Aryaman Bhatnagar
(Advisor: Dr. Emily D. Sanders)
will defend a master’s thesis entitled,
Topology Optimization of Elastic Catenary Cable Networks
On
Wednesday, October 28, 2026 at 2:00 p.m. (EDT)
Online via Zoom
Zoom link: https://gatech.zoom.us/j/5879702561
Abstract
A cable supports load by deforming into an equilibrium configuration — the catenary — in which
internal tension balances applied forces and self-weight at every point. The classical catenary
assumes inextensibility, leading to a convenient closed-form solution of the catenary’s shape, but
it neglects the elasticity of real materials. When the material’s elasticity is considered, a nonlinear
system of equations, with no closed-form solution, is needed to capture the coupling between axial
strain and structural form. Designing a network of such cables — an elastic catenary structure —
for minimal compliance, poses two key challenges: (1) the stiffness of the system depends on the
current deformed configuration (i.e., geometric nonlinearity) and (2) self-weight loads evolve with
the design (i.e., design-dependent loads), leading to a non-monotonic compliance objective
function that decreases or increases with volume when external loads or self-weight, respectively,
dominate. In this thesis, a topology optimization framework that overcomes these two challenges
is proposed for design of optimized catenary structures. A dense network of candidate cables are
sized to minimize compliance under a volume constraint. In each design iteration, the structural
response is computed using nonlinear structural analysis, in which the global tangent stiffness
matrix is assembled from individual elastic catenary elements. A sensitivity separation scheme is
adopted to decompose the objective function into monotonically increasing and decreasing
components such that a convex approximate subproblem with non-monotonic objective facilitates
use of optimality criteria methods. Key contributions include: (1) analytical sensitivities of catenary
structural compliance under design-dependent loading; (2) an open-source MATLAB code for
topology optimization of elastic catenary structures; (3) case studies investigating how geometry
and load path co-evolve, regimes where elastic catenary solutions diverge from inextensible
models, and the practicality of the proposed method for form finding of grid shells.
Committee
• Dr. Emily D. Sanders – Woodruff School of Mechanical Engineering (advisor)
• Dr. Edvard P.G. Bruun – School of Civil and Environmental Engineering
• Dr. Antonia Antoniou – Woodruff School of Mechanical Engineering