基于数学方程的异形曲面桥塔在桥梁工程中的应用

Application of Irregular Curved Surface Bridge Pylon Based on Mathematical Equations in Bridge Engineering

摘要:

为解决异形曲面桥塔形状复杂带来的设计图纸表达困难、坐标定位不准确、模型复现困难等工程应用不便的问题，依托某景观桥梁，通过对比不同异形曲面构建方法的优劣，选择了数学方程的曲面构建方法。依据数学理论，通过提取桥梁异形曲面桥塔的典型曲面特征，突破传统数学方程通常用于简单、规则曲面的认知，依托微分几何原理构造出完整、严谨的异形扭转曲面方程。结果表明，基于数学方程的曲面构造方法具有形式简洁、定位精确、便于在图纸上表达、便于后期模型复现的优势，通过合理的构造方法可用于复杂、非规则的异形曲面。该方法的拓展应用有效解决了异形曲面结构施工过程中的诸多难题，显著提高了工程施工的速度和准确度，取得了良好的经济效益。

Abstract:

To address the engineering application inconveniences caused by the complex shapes of irregular curved surface bridge pylons, such as the difficulty in expressing design drawings, inaccurate coordinate positioning, and the difficulty in replicating models, relying on a landscape bridge, and by comparing the advantages and disadvantages of different irregular curved surface construction methods, the curved surface construction method of mathematical equation is selected. On the basis of mathematical theory, and by extracting the typical curved surface characteristics of irregular curved surface bridge pylon, the traditional mathematical equations that are usually used for the understanding of simple and regular curved surfaces are broken through. Relying on the principles of differential geometry, a complete and rigorous equation for the irregular torsional curved surface is constructed. The result shows that the curved surface construction method based on mathematical equations has the advantages of simple form, precise positioning, ease of expression on the drawing, and ease of model reproduction in the later stage. Through reasonable construction methods, it can be used for complex and irregular special-shaped curved surface. The expanding application of this method can effectively solve many difficulties in the construction of irregular curved surface structure, and significantly improve the speed and accuracy of engineering construction, which has achieved the good economical benefits.