【正文】 n, reprinted with permission) Rt ix Mi _vt ix e1T where Rt ix 5 residual force at node i in direction x at time t。ades) are restrained in the vertical direction but allowed to move in the direction perpendicular to the fa231。 architect Massimiliano Fuksas, structural engineers Schlaich Bergermann and Partner and Mero TSK Group) illustrates how a sculptural shell is discretized in foursided and triangulated (at the supports) meshes Fig. 3. Hippo House (Germany, built in 1997), designed by architect Grieble and Schlaich Bergermann and Partners, shows the discretization of a translational surface into planar quadrangular meshes (photograph courtesy of Edward Segal, reprinted with permission) a fine structural work (skeleton) of individual small subelements. The first design consideration lies in setting the exact boundary conditions within which the shell shape can be developed. The curved shape is of vital importance to achieve stability through membrane stiffness. Shell bending needs to be avoided by finding the ―right‖ geometry, so that under the selfweight only membrane action results. Membrane action makes efficient use of material. The important structural design challenge lies in the determination of a threedimensional (3D) surface that will hold the skeletal shell. In the twentieth century, both architects and engineers [Gaudi (Huerta 2021), Otto (Otto et al. 1995), and Isler (Billington 2021)] experimented with physical form finding techniques, which for a given material, created a set of boundary conditions and gravity loading that found the efficient 3D structural shape. The importance of finding a funicular shape for steel shells lies in the fact that the selfweight (gravity loads caused by steel and glass) contributes largely to the load to be resisted. The subelements need to be loaded axially to make most efficient use of the section profile. Numerical form finding techniques [force density (Schek 1974) and dynamic relaxation (Day 1965)] have been successfully applied to weightless systems whose shape is set by the level of internal prestress and boundary supports. However, when it es to funicular systems whose shape is not determined by initial prestress but by gravity loads (such as the case for masonry, concrete, or steel shells), fewer numerical methods have been developed. This is mainly because of the difficulty of finding optimal forms for those shells that rely on both tensile and pressive membrane stresses to resist dead load. Kilian and Ochsendorf (2021) presented a shapefinding tool for statically determinate systems based ona particlespring system solved with a RungeKutta solver, used in puter graphics for cloth simulation. Block and Ochsendorf (2021) published the thrust work analysis to establish the shape of pure pression systems. For the initial design petition for the Dutch Maritime Museum roof project, the dynamic relaxation method usually used for prestressed systems was adapted to deal with 3D funicular systems with tension and pression elements under gravity loads. Competition Design for a Steel Glass Shell over the NSA Courtyard The Dutch Maritime Museum planned a thorough museum renovation in the near future. The restricted space in the seventeenth century historic building hinders the movement of visitors. The courtyard needed to be integrated into the museum’s circulation space, sheltered from weather, and kept to a minimal indoor temperature. An invited design petition was held for a new glass roof that added value to the historic building. In 2021, Ney and Partners, a Brusselsbased engineering design consultancy, won this petition with a steel and glass shell design. The shell manufacturing and construction processes took place between 2021 and 2021. In 2021, the project was awarded the Amsterdam Architectural Prize. Initial Planar Geometry In the late seventeenth century, the historic building housing the museum (shown in Fig. 4) was the headquarters of the admiralship. It was the instrument and symbol of the Dutch maritime power. The development of this seafaring nation was closely linked to the production of sea charts and the associated sciences, such as geometry, topography, and, astronomy. The classic building also uses geometry as a basis for design. The choice for the initial twodimensional (2D) geometry of the glass roof tells the spectator a story about the building’s history and its close relationship to the history of the sea. At the origin of this 2Dgeometry lies a loxidromemap with 16 wind roses (shown in Fig. 4). This geometric drawing is found on sea charts displayed inside the museum. This geometric 2D diagram is the basis for the structural mesh. A lightemitting diode, with variable color and intensity, is placed at the intersection of the structural subelements. The cupola’s structural mesh reads as a fine line drawing against the sky, and bees a powerful scenographic instrument and a symbolic hemisphere. Physical Numerical Form and Its Analysis Starting from this geometric 2D mesh pattern, an exact 3D shell surface needs to be developed that will hold the shell. The material choice for the skeletal shell is set to steel (taking both pressive and tensile loads). The existing situation imposes the contextual boundary conditions. ? The shell’s height cannot appear above the historic building’s ridge. ? The courtyard fa231。 (b) prefabricated Crystal Palace (United Kingdom, built in 1851) was dismantled soon after its intended use (reprinted from originally from Tallis’ History and Criticism of the Crystal Palace. 1852)。 and the Smithsonian Institute, Washington, DC (Foster and Partners, and Buro Happold in 2021)]. The shapes of these glasscovered, singlelayered steel skeletal shells were driven by a bination of sculpt