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Altair > Case Studies > Structural Optimization of Concrete Shells in Seismic Areas: A Case Study

Structural Optimization of Concrete Shells in Seismic Areas: A Case Study

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Sensors - Vibration Sensors

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The Challenge

The Form Finding Lab at Princeton University was faced with the challenge of designing expressive structures that can safely be employed in seismic areas. The focus was on shell structures, which are thin, curved, and typically large span structures made out of a wide range of materials ranging from steel and glass, to concrete and even bricks or mud. These 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. However, powerful computational tools were needed to analyze the behavior of these structures under earthquake loading. The researchers needed to investigate the effects of a shell’s shape on a buildings’ performance during an earthquake and to simulate the influence of thickness variations on the response due to shaking caused by the earthquake.

About The Customer

Princeton University is a vibrant community of scholarship and learning that stands in the nation's service and in the service of all nations. Chartered in 1746, Princeton is the fourth-oldest college in the United States. Princeton is an independent, coeducational, nondenominational institution that provides undergraduate and graduate instruction in the humanities, social sciences, natural sciences and engineering. As a world-renowned research university, Princeton seeks to achieve the highest levels of distinction in the discovery and transmission of knowledge and understanding. The Form Finding Lab at Princeton University, USA is a research group that focuses on structural systems that derive their strength from their curved shape dictated by the flow of forces. The director of the Form Finding Lab is Sigrid Adriaenssens, PhD, structural engineer specialized in the form finding of structural surfaces.

The Solution

The researchers of the Form-Finding lab resorted to HyperWorks, Altair’s advanced simulation software suite, to perform their simulations and analyses. The suite was used to investigate the effects of a shell’s shape on a buildings’ performance during an earthquake and to simulate the influence of thickness variations on the response due to shaking caused by the earthquake. Geometries could readily be imported from other CAD-software into HyperMesh, and after inserting further model properties, the effects of different earthquakes could be simulated using HyperWorks’ integrated OptiStruct solver. The resistance and behavior during earthquakes could thus be predicted for a series of geometries. Additionally, the built-in optimization tools in OptiStruct allowed not only to search for a better overall shape within the given constraints, but could also be used to predict the regions of the shell’s localized thickness where changes would provide the shell with the desired vibrational properties.

Operational Impact

The HyperWorks suite was used to obtain a global understanding of how the form of a shell structure influences its response to an earthquake. 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 corresponding 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. The researchers plan to continue this investigation by applying the understandings of how form influences the flow of earthquake forces in shells to real structures, such as the ones of Félix Candela. Furthermore they anticipate using the gathered data to design prototype shell structures from innovative and low-cost materials that can resist earthquakes.

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