# Optimization of gridshells as formwork systems for concrete shells

Rombouts J., Lombaert G., De Laet L., Liew A., Block P. and Schevenels M.
World Congress of Structural and Multidisciplinary Optimization
Beijing
2019

Shell structures are material-efficient structures capable of covering large spans with minimum weight. If concrete is used as the building material for the shell, it must be initially supported by formwork. These generally rigid formworks and their supporting falsework structure are time and material consuming to make. Therefore, research has gone to the development of flexible formworks to reduce the time and material spent on the construction of the shell. Formworks made of cable-nets and membranes are limited to shapes with negative Gaussian curvature everywhere, unless a pneumatic system is applied, in which case the whole area underneath the shell is occupied during construction and hardening of the concrete. As an alternative, Tang and Pedreschi [1] and Cuvilliers et al. [2] have suggested elastic gridshells as falsework system. The design of such a system is complicated by large deformations of the bending elements. Moreover, since gridshells are inherently flexible, significant displacements generally occur when applying the wet concrete.

This paper presents a design tool to effectively design a gridshell serving as the falsework for a concrete shell. The gridshell is assumed to be constructed from an initially flat grid of straight slender beams, using lashing straps to brace the erected gridshell. An optimization algorithm is proposed that fits the shape of the gridshell under loading to a given target shape by manipulating the lengths of the lashing straps. Meanwhile, the optimization algorithm reduces the construction effort by minimizing the number of straps, and the diameter of the grid beams. Moreover, the feasibility of the design is ensured by constraining the axial force in the cables and limiting the displacements under increased loading. Gradient-based optimization is applied, and an implicit dynamic relaxation approach [3] is used to solve the nonlinear equilibrium equations, ensuring that the required computation time is acceptable. Nonlinear effects such as buckling are taken into account by using co-rotational beam elements to model the grid beams. The resulting design tool is applied for the design of a scale model, demonstrating the feasibility of the suggested falsework system, and the effectiveness of the optimization algorithm used in the design tool.

[1] G. Tang and R. Pedreschi. Deployable gridshells as formwork for concrete shells. In Proceedings of the International Society Of Flexible Formwork (ISOFF) Symposium 2015, 2015.

[2] P. Cuvilliers, C. Douthe, L. Du Peloux, and R. Le Roy. Hybrid structural skin: prototype of elastic gridshell braced by a fibre-reinforced concrete envelope. Journal of the international association for shell and spatial structures, 58(1):65–78, 2017.

[3] J. Rombouts, G. Lombaert, L. De Laet, and M. Schevenels. A fast and accurate dynamic relaxation approach for form finding and analysis of bending-active structures. International Journal of Space Structures, 2019.

BibTeX

@inproceedings{Rombouts2019,
author    = "Rombouts, J. and Lombaert, G. and De Laet, L. and Liew, A. and Block, P. and Schevenels, M.",
title     = "Optimization of gridshells as formwork systems for concrete shells",
booktitle = "World Congress of Structural and Multidisciplinary Optimization",
year      = "2019",
editor    = "",
volume    = "",
number    = "",
pages     = "",
publisher = "",
month     = "",
doi       = "",
note      = "",
}

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