I³MS - Saxena Seminar

Prof. Dr. Anupam Saxena - Contact in Topology Optimization: Challenges and Solution Strategies

Department of Mechanical Engineering, Indian Institute of Technology, Kanpur

Abstract

Topology Optimization of large deformation planar continua will be
formulated. Two parameterization schemes, namely, frame- and continuum-
based, will be exemplified using small deformation theory for familiarity
with existing, gradient- and function- based, topology optimization
schemes. Within continuum parameterization, rectangular and hexagonal
tessellations will be discussed. The first set of challenges pertaining to
connectivity singularities, namely, checkerboards and point flexures will
be highlighted, and remedies will be mentioned. Constituents of planar
continua undergoing large deformation have a tendency to come in contact.
This aspect can either be avoided, or used to advantage
to design continua that can deliver the desired, intricate deformation
characteristics. Many challenges, when adapting topology optimization to
incorporate contact interactions, will be highlighted and solution
strategies will be discussed. These challenges pertain to mesh handling,
generation/evaluation of binary continua, non-convergence in finite
element analysis, generation of rigid contact surfaces in vicinity of
largely deforming constituents, and other factors. It will be argued that
zero-order searches, albeit computationally costly, seem more viable in
addressing these problems. The talk will culminate with examples on large
deformation monolithic gripper-manipulator, and path generating continua
that can exhibit one or more desired kinks in the path by effectively
employing contact interactions. Some open problems will also be
highlighted.