Abstract
Topology optimization is a modern method for optimizing the material distribution in a given space, automatically searching for the ideal design of the product. The method aims to maximize the design performance of the system regarding given conditions. In engineering practice, a given space is first described using the finite element method and, subsequently, density-based method with solid isotropic material with penalty. Then, the final shape is found using a gradient-based method, such as the optimality criteria algorithm. However, obtaining the ideal shape is highly dependent on the correct setting of numerical parameters. This paper focuses on the sensitivity analysis of key formulations of topology optimization using the implementation of mathematical programming techniques in MATLAB software. For the purposes of the study, sensitivity analysis of a simple spatial task—cantilever bending—is performed. This paper aims to present the formulations of the optimization problem—in this case, minimization of compliance. It should be noted that this paper does not present any new mathematical formulas but rather provides an introduction into the mathematical theory (including filtering methods and calculating large-size problems using the symmetry of matrices) as well as a step-by step guideline for the minimization of compliance within the density-based topology optimization and search for an optimal shape. The results can be used for complex commercial applications produced by traditional manufacturing processes or by additive manufacturing methods.
Highlights
Topology optimization is a calculation of the distribution of materials within a structure without a known pre-defined shape
The density-based method is the last of the methods commonly used for solving the topology problem. This method can be viewed as mature and is easy to implement. We focused on this method, which uses a continuous design variable ranging from
Optimization using MATLAB software was performed on multiple meshes
Summary
Topology optimization is a calculation of the distribution of materials within a structure without a known pre-defined shape. This distribution calculation yields a “black and white pattern” where black places indicate full material while white places represent voids (i.e., places where material can be removed). Because the distribution is solved over a general region, topology optimization allows us to acquire a unique, innovative, and effective structure. The principle of topology optimization is presented on the example of cantilever bending, where the initial geometry (given space) is depicted on the left and the optimal shape on the right. It allows the designer to reduce the weight of the part without losing too much of its previous properties such as stiffness, natural frequency, etc
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
