Research

Multiscale Multiphysics Topology Optimization

Topology optimization is concerned with determining optimal layout of a specified amount of given materials within a design domain that optimizes the desired performance measures. Performance can be measured in terms of compliance (maximizing stiffness), energy absorption capacity, wave propagation properties, etc.

Areas of interest

Topology optimization of nonlinear systems.
Metamaterial designs using topology optimization.
Multiscale material design using topology optimization.
Development of novel material systems using additive manufacturing.
Isogeometric methods in topology optimization.
Geometric and material nonlinearities in topology optimization.
Sensitivity analyses of complex nonlinear coupled transient systems.
Uncertainty quantification in topology optimization.
Level set methods for topology optimization.
Dual methods for nonconvex topology optimization.

Diagram: multiscale-multiphysics topology optimization at the center of six linked areas: multiscale multiphysics models, large-scale response simulation, nonlinear response sensitivity, design constraints (performance, manufacturing), uncertainty quantification, and non-convex optimization

Topology-optimized beam designs under distributed load

Density-based topology optimization: design domain, element discretization, and resulting layout

3D L-bracket design domain and optimized result

Optimized periodic metamaterial microstructures

Optimized metamaterial microstructures with larger voids

Cantilever design domain and optimized cantilever designs

3D cantilever design domain and optimized result

3D simply supported beam design domain and optimized result

Videos

Selected Simulation and Optimization Results

Topology Optimization - 3D Examples (Stream in HD for best results)

Problem Data:

1.26 million DOFs

0.1 Volume fraction

Topology Optimization - 2D Examples (Stream in HD for best results)

Multimaterial Topology Optimization - 2D/3D Examples

Stiffness: Yellow Phase < Blue Phase < Red Phase

Density: Yellow Phase < Blue Phase < Red Phase

Selected Publications

Li, L., Zhang, G. and Khandelwal, K. (2017). “Design of Energy Dissipating Elastoplastic Structures under Cyclic Loads using Topology Optimization." Structural and Multidisciplinary Optimization. (DOI)
Li, L., Zhang, G. and Khandelwal, K. (2017). “Topology Optimization of Energy Absorbing Structures with Maximum Damage Constraint.” International Journal of Numerical Methods in Engineering. (DOI)
Li, L., Zhang, G. and Khandelwal, K. (2017). “Topology Optimization of Gradient Elastic Material Structures.” Structural and Multidisciplinary Optimization. (DOI)
Li, L. and Khandelwal, K. (2016). "Topology Optimization of Geometrically Nonlinear Trusses with Spurious Eigenmodes Control." Engineering Structures. (DOI).
Zhang, G., Li, L. and Khandelwal, K. (2016). "Topology Optimization of Structures with Anisotropic Plastic Materials using Enhanced Assumed Strain Elements." Structural and Multidisciplinary Optimization. (DOI). Read-Cube Link
Kiran R., Li, L. and Khandelwal, K. (2016). "Complex Perturbation Method for Sensitivity Analysis of Nonlinear Trusses." Journal of Structural Engineering. (DOI).
Li, L. and Khandelwal, K. (2015). "Topology Optimization of Structures with Length-scale Effects using Elasticity with Microstructure Theory." Computers & Structures. Vol. 157, pg. 165-177. (DOI).
Li, L. and Khandelwal, K. (2015). "An Adaptive Quadratic Approximation for Structural and Topology Optimization." Computers & Structures, Vol. 151, pg. 130-147. (DOI).
Li, L. and Khandelwal, K. (2015). "Volume Preserving Projection Filters and Continuation Methods in Topology Optimization." Engineering Structures. Vol 85, pg. 144-161 (DOI).
Li, L. and Khandelwal, K. (2014). "Two-Point Gradient-Based MMA (TGMMA) Algorithm for Topology Optimization." Computers & Structures, Vol. 131, pg. 34-45. (DOI).
Tovar, A. and Khandelwal, K. (2013). "Topology optimization for minimum compliance using a control strategy." Engineering Structures, Vol. 48, pg. 674-682.(DOI).