## Theses and Dissertations

Thesis

Summer 2015

#### Degree Name

MS (Master of Science)

#### Degree In

Civil and Environmental Engineering

Colby C. Swan

#### Abstract

Structural topology optimization is a mathematical approach developed to perform design optimization with the purpose of reducing the material usage, while maximizing structural performance, in accordance to specific design constraints. The principles behind this technique have been around for many decades, but recent advancements in the processing power of computers have allowed for the solving of complex problems, such as the optimization of tall wind turbine towers, bridges, and the bracing systems in skyscrapers.

There are two approaches commonly used in structural topology optimization: discrete and continuum. This thesis uses continuum topology optimization, which involves adjusting the distribution of a porous elastic solid material to extremize the design objective(s) and to satisfy constraints. The material porosity is the design variable that is adjusted during the optimization process. The design domain is broken down into a system of continuum degenerated finite elements, which are used for both structural analysis and to create a mesh representation of the structural system, just as pixels make up a picture. Solid elements are modeled as having no porosity, while void spaces have total porosity. As the optimization process occurs, the shape of the boundaries, and the number and size of internal holes are altered in order to best meet the design objective(s) and constraint(s). The purpose of performing continuum structural topology optimization of structural elements is to obtain promising concepts which provide a basis upon which to begin the design process.

The steps taken in this thesis to optimize the wind turbine tower are:

1. Create a solid model of the tower domain

2. Define the material properties

3. Determine the equivalent static design wind forces using the extreme loading conditions outlined in IEC 61400

4. Formulate the optimization problem by specifying the objective and constraint functions.

5. Solve the optimization problem and interpret the results.

This study on continuum topology optimization on the tower shell, indicates even with a significant reduction in material from the original design space, the structure is capable of meeting the design criteria. The results indicate that opening void spaces in the shell of the tower and creating an open lattice shape may be an effective method to reduce the volume of wind turbine towers, as it has in other applications. This concurs with the stated goal of my research, which is to show that topology optimization has the potential to be used in a multitude of practical applications in order to increase efficiency, and reduce cost of the production of wind power.

#### Public Abstract

Structural topology optimization is a mathematical approach, which can refine the physical layout of the material within a system to the optimal distribution based on a set of design criteria. The procedure has traditionally been used to achieve a reduction in mass of small manufactured parts, but can also be used to solve larger, more complex problems such as the design of bridges, skyscrapers, and wind turbine towers.

This thesis’ study on the effectiveness of topology optimization on the tower of a wind turbine had two stated objectives: to explore the field of structural topology optimization and its potential uses, and to then use topology optimization to solve for the ideal open lattice shape for the turbine tower under specific loading conditions.

The results of this thesis indicate that significant reduction in material from the original design space is possible while still meeting the design criteria. The results indicate that by opening holes in the shell of the tower, to create a design similar to that of an open lattice structure, one can achieve a structure that efficiently uses the volume of material in wind turbine tower. This aligns with the purpose of my research, which is to show that topology optimization has the potential to be used in a multitude of practical applications to increase efficiency, and reduce cost of production of wind power.

#### Keywords

publicabstract, Civil Engineering, Optimization, Structures, Topology, Towers, Wind Turbine

x, 76 pages

#### Bibliography

Includes bibliographical references (pages 71-76).