# Lightweight Research in Engineering: A Review
## 4 Lightweight Pathways and Research Progress
### Structure Lightweight
#### 4.2.3 Topology Lightweight
[55] proposed a level set method for structural stiffness topology optimization by implicitly embedding the boundary of the structure into a zero-level set model of a high one-dimensional scalar function. The dynamic motion of the level set function is controlled by a Hamiltonian-Jacobi-type partial differential equation, which indirectly realizes the dynamic evolution of the structure boundary topology and shape. The normal motion velocity in the partial differential equation is established based on the shape sensitivity analysis result of the optimized objective function, combining finite element method and finite difference method, to realize numerical calculation of the elastic equilibrium equation and the Hamilton-Jacobi equation. The method can optimize the topology and shape of the structural design boundary and obtain the smooth boundary form simultaneously. There is no intermediate density material phenomenon like the homogenization method or the density function penalty method and the chessboard format numerical calculation singularity problem. [PERSON] et al. [56] proposed a new semi-implicit level set method for structural shape and topology optimization. The structure boundary is implicitly expressed as the zero-level set of high-dimensional scalar functions, including appropriate time-marching schemes, to achieve discrete level set processing. The main feature of the present method is it does not suffer from any time-step size restriction, as all terms relevant to stability are discretized in an implicit manner. The semi-implicit scheme with additive operator splitting treats all coordinate axes equally in arbitrary dimensions with good rotational invariance. Hence, the present scheme for the level set equations is stable for any practical time steps and numerically easy to implement with high efficiency. [PERSON] et al. [57] took the engine hood of a certain type of vehicle as the research object, and took the topology optimization method as the guidance, designed three different schemes (original structural optimization, small hole reconstruction, and overall reconstruction) to optimize the structure of the hood, and analyzed its mechanical properties. Based on the original structure, the topology optimization of the uniformly distributed holes in the part with less load on the structure is relatively conservative, and the lightweight margin is small, but the feasibility is large. In the original structural scheme, some holes have been dug in the cover plate in order to reduce the weight, and the holes in the original structure cannot be rearranged, so that fewer parts can be lightened, which limits the topology optimization design. Therefore, the small holes in the original structure of the cover plate are filled, leaving only three large pairs of holes in the cover plate structure, and then topology optimization is performed, and the holes on the inner plate are rearranged according to the optimization result. All the holes in the original hood structure are filled, and then analyzed by topology optimization software to re-divide and design the overall structure. The topography of the outer ring of the cover plate is unlikely, and the outer ring of the cover plate may have an assembly relationship with other parts of the body. Therefore, in the optimization scheme, the outer-ring structure of the cover plate is separated, and as an untreated structure, only the internal structure is optimized. Many scholars [58; 59; 60] optimized the stiffened layout of thermoelastic structures and thin-walled structures under inertial load successively. [PERSON] et al. [61; 62] carried out topological optimization of size-dependent sandwich structure and functionally graded material structure respectively. [PERSON] et al. [63] proposed a topology optimization based on node nonlocal density interpolation structure, which avoided the checkerboard pattern and the \"island\" phenomenon successfully.