*********************************
There is now a CONTENT FREEZE for Mercury while we switch to a new platform. It began on Friday, March 10 at 6pm and will end on Wednesday, March 15 at noon. No new content can be created during this time, but all material in the system as of the beginning of the freeze will be migrated to the new platform, including users and groups. Functionally the new site is identical to the old one. webteam@gatech.edu
*********************************
Ph.D. Thesis Defense Announcement
Topology Optimization with Multiple Materials, Multiple Constraints, and Multiple Load Cases
By
Xiaojia Shelly Zhang
Advisor:
Dr. Glaucio H. Paulino (CEE)
Committee Members:
Dr. Eric de Sturler (Math, Virginia Tech), Dr. Alexander Shapiro (ISYE), Dr. Yang Wang (CEE),
Dr. Alok Sutradhar, (MAE, Ohio State), Dr. Lucia Mirabella (Corporate Technology, Siemens Corporation)
Date & Time: Monday, July 30, 2018, 1:30PM
Location: Sustainable Education Building 122
ABSTRACT
Topology optimization is a practical tool that allows for improved structural designs. This thesis focuses
on developing both theoretical foundations and computational frameworks for topology optimization to
effectively and efficiently handle many materials, many constraints, and many load cases. Most work in
topology optimization has been restricted to linear material with limited constraint settings for multiple
materials. To address these issues, we propose a general multi-material topology optimization formulation
with material nonlinearity. This formulation handles an arbitrary number of materials with flexible material
properties, features freely specified material layers, and includes a generalized volume constraint setting.
To efficiently handle such arbitrary constraints, we derive an update scheme that performs robust updates
of design variables associated with each constraint independently. The derivation is based on the
separable feature of the dual problem of the convex approximated primal subproblem with respect to the
Lagrange multipliers, and thus the update of design variables in each constraint only depends on the
corresponding Lagrange multiplier. This thesis also presents an efficient filtering scheme, with
reduced-order modeling, and demonstrates its application to 2D and 3D topology optimization of truss
networks. The proposed filtering scheme extracts valid structures, yields the displacement field without
artificial stiffness, and improve convergence, leading to drastically improved computational performance.
To obtain designs under many load cases, we present a randomized approach that efficiently optimizes
structures under hundreds of load cases. This approach only uses 5 or 6 stochastic sample load cases,
instead of hundreds, to obtain similar optimized designs (for both continuum and truss approaches).
Through examples using Ogden-based, bilinear, and linear materials, we demonstrate that proposed
topology optimization frameworks with the new multi-material formulation, update scheme, and discrete
filtering lead to a design tool that not only finds the optimal topology but also selects the proper type and
amount of material with drastically reduced computational cost.
