Shape Function Analysis of Three Dimensional Pre-Tensioned Spherical Dome

Abstract

   Predicting the shape function of a pre-tensioned spherical dome is very important for the safety of a dome structures design and performance under cyclic loading. This paper presents a new shape function mathematical model which is proposed for use with three dimensional pre-tensioned spherical dome that should provide for a more accurate stresses. The new model is proposed based on an improved Airy stress function principle; to retain objectivity of the results for three dimensional pre-tensioned spherical dome. This model is adopted in this study for its simplicity and computational efficiency. The objective of this work is to analyze the response and to describe the behavior of pre-tensioning dome structure under loading. The model provides a very powerful tool for the solution of many problems in elasticity; such applications include tensor analysis of the stresses and strains. Correlation between the proposed model with experimental studies results of pre-tensioned specimens are conducted and show a reasonable agreement. The results are drawn as to the applicability of this approach. Stresses within dome surface  are  constant  and  the  shear  stress  is  zero  when  subjected  to  a  hoop  stress.  The maximum stress occurs at the boundary of the dome intersecting the y-axis and is decreased  along  the  boundary  of  the  disc  as  it  nears  the  x-axis.  The maximum compressive stress occurs at the boundary intersecting with the x-axis and decreases as it nears the z-axis along the interfacing boundary.