To-date, there is no closed-form solution that can predict the maximum deflection of hypar umbrellas due to their highly varying and complex geometry. This paper uses machine learning via genetic programming (GP) and gene expression programming (GEP) to develop closed-form equations that predict the maximum corner deflection of N-edged hypar umbrellas for the first time. The maximum corner deflection from finite element analyses was used to generate a large dataset of 53,754 training/testing data. It is observed that both GP and GEP can effectively parameterize the maximum deflection of N-edged hypar umbrellas, with GEP producing more concise, but relatively less accurate, equations than GP. The results of the study can be used to assist with conceptual design of hypar umbrellas and while illustrating the use of machine learning techniques for the design and analysis of structures with highly varying geometries.

Relevant Publications

ElDarwich, H., Mansouri, I., Garlock, M., Wang, S. (2024). Predicting maximum deflection of N-edged thin-shelled hyperbolic-paraboloid umbrella using machine learning techniques. Thin-Walled Structures, 205

The striking tiled domes of the Ballet School of the Instituto Superior de Arte (ISA) in Havana are internationally acclaimed Cuban architectural icons. However, due to their deceptive tiled appearance and their only recently rediscovered hybrid tile–concrete construction system, the domes have eluded structural study and characterization. Yet, such studies are increasingly demanded not only because of their unique morphology and monumental status, but also because of their visible damage. This work defined a suitable numerical analysis method for diagnosing these hybrid structures by applying both linear elastic and nonlinear (using the damaged concrete plasticity constitutive model) numerical analyses. A site investigation campaign provided materials and geometric data that informed model creation and damage documentation which validated the analysis results.

A new synthesis of architectural and technical sources covering the development and spread of the hybrid structural system allowed the ISA domes to be placed, for the first time, in their proper structural context and, consequently, for their conception and design to be understood more fully. Because the investigation indicated significant risk of irreversible damage or failure without timely intervention, preliminary intervention explorations were conducted. Based on a holistic understanding of the structures, a technically, architecturally, and culturally optimal solution was identified.

Relevant Publications

Hughes, M., Celli, S., Heubner, C., Garlock, M., Ottoni, F., Del Curto, D., Wang, S., Glisic, B. (2023). Nonlinear finite-element analysis for structural investigation and preservation of reinforced hybrid thin tile-reinforced concrete domes of the historic school of ballet classrooms in Havana, Cuba. Journal of Performance of Constructed Facilities (ASCE), 37 (1)

Félix Candela was a celebrated builder of thin concrete hyperbolic paraboloidal (hypar) shells with a lasting legacy on the rationalist architectural movement of the 20th century. The iconic hypar umbrella became one of Candela most defining works of structural art due to its structural efficiency, economical constructability, and striking elegance. We employ finite element modeling to ascertain the structural performance of hypar umbrellas exhibiting three (triangular), four (square), and six (hexagonal) edges.

This research constitutes an ongoing effort aimed at revitalizing the adoption of thin hypar shells within contemporary architecture and engineering. By exploring the mechanisms governing their response, we present a pathway towards the potential reemergence of Candela's umbrellas to address the increasingly diverse challenges facing the structural engineering discipline in the 21st century.

Relevant Publications

Wang, S., Contreras-Jimenez, J. A., Jorquera-Lucerga, J. J., Garlock, M. (2022). Structural analysis of Félix Candela’s hexagonal hyperbolic paraboloidal umbrellas. Engineering Structures, 266

Wang, S., Garlock, M., Glisic, B. (2022). Geometric and area parameterization of N-edged hyperbolic paraboloidal umbrellas. Engineering Structures, 250

Wang, S., Levine, A., Garlock, M., Contreras-Jimenez, J. A., Jorquera-Lucerga, J. J. (2020). Structural evaluation of Félix Candela’s 8-sided hyperbolic paraboloidal umbrellas. Engineering Structures, 222