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<p>Architectural forms in practical engineering projects exhibit significant diversity and complexity, often exceeding the representational capacity of traditional curves or even B-spline curves. This limitation creates substantial challenges in establishing accurate initial models.Given a set of key points on a B-spline and the introduction of a reference plane, the internal and external boundaries were determined using a B-spline curved surface formed by the key points and a parametric B-spline curve on the reference plane, where the reference plane was divided using Delaunay triangulation. Then, an initial structure with a complicated boundary was obtained. To address the challenges of computational efficiency and mesh distortion, the strain energy sensitivity to the key points was derived using the relationship between the strain energy and the key points. A new method was established to minimize the strain energy while improving the computation efficiency. The optimization model, sensitivity analysis, optimum algorithm, and mechanics analysis program were all implemented in FORTRAN language, with two free-form continuous shell structure surfaces to demonstrate the correctness and effectiveness of the method. The failure pattern, displacement contours and load–displacement curves were studied, for cases with optimized typical positive and negative Gaussian curvature. Finally, the ultimate load before and after optimization, as well as the effect of concrete strength, shell thickness and reinforcement location on the ultimate load, were studied using the finite element analysis software ABAQUS.</p>

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Shape optimization and mechanical properties analysis of the free-form surface

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年7月29日

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  • Cui Guoyong,
  • Cui Changyu

摘要

Architectural forms in practical engineering projects exhibit significant diversity and complexity, often exceeding the representational capacity of traditional curves or even B-spline curves. This limitation creates substantial challenges in establishing accurate initial models.Given a set of key points on a B-spline and the introduction of a reference plane, the internal and external boundaries were determined using a B-spline curved surface formed by the key points and a parametric B-spline curve on the reference plane, where the reference plane was divided using Delaunay triangulation. Then, an initial structure with a complicated boundary was obtained. To address the challenges of computational efficiency and mesh distortion, the strain energy sensitivity to the key points was derived using the relationship between the strain energy and the key points. A new method was established to minimize the strain energy while improving the computation efficiency. The optimization model, sensitivity analysis, optimum algorithm, and mechanics analysis program were all implemented in FORTRAN language, with two free-form continuous shell structure surfaces to demonstrate the correctness and effectiveness of the method. The failure pattern, displacement contours and load–displacement curves were studied, for cases with optimized typical positive and negative Gaussian curvature. Finally, the ultimate load before and after optimization, as well as the effect of concrete strength, shell thickness and reinforcement location on the ultimate load, were studied using the finite element analysis software ABAQUS.