Stable Topology Optimization: A Barycentric Coordinates Approach

Education - Lecture/Discussion - WPI Only

Wednesday, February 20, 2013
12:00 PM-1:00 PM

Kaven Hall

Glaucio H. Paulino

A prevalent problem in the field of topology optimization has been instabilities such as the appearance of checkerboard patterns when using low-order triangles and quads. As we will show, discretizations based on polygonal finite elements, naturally provide stable solutions. The better performance of polygonal discretizations is attributed to their enhanced approximation characteristics, which also alleviate shear locking in elasticity and lead to a stable low-order mixed variational formulation of incompressible Stokes flow. We will present a simple but robust algorithm that utilizes centroidal Voronoi tessellations to generate convex polygonal meshes that possess enhanced regularity and isotropy. We will assess the performance of polygonal discretizations in elasticity and Stokes flow and discuss their applications to topology optimization problems in both solids and fluids. The applications addressed involve diverse fields such as bio-inspired design of innovative building systems and design of patient-specific large craniofacial segmental bone replacements.

Prof. Paulino is the Donald and Elizabeth Willett Endowed Professor of Engineering at the University of Illinois at Urbana-Champaign (UIUC). He joined the Civil and Environmental Engineering Department (CEE) as an Assistant Professor in 1999, was promoted to Associate Professor in 2001, and to Full Professor in 2005. From 2009 to 2011 he was director of the Mechanics of Materials program at the National Science Foundation. He was also acting director of the Nano and Biomechanics program at NSF. His seminal contributions in the area of computational mechanics include development of methodologies to characterize the deformation and fracture behavior of existing and emerging materials and structural systems; and topology optimization for large-scale multiscale/multiphysics problems. More information about his research and professional activities can be found at the following url:

Suggested Audiences: College


Last Modified: February 18, 2013 at 5:52 PM

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