Form exploration of shells in seismic areas

News broadcasts showing images of collapsed buildings, ravaged roads and torn-apart cities regularly remind us about the destructive power of earthquakes. While decades of research have greatly improved the understanding of these cataclysmic events, building professionals and researchers continuously try to adapt and employ the most sophisticated numerical methods to improve the behavior of buildings during a seismic event in order to safeguard their occupants.

Xochimilco Box 1 Sheet 37 1
Las Manantiales Restaurant in Mexico City, a concrete shell designed by Félix Candela that behaved excellently during the 1985 Mexico City earthquake. (Image courtesy Félix and Dorothy Candela Archive, Princeton University)

Researchers at the Form-Finding Lab of Princeton University ( are exploring the design of elegant and expressive structures that can safely be employed in seismic areas. They focus on shell structures, which are very thin, curved and typically large span structures made out of wide range of materials going from steel and glass, to concrete and even bricks or mud.

These shell structures have empirically shown their excellent performance during earthquakes, as exemplified by the undamaged survival of the shells by the acclaimed shell builder Félix Candela during the great 1985 Mexico City earthquake. Powerful computational tools, however, are needed to analyze the behavior of these structures under earthquake loading. HyperWorks, Altair’s advanced simulation software suite was used to investigate the effects of a shell’s shape on a buildings’ earthquake performance and to simulate the influence of thickness variations on the response due to shaking by an earthquake.

Optimization methods were employed to find better thickness distributions of shells and thus improve their vibrational properties.

The resistance and behavior during earthquakes could thus be predicted for a series of geometries. Additionally, optimization tools were employed not only to search for a better overall shape within the given constraints, but also to predict in what regions of the shell localized thickness changes would provide the shell with the desired vibrational properties.

The vibrational properties of singly curved and double curved shell structures are influenced by the span and form of the shell

As such, the HyperWorks suite was used to obtain a global understanding of how the form of a shell structure influences its earthquake response. The overall shape of a shell, and in particular its curvature, was shown to have a major influence on the vibrational properties and thus earthquake behavior. By increasing curvature, and thus the stiffness of the shell, the fundamental frequencies of the structures increased, ensuring that their vibration modes were triggered less by earthquakes. While thickness distribution was shown to be only of secondary importance, sizing optimization was nevertheless a useful tool to reduce stress concentrations. These understandings can greatly further the design of safe new shells in earthquake areas.

Authors: Tim Michiels, Sigrid Adriaenssens

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