Ongoing Initiatives

Continuum-Based Topology Optimization of Frames via Geometry Projection

One of the challenges of continuum-based topology optimization is that the resulting optimal topologies are often difficult to translate into manufacturable concepts.  Optimal topologies typically exhibit members of varying cross section which cannot be easily manufactured.  In the case of frames, one wishes to employ stock material, such as bars, tubes, I-beams, etc.  Discrete topology optimization via the ground structure approach naturally handles this requirement, but it cannot incorporate multiaxial stress criteria since the analysis model is inherently one-dimensional; also, it cannot easily handle the situation when the members overlap, as would be the case if, e.g., one welds two bars one on top of each other.  In our research we project the geometry of a finite set of bars of constant (in-plane) width onto the analysis grid, and penalize the (out-of-plane) thickness so that the optimizer can remove bars from the design space.  The continuous and differentiable projection renders a density field, such as the one used in SIMP topology optimization.  Hence, by using the chain rule we obtain sensitivities of the structural responses with respect to the bar design variables.

In collaboration with Daniel Tortorelli (University of Illinois at Urbana-Champaign).

Funding: University of Connecticut


This picture shows the main ingredients of a Geometry Projection Method for Continuum-Based Topology Optimization of Frames, including a flow chart of the method, an illustration of the geometry projection operation based on the signed distance function, and an example topology optimization run on a cantilever beam.
Geometry Projection Method for Continuum-Based Topology Optimization of Frames

Design Optimization of Bone Scaffolds Fabricated via Micro-Robotic Deposition

Natural and synthetic bone graft materials, or scaffolds, are used in a range of orthopedic, cranio and maxillofacial applications to treat bone defects caused by trauma, disease, or congenital defects.  In this project we employ a cellular solids model to establish closed-form relations between the manufacturing parameters and elastic properties of hydroxyapatite (HA) and β-tricalcium phosphate (β-TCP) scaffolds fabricated via micro-robotic deposition, which have been shown to enhance bone regeneration.  The scaffolds consist of alternating layers of extruded rods, that upon sintering form a 3-d lattice.  From a mechanical design point of view, the scaffold must be porous enough so as to favor bone growth inside the scaffold, and it must be strong enough so as to bear the loads imposed by the surrounding bone on the implant.  The second part of our project consists of coupling the cellular solids model with a continuum-based structural optimization method in order to design patient-specific scaffold layouts (i.e. with varying rod orientation and separation).


This picture shows the main elements of a Cellular Solids Model for the Stiffness-Based Design of Bone Scaffolds Fabricated Via Micro-Robotic Deposition, including a photo of a fabricated scaffold, a finite element mesh for the numerical calibration of the cellular solids model, and design charts derived from the model.
A Cellular Solids Model for the Stiffness-Based Design of Bone Scaffolds Fabricated Via Micro-Robotic Deposition

Funding: University of Connecticut

Topology Optimization of Welded Plate Structures

In this project we investigate a computational topology optimization method for the design exploration of welded fabrications. We aim to render optimal topologies that are made of distinct plate load paths (possibly with holes), thereby facilitating the translation of the optimal topology into a structural design concept that can be readily manufactured by welding of cut plates. This methodology will greatly decrease the time that designers have to spend producing a manufacturable fabrication out of the results of conventional topology optimization, which typically produces load paths of variable cross section that cannot be easily captured with plates.

This picture shows an example (a cantilever beam) of the application of the geometry projection-based topology optimization method to the design of structures made of plates.
Topology Optimization to Produce Plate Structures

Funding: Caterpillar Inc.