1. Topology Optimization of Tower Design
Bohan Zhou, Jialin Liu, Qingze Huo
MS students in Department of Mechanical Engineering
Methodology
The tower design problem is a science-related competition sponsored by
Science Olympiad. The contest is aimed to initiate the innovative thinking
of design for middle school and high school students. However, the
calculation of arranging the material to enhance the load-bearing capacity
with smaller weight is extremely complicated. Therefore, we want to use
the power of topology optimization to obtain a conceptual design model.
This best efficiency model can give the competitors some useful ideas.
Fig. 1 An example of tower design
Introduction
 Design variable is the density of the material within the design space;
 The volume fraction is the lower bound of the optimization;
 Different Volume Fraction is tested to find a reasonable structure;
 The objective of the design is minimizing the compliance of the tower;
 Optimization steps are iterated in order to obtain the truss-structure;
 Synthesis the analysis models and getting the optimization result
Fig. 2 Design Model
Analysis Model
The tower design problem is simplified to build a computational model. The
main assumptions we made to insure the simplification are:
•The material (Balsa) of the tower has isotropic and homogeneous
properties according to the literature;
•The base of the tower is grounded for 3 dimensions;
•The tower is only subject to vertical pressure or concentrated force.
The computational model is applied in Hyperworks software to conduct
topology optimization.
Topology optimization
Topology optimization is a mathematical method of discovering the best
concept design for a defined design space, set of load, set of constraints and
boundary conditions. In this part, concepts of design are discussed by applying
topology optimization.
 3D topology optimization
Fig. 4 (a) Block design space (b) Topology optimization result
(a) (b)
(a) (b)
Fig. 5 (a) Hollow design space (b) Topology optimization result
(a) (b)
Fig. 6 (a) Modified design space (b) Topology optimization result
Design and stress analysis
• Using the conceptual result in 3D topology optimization, we come up with the
modified structure form of this tower with a mass of 53.32 grams. The diameter
of braces in y direction is 10 mm and the diameter of the horizontal beam is
6mm.
Fig. 7 Final design structure
• In stress analysis section, utilizing abaqus software to analyze the stress. The
material properties are as same as those used in topology optimization: a Young’s
modulus of 3000MPa, a Poisson’s ratio of 0.29, and a density of 160kg/m3.
Fig. 8 Stress analysis for final structure
• The maximum stress values on the contact surface between tower and block. The
maximum von Mises stress value is about 1 MPa. Von Mises stress is about 20
MPa. It means the structure is over-qualified to actually bear the 15 Kg load.
With consideration of the above optimization result we modify the design
space to a hollow design space.
Based on the result from above figure 5(b), improved our design space again
 2D topology optimization
Fig. 1 An example of tower design
Using TopOpt application to apply 2D topology optimization
Fig. 9 (a) Improved final structure (b) Stress analysis for improved final structure
(a) (b)
Starting with a block design space; obtaining an initial conceptual structure
As we can see in the Fig.6(b), a light enough truss-structured model is obtained.
• In order to gain a lighter structure within von Mises yield limit, deduce the
diameter of the above structure to 50 percent. The improved final structure is
shown in fig.9, and it is also pass the strength analysis. The structure has a small
enough diameter to be executable for middle school students to produce, with a
weight of 12.8 grams.
Conclusion
• Based on topology optimization, finally we got a relatively approrperate model for this design project.
Through analysis, we conclude that this topology optimization design is feasible.