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<p>This study optimizes the shape of mooring pontoons for deep-water floating bridges to reduce their motion amplitude under wave action. To this end, a Fourier series expansion in spherical coordinates is proposed to represent arbitrary smooth spatial geometries, with Fourier coefficients serving as the design variables. The gradient of the objective function with respect to the design variables is then obtained via the discrete adjoint method. The optimization aims to reduce the surge motion and the coupled surge and pitch motion amplitudes of the pontoon. The results show that the optimized shape reduced the surge and pitch motion amplitudes by a maximum of 77.84% and 89.73%, respectively, under different wave numbers <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="158_2025_3985_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="27" /> </InlineMediaObject> <EquationSource Format="TEX">\(kR\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="italic">kR</mi> </mrow> </math></EquationSource> </InlineEquation>. Additionally, the optimization effectively suppresses the free surface wave height around the structure. The influence of the Fourier coefficient truncation order on the optimization results is also examined, and an equivalent cross-sectional shape of the pontoon is proposed, which significantly reduces surge and pitch motions under various wave conditions. This study provides valuable insights for optimizing and designing floating foundations.</p>

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Shape optimization of floating bridge pontoons with mooring constraints under wave actions

  • 期刊论文

  • 发表日期：

    2025年3月25日

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  • Chenyu Lu,
  • Lijia Xu,
  • Anxin Guo,
  • Jiabin Liu

摘要

This study optimizes the shape of mooring pontoons for deep-water floating bridges to reduce their motion amplitude under wave action. To this end, a Fourier series expansion in spherical coordinates is proposed to represent arbitrary smooth spatial geometries, with Fourier coefficients serving as the design variables. The gradient of the objective function with respect to the design variables is then obtained via the discrete adjoint method. The optimization aims to reduce the surge motion and the coupled surge and pitch motion amplitudes of the pontoon. The results show that the optimized shape reduced the surge and pitch motion amplitudes by a maximum of 77.84% and 89.73%, respectively, under different wave numbers \(kR\) kR . Additionally, the optimization effectively suppresses the free surface wave height around the structure. The influence of the Fourier coefficient truncation order on the optimization results is also examined, and an equivalent cross-sectional shape of the pontoon is proposed, which significantly reduces surge and pitch motions under various wave conditions. This study provides valuable insights for optimizing and designing floating foundations.