Abstract
The Marguerre equations governing the finite deflections of spherical caps are adopted in the form of three equilibrium equations with u9 v9 and w, the usual displacement quantities, which are also the dependent variables in the differential equations. The equations are solved for different load situations using a finite difference nonlinear relaxation technique. A number of axisymmetric problems are solved including the following: a) uniformly loaded cap, b) cosine loaded cap, and c) uniformly loaded cap with clamped apex region. Complete response solutions are presented up to and including instability for two asymmetric problems—the quarter and semicircular (uniformly) loaded clamped caps. The results indicate that the smaller the load area, the lower the associated buckling pressure. An important finding is that the finite difference approximation to the V operator is grossly inaccurate in the vicinity of the pole for asymmetric problems. A general remedy is suggested.
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