Thumbnail Image

Membrane deformation of transitional shells by finite differences

Lawrence, Samir Albert
Scope of Study: A systematic finite difference procedure for the solution of the differential equations of the membrane deformations of translational shells is presented.
The solution for the vertical deformation w is obtained in terms of the stress resultant Ny. In this solution some simplifications are made in evaluating the term R. These simplifications are accomplished by the use of power series and the neglect of fourth order powers of the slopes in comparison with unity.
The solutions for the horizontal deformations u and v are obtained in terms of w.
Findings and Conclusions: The systematic finite difference procedure makes the solution for the membrane deformations of translational shells a simple and straight forward process.
The simplifications made in the term R eliminate complicated numerical differentiation and permit the evaluation of R in terms of the Ny membrane forces only.