Solid Isotropic Material With Penalization And Level Set Method In Structural Topology Optimization Design

Continuum Structural Topology Optimization design is a hot research field, which enables more economical use of structural materials, and stress distribution is more reasonable. It can greatly reduce the structural weight and improve structural performance. It brings direct economic benefits. Therefore, it is significant to design engineering structures by topology optimization design. It improves the design scientifically and accurately.This paper is aimed at common project on comparison of optimization of beam structure, and it will come true by using Solid Isotropic Material with Penalization (SIMP) and the Level Set Method (LSM) topology optimization methods. It also combines finite element analysis, to achieve the result. Mainly studied the following:1. It establishes optimal model based on SIMP. It studies SIMP algorithm, and combined with MATLAB programming of the short cantilever beam, MBB beam, Michell-type structure and the crane beams of the model structure topology optimization design and analysis;2. It illustrates the basic concept of the level set method, Hamilton-Jacobi partial differential equations of the numerical calculation, and the level set evolution process;3. It studies some basic ideas in solving the level set method in the continuum topology optimization. It also discusses the continuum topology optimization level set function description, optimization model, level set method of theoretical derivation and numerical implementation. Engineering components of the beam are optimized by using MATLAB programming. It analyzed and compared researches the optimization results of the LSM to SIMP. SIMP is a uniform method for further improvement. The program becomes mainstream of optimization method because it reduces the amount of design variables, simplifies the program, and improves the variety of calculation. However, it still remains that checkerboard patterns, gray unit values such as instability. It mentions not only the topology of penalty factor, but also with the initial finite element mesh (i.e. mesh dependency).As showed in this research work, the level set method for structural optimization in the field of application has unique advantages to track topology changes to optimize and has the boundary clear smooth and effective solution to the SIMP existing such as checkerboard patterns numerical instability. Thus the level set method is a promising research direction with the advantage of an important theoretical value.