.cn
Dalian University of Technology
, Dalian 116024, P.R.C.
Search for other works by this author on:
Hong-wu Zhang,
Hong-wu Zhang
State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics,
Dalian University of Technology
, Dalian 116024, P.R.C.
Search for other works by this author on:
Jiao Shi
Jiao Shi
College of Water Resources and Architectural Engineering,
Northwest A&F University
, Yangling 712100, P.R.C.
Search for other works by this author on:
Kun Cai
State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics,
Dalian University of Technology
, Dalian 116024, P.R.C.
Biao-song Chen
State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics,
Dalian University of Technology
, Dalian 116024, P.R.C.e-mail: chenbs@dlut.edu.cn
Hong-wu Zhang
State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics,
Dalian University of Technology
, Dalian 116024, P.R.C.
Jiao Shi
College of Water Resources and Architectural Engineering,
Northwest A&F University
, Yangling 712100, P.R.C.J. Appl. Mech. Sep 2008, 75(5): 051006 (11 pages)
Published Online: July 15, 2008
Article history
Received:
May 24, 2007
Revised:
March 27, 2008
Published:
July 15, 2008
Citation
Cai, K., Chen, B., Zhang, H., and Shi, J. (July 15, 2008). "Stiffness Design of Continuum Structures by a Bionics Topology Optimization Method." ASME. J. Appl. Mech. September 2008; 75(5): 051006. https://doi.org/10.1115/1.2936929
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