Spirally sinusoidal stress distributions in elastic helicoidal shells

The Static‐Geometric Duality and a Staggered Mesh Scheme in the Numerical Solution of Some Shell Problems

“…The finite difference solution was tested against the available shallow shell solutions [4,5,9] and asymptotic solution [4]. The results are in excellent agreement with the shallow shell solution for A ;S 0.2 and (APmin) -1 ;S 0.2 and with the asymptotic solution for f..l ;;:: 10.…”

“…The asymptotic solution obtained in [4] shows that there is an edge zone phenomenon for f..l » 1. * Expressions for stress measures which are exact to within the error inherent in a first approximation shell theory were used instead of (2.8) in [3].…”

“…discussed in [4]. An asymptotic solution for nonshallow but "sufficiently thin" shells was also obtained in [4J for moderate values of A.. For the range of values of A. and y = 'o/h not covered by these solutions, a finite difference solution is appropriate.…”

“…* Expressions for stress measures which are exact to within the error inherent in a first approximation shell theory were used instead of (2.8) in [3]. It should be noted that for shell theory to be applicable, we must have…”

“…(r) and cf> (r) are then determined by two (1. 3) with (X = (a 2 + r2)1/2, and L* obtained from L by replacing Vs by -Vb-In the absence of surface load, the load terms fl and f2 are given by…”