This paper is concerned with the hydrodynamic response of a novel offshore fish farm that combines a floating spar wind turbine and a fish cage (named as COSPAR for brevity). The open net steel cage is octagonal in shape with a partially porous wave fence at its top end to attenuate wave energy for a calm fish farming environment as well as to keep predators out. The deep draught spar is made from concrete for its bottom half and from steel for its top half. The spar carries a control unit and a 1[Formula: see text]MW wind turbine that provides the required power to operate the offshore salmon fish farm. The COSPAR fish cage has four catenary chains as mooring lines attached to mid length of the spar (outside the fish cage) so as to mitigate tension force in the mooring lines and to reduce the benthic footprint. ANSYS Design Modeler and Aqwa are used to perform the hydrodynamic response analysis of free-floating condition of COSPAR in the frequency domain and coupled analysis involving COSPAR and the mooring lines in the frequency domain and time domain. Environmental conditions, representing 5-year, 20-year and 50-year wave return periods with a constant current flow at an exposed fish farming site in Storm Bay of Tasmania, Australia, are adopted for the analyses. A comparison study is made against having a floating fish cage only (i.e. without the bottom half concrete of the spar) with four catenary chains attached to side vertical columns of the cage so that the fish cage behaves like a semi-submersible cage. Based on the comparison study, the COSPAR fish cage shows enhanced hydrodynamic responses in the following respects: (1) more stable motion responses in heave and pitch against wave and current forces, (2) less susceptible to the viscous damping when it is assumed by a linearized drag force of Morison elements in the frequency domain and (3) reduction of tension forces in the mooring lines. Interestingly, the pitch motion response of COSPAR fish cage in the frequency domain is in close agreement with the time domain result due to its greater pitching stiffness that reduces nonlinear effects from viscous drag and mooring interaction.
Buckling loads of arches could be significantly affected by the assumptions made on the load behavior during buckling. For a funicular arch whose centerline coincides with the compression line, we may consider two types of load behaviors based on how the line of load action shifts during buckling. This paper presents the governing differential equations for the elastic in-plane buckling problem of funicular circular arches under uniform radial pressure based on the two different load behavior assumptions, as well as analytical and numerical methods for analysis. For the analytical method, buckling criteria of rotationally-restrained ended circular arches with an internal rotational spring are formulated by using the general solution of the governing differential equation. For the numerical method, the Hencky bar-chain model (HBM) and its simple matrix formulations for general funicular arches are established. The buckling loads and mode shapes of funicular circular arches are solved by using HBM and verified against exact solutions obtained from the analytical method. For funicular catenary arches and parabolic arches, the buckling load solutions by HBM with various number of segments are also obtained and compared with the solutions presented by the previous researchers.
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