Closed-form solution of axisymmetric slender elastic toroidal shells

Toroidal shells are widely used in structural engineering. The governing equations of toroidal shells are very complicated because of its variable coefficients with singularity. To find their analytical solution, traditionally, the complex form governing equations were proposed and some useful solutions were obtained. Unfortunately, no any closed-form solution has even been obtained for either general or slender toroidal shells. This paper focus on a special case of toroidal shells, i.e., slender symmetrical toroidal shells. For the first time, the closed-form solution of this kind of shell has been successfully obtained from displacement form governing equations. The closed-form solution is demonstrated for the example of thermal compensation devices. The correction of well-known Dahl formula for slender toroidal shell has been proposed based on the solution obtained in this paper. DOI: 10.1061/(ASCE)EM.1943-7889.0000175 CE Database subject headings: Shells; Axisymmetry; Bending; Deformation; Elasticity; Closed form solutions. Author keywords: Toroidal shells; Axisymmetry; Revolution shells; Slender shells; Bending; Deformation; Elastic materials.