Page 145 - JCAU-6-2

Journal of Chinese
Architecture and Urbanism RuiXue Multi-Hall in reciprocal structures

inventions encompassed inclined-support truss bridges 2.5. Research on the geometric theory of mutual
and woven-arch bridges. support structures worldwide
Da Vinci’s journey in the realm of reciprocal geometries In the 21 century, with the establishment of numerous
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began with the initial two-dimensional linear interweaving structural practices involving reciprocal geometry and
of truss bridges, evolving into the two-dimensional curved the rapid development of parametric software, top-down
extensions seen in woven-arch bridges. He artfully applied generative tools, and various generative algorithms have
the principles of weaving to explore reciprocal geometries increasingly found applications in reciprocal geometry
grounded in regular geometric shapes, such as triangles and structural designs.
polygons. Furthermore, these geometric principles served as a In 2011, Pavel initiated a study on the geometric
foundation for the development of dome structures that could characteristics of reciprocal structural units, suggesting
be expansively extended outward (De Honnecourt, 2012). that plate reciprocal units have more complex connection

2.4. Phase three: Theoretical clarity and diverse methods and shape-influencing parameters (Baverel &
practical stages Pugnale, 2014). In 2013, Pavel explored the assembly of
double-layer structures with spatial thickness, utilizing
Since the beginning of the 21 century, exploration genetic algorithms and dynamic relaxation form-finding
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into reciprocal structures, both geometrically and methods (Douthe & Baverel, 2013). In 2018, Pavel
structurally, has become increasingly diverse, gradually integrated form-finding methods for reciprocals under
evolving into a systematic field of research and synthesis. geometric parameter constraints with the optimization
At the turn of the 20 and 21 centuries, scholars such of mechanical parameters. Pavel employed a translation
st
th
as Graham Brown, John Chilton, and Olga Popovich- optimization algorithm for rods to make the reciprocal
Larsen played a pivotal role in advancing systematic units as coplanar as possible or easily approximated
studies (Larsen, 2007; Popovic Larsen, 2014; Larsen, by larger surfaces (Mesnil et al., 2018). These research
2019), laying the foundation for refining the definition findings were then applied by Pavel to the design and
and the fundamental theoretical framework of reciprocal construction of a 50 sqm² exhibition hall. This application
structures. Piekarski (2023) developed a static analysis led to the proposition of a coplanar optimization method
model for structural grillages, taking into account the for reciprocal mesh construction and the establishment
bending stiffness, shear stiffness, and axial stiffness of of the external frame-shell hybrid structure system in
reciprocal beams. The results provide valuable theoretical construction (Douthe et al., 2018; Kuzmenko et al., 2021).
support for the structural design and application of
reciprocal beam grillages. In 2014, Uwe Tessendorf’s team at ETH Zurich
introduced a space mesh tangent transformation algorithm
Overall, reciprocal geometry underwent substantial (Thönnissen & Werenfels, 2011). Concurrently, Dario
theoretical development and extensive practical exploration Pagliari’s team at the University of Aalborg proposed
during the 21 century. This period of exploration was a space mesh node transformation algorithm (Parigi
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predominantly centered around rotational reciprocal & Pugnale, 2014). In addition, the team led by Song
geometry, with limited research on woven reciprocal Peng at Nanyang Technological University developed a
geometry. Gradually, this exploration began to delve into software package for interpenetrating geometry meshing,
the core issue of reciprocal geometry research, which employing an interpenetrating geometry unit tessellation
revolves around studying the simplest geometric forms algorithm (Song et al., 2013).
and the fundamental principles governing the structural
performance of reciprocal geometry units. 2.6. Digital construction practice
Advancements in computational design technology The development of digital technology in the 21 century
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and research on diverse geometric prototypes and has spurred advancements in the research and application
materials have greatly expanded the generation of reciprocal structures, thereby diversifying this field. An
mechanisms, prototype meshes, and even the structural exemplary illustration of these achievements is Wang Shu’s
units of reciprocal geometry, offering more extensive “Decayed Dome,” which was exhibited at the 2010 Venice
forms of expression. However, as long as the fundamental Biennale (Frampton et al., 2017). Renowned Japanese
structural characteristic of reciprocal geometry, which architect Shigeru Ban has also played a significant role by
involves “mutually supporting and transmitting forces,” conducting workshops on wooden reciprocal structures at
is understood, this geometric form, closely linked to the esteemed institutions such as Rice University and Tongji
expression of structural performance, continues to hold University. Moreover, he has ventured into the exploration
significant long-term development potential. of diverse reciprocal structures for timber, as observed in

Volume 6 Issue 2 (2024) 3 https://doi.org/10.36922/jcau.1635