AbstractThe use of conventional beam elements in the stiffness method of analysis is investigated to identify deficiencies associated with their use in static, dynamic and buckling analyses.
A new procedure is proposed to overcome these deficiencies using a recently developed element. This element consists of the conventional beam element capability together with a series of additional Legendre' type functions . These functions can be generated to any required order to suit the accuracy of analysis. A set of algorithms are also developed to suit the new formulation in order to reduce computation time.
In static analysis, the use of the new element is demonstrated by its use in a series of practical examples involving a variety of geometries and loading conditions. The element is also extended to two and three dimensional structural forms. A conventional bar element is also studied and the capabilities compared with a series of alternative new elements subjected to a variety of practical loadings.
The natural frequencies associated with the free vibration of structures is then considered. The eigenvalues linked with this type of analysis are determined using a form of substructuring which involves the condensation of the extra degrees of freedom generated from the use of the new element. The associated eigenvectors are computed using a random generation techniques for which a new computer program has been developed.
Linear elastic instability of slender beams is also investigated. The buckling loads associated with this type of analysis are computed in the same manner as for the natural frequencies. The use of the new element is extended to a space frame with asymmetrical loading.
The free vibration of deep beams constitutes the final study. Many existing elements are reviewed and a new element is proposed and benchmarked.
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