Strength, Stability and Dynamics of Rigid Shells: Analysis of Recent Research

Many numerical methods of analysis of rigid shells, such as the displacement-based finite element method (FEM), finite difference energy method, method of separation of variables, kinematic method of the theory of limit equilibrium, and so on, were proposed and tested until 2000. Most problems of static and dynamic analysis of canonical shells were successfully solved at the same time. All these methods were used actively after the 2000, too. However, new problems began to appear before structural engineers, architects, and builders. These problems are associated with multi-layer shell walls, with the emergence of new composite construction materials, and therefore, with the solution of physically nonlinear problems. Geometricians presented several hundred new forms of middle surfaces of shells, and that is why the need to select optimal forms from several alternatives using criteria of optimality came into existence. The selection of necessary computing software from many of their types began to be a problem. New problems demanded new methods of approach for their solution. In this paper, a critical evaluation of proposed solutions on strength, stability, and vibration analysis of shells was conducted in connection with new problems that appeared after the year 2000. Rigid shells in the form of analytical surfaces, designed using the canon of parametric architecture, were taken as an example. Analytical middle surfaces of shells, which attracted the attention of architects after 2000, are pointed out, and suitable methods of analysis of these shells are noted for the first time. The review was compiled based on 112 fundamental scientific works published after 2000. Other scientific reviews devoted to the investigation of joint problems of geometry, application, and calculation of assembled rigid thin-walled shells with analytical middle surfaces were not found.