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Optimization calculations are currently an actual and in-demand direction of computer-aided design. It allows not only the identification of the future characteristics of an object, but also the implementation of its exact model using a set of various optimization algorithms. The advent of digital modeling has significantly facilitated the approach to optimization and its methods. Many software systems are equipped with capabilities not only for calculating the design, but also for finding its optimal variant. The calculation programs can include a special optimization module that can be based on one or more mathematical methods. The purpose of the present study is to explore a process of shape optimization through the calculation of two shells: the simple one (spherical dome) and complex one (helicoid) in Comsol Multiphysics using three optimization methods: MMA, SNOPT and IPOPT. Additionally, special attention is paid to the construction of a mesh for calculations and two types of selected element sizes: finer and fine. Then, the important task is to compare the obtained results and to find the most optimal method and most effective design solution for each shell. When calculating the sphere, the most suitable solution was obtained using the IPOPT method, with the help of which it was possible to achieve an optimal reduction in the dome along the z-axis. When calculating the helicoid, all methods showed approximately the same values and equally changed the angle of inclination of the surface relative to the horizontal plane.

This paper deals with the use of the shells in the architecture of concert halls through research on the historical development of the concert building’s space. These elements are widely applied in civil engineering and architecture due to the good operational qualities, very rich spectrum of forms, the simplicity of production and its technical efficiency. The article considers two types of shells: conoid and truncated cone to choose the most optimal form for covering the concert hall.

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