UBC Theses and Dissertations
Large deflection analysis of shallow framed structures. Radomske, Brian Arthur
Elastic structures exhibit instabilities which arise through the occurrence of finite displacements even when constitutive properties remain linear. A non-linear analysis which recognizes rotations in the strain displacement relationship is formulated for analyzing three-dimensional framed structures. A finite element method is used whereby the rotations within each element are restricted in size by use of a local element reference frame attached to the element. Two such coordinate systems are developed. Then an incremental solution technique based on an instantaneous linearization of a Taylor series expansion of the forces about the displacement configuration at the beginning of each increment is developed. The snap-through buckling of shallow frames, arches and domes is studied with a view to documenting the effect on the equilibrium paths of the type of moving coordinate frame, the number of elements, and the size of the increment step.
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