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H.A. Mang, R.H. Gallagher:
"Finite Elemente Analysis of Thin Shells of General Form for Displacement-Dependent Loads";
in: "1981 ASME Winter Annual Meeting on Nonlinear Finite Element Analysis of Thin Shells", ASME, Washington, D.C., USA, 1981, 65 - 82.

Consideration of the dependence of hydrostatic pressure on the displacements may result in more or less significant changes of buckling and ultimate loads, respectively, of thin arches and shells. The finite element method has made it possible to quantify these changes. Within the framework of this method, the follower-load of hydrostatic pressure is refected by the so-called pressure-stiffness matrix. For shells with loaded free edges, this matrix becomes unsymmetric. The theoretical goal of hte present paper is to demonstrate that symmetrization of the pressure stiffness matrix yields buckling loads which are identical to the eigenvalue resulting form first-order perturbation analysis of the actual unsymmetric eigenproblem. This result is importatn if the existing computer program is restricted to the handling of symmetric matrices. In the buckling pressures of arches and shells increases with a decreasing number of waves of the buckled shape.