Development and validation of a numerical topology optimization scheme for two and three dimensional structures
Date of Original Version
A novel finite element topology optimization procedure is presented based on the application of probability density and cumulative distribution functions. The procedure utilizes a family of Beta functions with constant probability mean which provide a smooth transition from a uniform to a bi-modal density distribution while conserving constant mean density and therefore constant mass. Validation of the method is demonstrated for several well-known two-dimensional minimum-weight structures. A general minimum-weight cylindrical structural layout for the support of any combination of axial and torsional loading has been developed to provide a test case for three dimensional numerical topological optimization. It is observed that this solution presents a challenge, especially for cases where the axial load is significantly larger than the torsional loading. For these cases, slender members are an essential part of the optimal topology. © 2010 Elsevier Ltd. All rights reserved.
Advances in Engineering Software
Taggart, D. G., and P. Dewhurst. "Development and validation of a numerical topology optimization scheme for two and three dimensional structures." Advances in Engineering Software 41, 7-8 (2010): 910-915. doi:10.1016/j.advengsoft.2010.05.004.