# Explicit three dimensional topology optimization via Moving Morphable Void (MMV) approach

## TL;DR

This paper introduces an explicit 3D topology optimization method using Moving Morphable Voids (MMVs) that reduces computational complexity by decreasing design variables and finite element degrees of freedom, improving efficiency.

## Contribution

The paper presents a novel explicit 3D topology optimization approach based on MMVs that significantly reduces computational effort compared to traditional methods.

## Key findings

- Reduces number of design variables and DOFs in FEA
- Overcomes computational bottlenecks in 3D topology optimization
- Enhances solution efficiency significantly

## Abstract

Three dimensional (3D) topology optimization problems always involve huge numbers of Degrees of Freedom (DOFs) in finite element analysis (FEA) and design variables in numerical optimization, respectively. This will inevitably lead to large computational efforts in the solution process. In the present paper, an efficient and explicit topology optimization approach which can reduce not only the number of design variables but also the number of degrees of freedom in FEA is proposed based on the Moving Morphable Voids (MMVs) solution framework. This is achieved by introducing a set of geometry parameters (e.g., control points of B-spline surfaces) to describe the boundary of a structure explicitly and removing the unnecessary DOFs from the FE model at every step of numerical optimization. Numerical examples demonstrate that the proposed approach does can overcome the bottleneck problems associated with a 3D topology optimization problem in a straightforward way and enhance the solution efficiency significantly.

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Source: https://tomesphere.com/paper/1704.06060