The multipurpose optimal design of elastic structures with a piecewise uniform cross section

Abstract This paper calls attention to a new method of dealing with deflections of beams, the cross sections of which vary by steps. It is shown that the effect of this variation on the shape of the deflection curve can be represented by a properly chosen force system acting on a beam of uniform cross section. There is no approximation involved in this substitution, whereby the original problem is reduced to one of computing deflections of beams of constant cross section.

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Computer Aided Optimal Design of Elastic Structures

Computer Aided Optimal Design: Structural and Mechanical Systems ◽

10.1007/978-3-642-83051-8_25 ◽

1987 ◽

pp. 831-900 ◽

Cited By ~ 7

Author(s):

C. Fleury

Keyword(s):

Optimal Design ◽

Elastic Structures ◽

Computer Aided

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Effects of the wall curvature on the flow in a duct of uniform cross-section

Acta Mechanica ◽

10.1007/s00707-003-0071-0 ◽

2004 ◽

Vol 167 (3-4) ◽

pp. 123-130 ◽

Cited By ~ 1

Author(s):

M. E. Erdogan ◽

C. E. Imrak

Keyword(s):

Cross Section ◽

Uniform Cross Section

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Rayleigh–Bloch surface waves along periodic gratings and their connection with trapped modes in waveguides

Journal of Fluid Mechanics ◽

10.1017/s0022112099004425 ◽

1999 ◽

Vol 386 ◽

pp. 233-258 ◽

Cited By ~ 65

Author(s):

R. PORTER ◽

D. V. EVANS

Keyword(s):

Finite Number ◽

Surface Waves ◽

Cross Section ◽

Electromagnetic Waves ◽

Mode Shapes ◽

Special Choice ◽

Trapped Mode ◽

Uniform Cross Section ◽

New Type ◽

Incident Waves

Rayleigh–Bloch surface waves are acoustic or electromagnetic waves which propagate parallel to a two-dimensional diffraction grating and which are exponentially damped with distance from the grating. In the water-wave context they describe a localized wave having dominant wavenumber β travelling along an infinite periodic array of identical bottom-mounted cylinders having uniform cross-section throughout the water depth. A numerical method is described which enables the frequencies of the Rayleigh–Bloch waves to be determined as a function of β for an arbitrary cylinder cross-section. For particular symmetric cylinders, it is shown how a special choice of β produces results for the trapped mode frequencies and mode shapes in the vicinity of any (finite) number of cylinders spanning a rectangular waveguide or channel. It is also shown how one particular choice of β gives rise to a new type of trapped mode near an unsymmetric cylinder contained within a parallel-sided waveguide with locally-distorted walls. The implications for large forces due to incident waves on a large but finite number of such cylinders in the ocean is discussed.

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