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.