Optimal Forms of Shallow Arches with Respect to Vibration and Stability
Titel:
Optimal Forms of Shallow Arches with Respect to Vibration and Stability
Auteur:
Plaut, Raymond H. Olhoff, Niels
Verschenen in:
Mechanics based design of structures & machines
Paginering:
Jaargang 11 (1983) nr. 1 pagina's 81-100
Jaar:
1983
Inhoud:
Shallow, linearly elastic arches of unspecified form but with given uniform cross section and material are considered. For given span and length of the arch, two different optimization problems are formulated and solved. In the first, we determine the form of the arch which maximizes the fundamental vibration frequency. The corresponding vibration mode turns out to be either symmetric or antisymmetric. In the second, a static load with given spatial distribution is considered, and the critical value of the load magnitude for snap-through instability is maximized. This instability may occur at a limit point or a bifurcation point. Optimal forms are determined for sinusoidal loading, uniform loading, and a central concentrated load. In both types of problems, arches with simply supported or clamped ends are considered, and the maximum frequencies and critical loads obtained are compared to those for a circular arch with similar end conditions. In all the cases with simply supported ends, it is found that a circular arch is almost optimal. For clamped ends, however, it turns out that the optimal arches have zero slope at the ends and that they are much more efficient than a circular arch.
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