Session: CIE-07-01: CAPPD General

Paper Number: 115128

115128 - Projected Barycentric Densities for Multi-Material Topology Optimization Using Shape Function With Penalization Approach 

The paper implements and proposes modifications to the Shape function with penalization (SFP) approach, initially proposded in Bruyneel(2011), to solve multi-material topology optimization (MMTO) problems. Utilizing the barycenteric nature of shape function used in Finite element method (FEM), SFP approach employs them to evaluate densities thus allowing one to solve MMTO with multiple materials while only requiring 2 or 3 varaibles per cell/element. Herein, we mathematically show that applying filtering to densities evaluated by SFP leads to barycentric filtered density fields. Applying projection directly to these filtered fields leads to loss of barycentric nature and therefore, a projection approach is proposed employing which allows one to generate barycentric projected densities.

The corresponding MMTO problem formulation is developed followed by sensitivity analysis required to conduct gradient based optimization. The obtained formulation is tested on some well known compliance minimization and compliant mechanism design problems demonstrating the method's ability to handle up to 7 materials while only employing 3 design variables per cell. Solutions show that the modified projection operator is successfully able to generate shape transition regions between material phases as well as at the solid-void interface. Observation regarding solution methodology, obtained topologies and effects of introducing different materials is also discusses.

[1] Bruyneel, Michael. "SFP—a new parameterization based on shape functions for optimal material selection: application to conventional composite plies." Structural and Multidisciplinary Optimization 43.1 (2011): 17-27.

Presenting Author: Nikhil Singh IIT Kanpur

Presenting Author Biography: Nikhil did his undergraduate from IIT Patna. Then went on to join IIT Kanpur for his masters. Currently, he is pursuing a PhD. from IIT Kanpur.

Authors:

Nikhil Singh IIT Kanpur
Anupam Saxena IIT Kanpur