On the asymptotic behavior of shell structures and the evaluation in finite element solutions

The objective of this paper is to demonstrate how the asymptotic behavior of a shell structure, as the thickness (t) approaches zero, can be evaluated numerically. We consider three representative shell structural problems; the original Scordelis–Lo roof shell problem, a herein proposed modified Scordelis–Lo roof shell problem and the partly clamped hyperbolic paraboloid shell problem. The asymptotic behavior gives important insight into the shell load bearing capacity. The behavior should also be known when a shell problem is used to test a shell finite element procedure. We briefly review the fundamental theory of the asymptotic behavior of shells, develop our numerical schemes and perform the numerical experiments with the MITC4 shell finite element.