A non-smooth-contact-dynamics analysis of Brunelleschi’s cupola: an octagonal vault or a circular dome?
A non-smooth-contact-dynamics analysis of Brunelleschi’s cupola: an octagonal vault or a circular dome?
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布鲁内莱斯基冲天炉的非光滑接触动力学分析：八角形拱顶还是圆形穹顶？
DOI：
10.1007/s11012-018-00934-9
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发表时间：
2019
期刊：
影响因子：
2.7
通讯作者：
A. Tasora
中科院分区：
文献类型：
--
作者：
V. Beatini;G. Royer;A. Tasora
佛罗伦萨圣玛丽亚·德尔·菲奥雷的圆顶是布鲁内莱斯基巧妙地用圆锥形砖块建造的，径向中轴线上的一个焦点。因此，圆顶是作为一个旋转的表面建造的，但部分被切割掉，以保留八角形的簇状拱顶形式。在模型中，将这种圆形布置与八角形水平围栏进行了比较，在该模型中，穹顶被概化为摩擦接触的刚性块的集合，并使用非光滑接触动力学方法进行分析。接触反应的高度不确定性意味着它们的测定有相当大的困难，通过在接触点增加柔度来表示砂浆接缝的变形性，通过正则化程序来面对这些困难。使用定制软件进行的数值实验突出了Brunelleschi排列中的力的均匀流动，但证明了主要用于建筑目的的人字形螺旋线引起的扰动，人字形螺旋线沿子午线超载，在平行线方向非常弱。这是由于块的垂直狭窄布置，这增加了子午线方向的刚度，但降低了摩擦力平衡环向应力的能力。
The cupola (dome) of Santa Maria del Fiore in Florence was ingeniously constructed by Brunelleschi using a conical bricklaying, radial-oriented toward a focus point on the central axis. Therefore, the dome is built as a surface of revolution but with parts cut away to leave the octagonal cluster vault form. This circular arrangement is compared with an octagonal horizontal corbelling in models where the dome is schematized as an assembly of rigid-blocks in frictional contact, analyzed with a Non-Smooth-Contact-Dynamics approach. The high indeterminacy of the contact reactions implies considerable difficulties in their determination, which are faced via a regularization procedure by adding a compliance at the contact points in representation of the deformability of the mortar joints. Numerical experiments, performed with a custom software, highlight the uniform flow of forces in the Brunelleschi arrangement, but evidence the disturbances induced by the herringbone spirals, mainly used for construction purposes, which are overloaded along the meridians and very weak in the direction of the parallels. This is due to the vertical narrow disposal of the blocks, which increases the stiffness in meridional direction, but diminishes the capacity of the friction-induced forces to equilibrate the hoop stress.