Investigating the Tansitional State Between Rectangular Plates and Shallow Shells

Abstract

The stiffness of rectangular plates can be increased by inducing a rise at the center of these plates; this rise converts the plates from two-dimensional stiffness elements into three-dimensional stiffness elements. This slight change in the geometry shifts the state of stresses from mainly bending stresses to tensilecompressive stresses. The rise at the center of a rectangular plate is increased gradually to the point where a shell element is formed. This paper focuses on this particular transition between the plate elements to the shell element which is called the transitional rise. Several finite element models were used to identify the transitional rise given fixed parameters. Stresses and deflections are also studied for each case. An optimized approach was used to minimize the cost and improve the serviceability of the structural elements. In this present study, numerous analyses were conducted using the finite element methodology on shell model. Finite element mesh was established for each different rise value starting from zero (plate). The rise is increased gradually to the point where shell stiffness becomes insensitive to the increase in the rise. An empirical relationship was established between the transition state between plate and shell elements. Parametric study is also conducted using several loading cases.)