Connector Node For Free-Form Grid Shells

Modern computational tools have revolutionised the design and analysis of free-form grid shells, simplifying complex processes like form finding and topology optimisation. This paper by Rudra Nevatia, a Consulting Engineer, examines the complexities of free-form grid shells, focusing on design challenges and innovative solutions.

Grid shells are structures with the shape and rigidity of a double curvature shell, consisting of a grid instead of a continuous surface. Pioneered in 1896, by Russian engineer Vladimir Shukhov, grid shells were first used in the Nizhny Novgorod exhibition pavilions, with Shukhov also developing the mathematics for their analysis. In 1975, Frei Otto designed the Multihalle grid shell in Mannheim, Germany, using a hanging chain model for form-finding and the SAP4 computer program for strength calculations. Modern computers and software have since simplified form finding, topology optimisation, and strength calculations for grid shells.

Generation of Free-form Surfaces

Free-form surfaces are classified into Translation Surfaces and NURBS. A Translation Surface is created by moving a curve, called the generatrix, parallel to itself along another curve, the directrix, resulting in a net with planar meshes or panels. NURBS, or Non-Uniform Rational B-Splines, describe free-form curves and surfaces mathematically. A NURBS surface is defined by a grid of curves running in the u- and v-directions, which are the intrinsic coordinates of the surface in two-dimensional space.

Meshing

Having defined a free-form surface, the next step is to convert the surface into a mesh. The most common mesh types are triangular and quadrilateral – warped or planar Valence of a node which refers to the number of structural elements connected at the node. A surface defined by a triangular mesh has higher valence as compared to a quadrilateral mesh. The higher the valence, the higher the number of variables required to be accommodated at nodes.

Free-form grid shells come with their unique set of challenges which must not be ignored.

Beam-Panel Connection

Beam-panel connections can be significantly simplified if the beam’s top surface is parallel to the tangent plane of the envelope surface, otherwise, a high kink angle appears between panels and beams. This property also affects the mechanical efficiency of beams against wind load and light transmission.

Geometrical Torsion at Nodes

The normal vector to an arbitrary curve on a curved surface rotates around its tangent vector. On a grid shell, a straight segment thus undergoes rotation about its longitudinal axis.

Buckling

As compared to continuum shells, grid shells have limited load paths which are prone to multiple forms of buckling as follows:

• Member buckling: Due to the low slenderness ratio of the member
• Snap through of one or several nodes: Caused by low moment capacity of the node
• Global instability: In high compression areas
• Combinations of the above modes

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