Topology Optimization Design of 3D Continuum Structure with Reserved Hole Based on Variable Density Method

Abstract

An objective function defined by minimum compliance of topology optimization for 3D continuum structure was established to search optimal material distribution constrained by the predetermined volume restriction. Based on the improved SIMP (solid isotropic microstructures with penalization) model and the new sensitivity filtering technique, basic iteration equations of 3D finite element analysis were deduced and solved by optimization criterion method. All the above procedures were written in MATLAB programming language, and the topology optimization design examples of 3D continuum structure with reserved hole were examined repeatedly by observing various indexes, including compliance, maximum displacement, and density index. The influence of mesh, penalty factors, and filter radius on the topology results was analyzed. Computational results showed that the finer or coarser the mesh number was, the larger the compliance, maximum displacement, and density index would be. When the filtering radius was larger than 1.0, the topology shape no longer appeared as a chessboard problem, thus suggesting that the presented sensitivity filtering method was valid. The penalty factor should be an integer because iteration steps increased greatly when it is a noninteger. The above modified variable density method could provide technical routes for topology optimization design of more complex 3D continuum structures in the future.

Data-driven topology optimization of spinodoid metamaterials with seamlessly tunable anisotropy

“…for spinodoids, ρ ∈ {0} ∪ [ρ min , 1] and θ 1 , θ 2 , θ 3 ∈ {0} ∪ [0, π/2]. Similar observations were reported and explained previously by, e.g., Shiye and Jiejiang (2016) and Kumar et al (2020b).…”

Sensitivity Analysis and Filtering of Machinable Parts Using Density-Based Topology Optimization

“…A wide range of values is considered fo the mentioned parameters, and calculation times, discreteness and machinability of the results are presented. It is important to note that other studies [1,24,25] make remarkable contributions in this area, but none of them are specifically oriented to a concrete manufacturing method and are often limited to a short set of values for the studied parameters, they don't take into account the mesh depencency, or study only the 2D case. Other works [26,27] concentrate on achieving these manufacturable parts by adding filters and additional constraints to the TO process, but a more direct aplication is searched in the present paper.…”

“…For penalization p, previous studies [1,24] indicate that a minimum value of 3 should be used for isotropic materials with a Poisson Ratio ν ~ 1/3, within the defined topology optimization method. The relative density of each element, as shown in Error!…”

“…However, as the penalization increases, the differences in the results become smaller [25]. To analyze the parameter's impact, values ranging from three (3) to six (6), inclusive, with increments of one (1) are chosen based on previous studies [1,24] indicate. By using these values, it becomes possible to observe the transitional changes in the resultant shapes when larger penalization values are employed.…”

“…Topology optimization (TO) is a design tool for obtaining optimal shapes with known conditions, based on the optimization problem definition; In other words, it aims to achieve the best possible result for a given function while applying specific constraints. Topology optimization has been increasingly used during the last years, as well as the research on the topic and the development of commercial software for obtaining topology parts, as mentioned by Shiye and Jiejiang [1]. Nevertheless, the foundations of TO theory were established over a century ago [2], with major applications to the actual theory with the guidelines developed by Dorn [3].…”