# Lightweight Research in Engineering: A Review
## 4 Lightweight Pathways and Research Progress
### Structure Lightweight
#### 4.2.2 Shape Lightweight  
Shape optimization structure can further improve the product's superiority and the performance of the product by further improving the topography and shape characteristics of parts under the condition of the overall topological relationship being roughly determined. For example, in the same part of the hole, whether the rectangle is suitable, or the circular is more superior, that is shape optimization. The different sections of the boom were analyzed, from the quadrilateral section to the nine-sided section and the large rounded corner section, and obtained the influence of the section shape on the function, stability, and expansion of the boom, which has a certain reference value for other scholars to study the shape optimization structure [40]. Based on the curve-surface equation, geometric design variable parametric mapping definition of the new method, and shape optimization design problem design variables less and more constraints, experts took the shape optimization design of two squirrel cage elastic support slots as an research object, the optimization design of squirrel cage elastic support slots with single symmetry, double symmetry, and ellipse periodic distribution was obtained. The slots were found to be excellent, and the shape is narrow at both ends [41]. [PERSON] et al. [42] proposed a new method of hole-shape optimization on general composite surface. The method of parameter mapping was used to optimize the hole shape on the surface structure, and the failure function value on the hole circumference curve was selected as the optimization design objective. The effects of Mises, Tsai-Hill, and Tsai-Wu failure criteria and three different material systems on the optimization results are compared when elliptic function is used to describe the hole shape. Finally, an example of spline function to describe the hole shape was given in 2011. Developing new methodologies for shape optimization of openings on three-dimensional curved panels that are used widely in aeronautical and aerospace engineering. To circumvent the difficulties associated with the hole boundary shape parameterization, a virtual punching method that exploits Boolean operations of the CAD modeler was proposed [43] for the definition of shape design variables. Compared with the parametric mapping method developed previously, the virtual punching method was shown to be an implicit boundary representation for this specific kind of structure. Instead, the parametric mapping method was based on the explicit boundary representation. A zero-order genetic algorithm (GA) was correspondingly implemented into the design procedure of the virtual punching method in order to execute the optimization process for two reasons. First, it makes it possible to avoid sensitivity analysis that is relatively difficult due to the implicit boundary representation formulation and the use of an unstructured mesh. Second, the computing cost of the GA is practically affordable in shape optimization because often only a small number of design variables are involved. Numerical tests are carried out for typical examples of the stress concentration minimization around openings on the curved panels in 2012. [PERSON] et al. [29] used the three-dimensional SolidWorks drawing software to establish a three-dimensional model of the Longmen Machining Center. Based on the original beam structure, the well-shaped ribbed plate (original beam structure), ten-shaped ribbed plate, X-shaped ribbed plate, and V-shaped of beam structure schemes were designed. The ANSYS software is used to compare and determine the V-shaped rib beam structure as the optimal solution. Isogeometric Analysis uses NURBS to achieve seamless connection of computer-aided geometric design (CAD), finite element analysis (FEA), and structural optimization [44]. This method uses the NURBS control point of the geometric model boundary as a design variable, which greatly simplifies the optimization process.