Finite Difference Approach to Hyperbolic Paraboloids

by M. I. Beg, Proj. Engr.; C.B.M., Inc., Chicago, IL,

Serial Information: Journal of the Structural Division, 1972, Vol. 98, Issue 2, Pg. 429-445

Document Type: Journal Paper


A square, shallow, elastic hyperbolic paraboloid shell is considered. Local failures of shell membrane and flexible edge beam in a ruled surface due to bending and twisting effects are considered under symmetric loading condition. Differential equations have been discussed with consideration of shell membrane and edge beam. Arbitrary boundary conditions in terms of Airy stress function have been used to make the solution determinant. Special considerations have been given to high and low corner junctions in the structure. Linear simultaneous equations have been formed and assemblage is shown in terms of vertical displacement components and stress functions. Convergence of the solution is shown using the finite difference method. The results are plotted in terms of functional contours for different boundary conditions.

Subject Headings: Paraboloid | Membranes | Beams | Boundary conditions | Elastic analysis | Failure analysis | Structural failures | Bending (structural)

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