The Influence of Dome Geometry on the Results of Modal and Buckling Analysis

Abstract

The main purpose of this paper is to compare the results of modal analysis for two types of domes. The first one is a low-rise Schwedler dome. The second one is a high-rise geodesic dome. The low-rise Schwedler dome is subjected to large displacement gradients and should be designed according to geometrical nonlinear analysis. In the case of high-rise geodesic dome, linear analysis is sufficient. In the modal analysis, the mass of the bars of the supporting structures was modeled as evenly distributed, while the mass of the covering and roof equipment was concentrated in the nodes. Classic calculations have been enriched with modal analysis taking into account normal forces. Normal forces affect the vibration frequency of the structure. Commonly used modal analysis does not take into account the influence of normal forces. In order to approximate the actual working conditions of the structure, calculations performed in Autodesk Robot Structure Professional 2022 can be performed in accordance with the modal analysis, taking into account the applied normal forces in the modal analysis. Additionally, stability loss was verified using linear or geometrical nonlinear buckling analysis. The exigence of including normal forces in modal analysis for low-rise domes is the novelty and main message of the work.

Keywords

• modal analysis
• finite element method
• Schwedler dome
• geodesic dome
• linear and geometrical nonlinear buckling analysis