Automatic Design in Matlab Using PDE Toolbox for Shape and Topology Optimization

Author(s):  
Yilun Sun ◽  
Lingji Xu ◽  
Jingru Yang ◽  
Tim C. Lueth

Abstract In this paper, we present a novel concept of using Matlab’s Partial Differential Equation (PDE) Toolbox to achieve shape and topology optimization during the automatic mechanical design process. In our institute, we are developing a toolbox called Solid Geometry (SG) Library in Matlab to achieve automatic design of medical robots and mechanisms. The entire design process is performed in one developing environment without additional data input and output. And those robots and mechanisms can be quickly manufactured by different kinds of 3D printers. Recently, we have also integrated the shape and topology optimization techniques into our automatic design process by using the PDE Toolbox of Matlab for finite element analysis because of its high efficiency and compactness. For optimization algorithms, we have already implemented two bionic structural optimization methods called Computer Aided Optimization (CAO) and Soft Kill Option (SKO) to optimize the stress distribution in the structure. Since the complicated material layout in the optimization results can be easily realized by the 3D printing technology, the mechanical performance of our medical robots and mechanisms can be greatly improved with the work presented in this paper.

Author(s):  
Piotr Fulmański ◽  
Antoine Laurain ◽  
Jean-Francois Scheid ◽  
Jan Sokołowski

A Level Set Method in Shape and Topology Optimization for Variational InequalitiesThe level set method is used for shape optimization of the energy functional for the Signorini problem. The boundary variations technique is used in order to derive the shape gradients of the energy functional. The conical differentiability of solutions with respect to the boundary variations is exploited. The topology modifications during the optimization process are identified by means of an asymptotic analysis. The topological derivatives of the energy shape functional are employed for the topology variations in the form of small holes. The derivation of topological derivatives is performed within the framework proposed in (Sokołowski and Żochowski, 2003). Numerical results confirm that the method is efficient and gives better results compared with the classical shape optimization techniques.


Author(s):  
Piotr Putek ◽  
Roland Pulch ◽  
Andreas Bartel ◽  
E Jan W ter Maten ◽  
Michael Günther ◽  
...  

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