In this thesis, an e cient approach for topology optimization of three-dimensional (3D) problems has been proposed where the density... Show moreIn this thesis, an e cient approach for topology optimization of three-dimensional (3D) problems has been proposed where the density representation is based on B-splines. Compared with the usual density representation and ltering in topology optimization, the new B-spline based approach is advantageous in both memory usage and CPU time. This is achieved through the use of tensor product representation of density distribution. As such, the storage of ltered density variables is linear with respect to the e ective lter size instead of the cubic order in the usual density lter. Numerical examples of 3D topology optimization of minimal compliance and heat conduction problems are demonstrated. We also show that our B-spline based density representation is especially bene cial to topology optimization methods such as the multiple density per element scheme where the storage of ltered density variables is a challenge. We show that the B-spline approach is also applicable to the multi-resolution scheme. M.S. in Mechanical Engineering, December 2013 Show less
