**2.2 Structural topology optimization**

The topology of a structure is defined as a spatial arrangement of structural members and joints or internal boundaries. For both discrete and continuum structures, topology optimization helps to arrange association form of members as can be realized in **Figure 2** [18].

The conceptual process is shown in **Figure 3**.

Structural optimization is concerned with maximizing the utility of a fixed quantity of resources to fulfill a given objective. In structural optimization the best "structural" design is selected regarding three categories: size optimization, shape optimization, and topology optimization [19]. The application of topology optimization to structures to reveal the best position and size of the parts in a continuum is the most favorite one. Michell presented the first solutions as seen in **Figure 4**. Today much more advanced techniques are used, and by the help of finite element method, it could be applied to complex problems. Weight savings are managed by engineers in several structures as a consequence of utilization of these

methods. There are many examples in literature on the application of these methods [13, 20, 21]. Today, many commercial finite element software has an optimization module (Altair OptiStruct, Simulia Tosca, OPTISHAPE-TS, etc.) to obtain lighter

**75**

*Topology Optimization Applications on Engineering Structures*

*One of the first proposed solutions to a structural topology optimization problem [13].*

structure, but several researchers have generated their codes [22, 23] or developed

Structural optimization concerns on getting the required task of the mechanical system and maximizing its efficiency by an ordered procedure. At the beginning the design variables should be selected carefully. Then, limitations of these variables and system performance factors will be defined. By changing variable values, it is possible to see the change in these factors so we are able to determine the best combination among the design space. As design variables, the size of the members or mechanical properties of materials could be selected similar to size optimization, and the configuration of members is also another possible parameter as in shape optimization. Material distribution and layout are the parameter that is concerned in topology optimization. As the objective function, the most used one is cost function (related to total weight) to be minimized. Stress and buckling conditions are mostly used constraints in literature [18]. The aim is to optimize parts or units for

**Figure 5** shows a sample application of topology optimization in finding the best material distribution. Minimizing objective function is acquired by checking different structure forms step by step. Each time design is narrowed down by selecting

scripts [24] using these software's programming languages.

specific load cases and extreme situations.

*Initial and optimized unit structure of a short cantilever.*

the best form among feasible sets.

*DOI: http://dx.doi.org/10.5772/intechopen.90474*

**Figure 4.**

**Figure 5.**

*Topology Optimization Applications on Engineering Structures DOI: http://dx.doi.org/10.5772/intechopen.90474*

**Figure 4.** *One of the first proposed solutions to a structural topology optimization problem [13].*

#### **Figure 5.**

*Truss and Frames - Recent Advances and New Perspectives*

**74**

**Figure 3.**

*Conceptual process [18].*

**Figure 2.**

*Variation of topology [18].*

methods. There are many examples in literature on the application of these methods [13, 20, 21]. Today, many commercial finite element software has an optimization module (Altair OptiStruct, Simulia Tosca, OPTISHAPE-TS, etc.) to obtain lighter

*Initial and optimized unit structure of a short cantilever.*

structure, but several researchers have generated their codes [22, 23] or developed scripts [24] using these software's programming languages.

Structural optimization concerns on getting the required task of the mechanical system and maximizing its efficiency by an ordered procedure. At the beginning the design variables should be selected carefully. Then, limitations of these variables and system performance factors will be defined. By changing variable values, it is possible to see the change in these factors so we are able to determine the best combination among the design space. As design variables, the size of the members or mechanical properties of materials could be selected similar to size optimization, and the configuration of members is also another possible parameter as in shape optimization. Material distribution and layout are the parameter that is concerned in topology optimization. As the objective function, the most used one is cost function (related to total weight) to be minimized. Stress and buckling conditions are mostly used constraints in literature [18]. The aim is to optimize parts or units for specific load cases and extreme situations.

**Figure 5** shows a sample application of topology optimization in finding the best material distribution. Minimizing objective function is acquired by checking different structure forms step by step. Each time design is narrowed down by selecting the best form among feasible sets.
