Geometric modeling and linear static analysis of thin shells in the form of cylindroids

Abstract

Aims. Thin shells in the form of cylindroids are fourth-degree ruled shells for which few works are devoted. In this paper, their geometric modeling is worked out and their middle surface are plotted, using the software MathCAD. Their stress-strain state are instigated with two building material: reinforcement concert and qualitative steel. Methods. This linear investigation is done for fixed and hinged supports and for various thicknesses in the software SCAD. The numerical values of their maximum and minimum displacements of their middle surfaces are given. Based on these displacements, conclusions are made for the whole paper. Results. The linear analysis for reinforced concrete and metallic shells, computed using the software SCAD gives the numerical and graphical results that are presented. Conclusions. The investigations of the stress-strain state are done for shells with the shape of cylindroid with two directrices ellipses and cylindroid Frazer. For the same thickness, loading and span, the reinforced concrete shells has minimum displacements. For thickness, 20 cm the steel shells have the same maximum displacements. For the thickness 30 cm the maximum displacement is more in steel shells. It is more optimal to use reinforced concrete shells than the one in steel. A large span (till 30 m) shells can be designed with reinforced concrete.

Keywords

• cylindroid surfaces
• linear investigation
• geometric modeling
• stress-strain state
• displacements
• middle surfaces