Structural optimization design can be defined as finding the solution of design variables that satisfy all constraints and minimizing the objective function of given parameters.

2. Design variables

Design variable refers to the quantity selected to describe the structural characteristics in the design process, and its numerical value is variable. Design variables can be geometric parameters of design section, such as section size, area and moment of inertia of each component, or geometric parameters of the whole structure, such as column height, beam spacing, arch height and node coordinates. There are usually two types of design variables: continuous design variables and discrete design variables.

(1) continuous design variable. Such variables are constantly changing in the process of optimization, such as the rise of arch and the coordinates of nodes.

(2) Discrete design variables. Such variables change by leaps and bounds in optimization, for example, the cross-sectional area of available steel and the diameter of steel bars are discontinuous.

3. The objective function

The objective function is an index used to measure the design quality. Which index is used to reflect the design quality is related to the technical and economic characteristics of the structure itself. The commonly used objective functions are: structural weight, structural volume and structural cost.

Step 4 limit

Generally, structural optimization has two constraints: geometric constraints and performance constraints.

(1) geometric constraints. That is, design variables are limited by geometric dimensions. For example, the minimum thickness limit of the web and flange of I-section.

(2) sexual constraints. In other words, some restrictions are imposed on the working behavior of the structure. For example, the strength and stability constraints of components, the stiffness and natural frequency of the whole structure.