A computational framework for the design of tensile structures

Marcio S. V. de Souza; Ruy M. O. Pauletti

doi:10.3934/acse.2024005

Article Contents

2024, Volume 2, Issue 1: 37-72. Doi: 10.3934/acse.2024005

This issue Previous Article Simulation calibration of differentiated knitted membranes with evolutionary optimisation tools Next Article Preface

A computational framework for the design of tensile structures

Marcio S. V. de Souza^, and
Ruy M. O. Pauletti

Structural and Geotechnical Department of the Polytechnic School of the University of São Paulo, Brazil

^*Corresponding author: Marcio S. V. de Souza
^*Corresponding author: Marcio S. V. de Souza

Received: February 2024

Revised: March 2024

Early access: March 30, 2024

Published online: March 30, 2024

Abstract / Introduction Full Text(HTML) Figure(23) Related Papers Cited by

Abstract

This paper introduced a parametric workflow for the design of tensile structures, encompassing form-finding, patterning, flattening, and geometrically nonlinear structural analysis of cables and membranes, and how these design steps can be sequenced and iterated. The concepts of parametric design and visual programming languages were outlined, with a particular focus on structural design. The implementation of these concepts was straightforward, and the paper explained their application into a new Grasshopper plug-in, called BATS - basic analysis of tensile structures, capable of performing the full design cycle of this type of structures.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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Figure 1. Linear workflow in the design of tensile structures

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Figure 2. Iterative workflows in the design of tensile structures

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Figure 3. Natural membrane element: a) reference configuration, b) initial configuration, and c) current configuration

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Figure 4. Form-finding process from an initial flat mesh

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Figure 5. (a, b) Plane cut segmentation to find initial straight lines and (c) geodesic curve definition

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Figure 6. (a) Division of a mesh from arbitrary curves generates meshes with nonuniform elements. (b) Removing the strips with node constraints in the edges to enforce they are coupled sort out the issue

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Figure 7. Flattening process of tensile surface strips. (a) Definition of the structural problem with the 3D geometry in the reference configuration and the projected geometry as a first trial for the 2D current configuration. (b) Resulted flattened strip with the corresponding displacement field from the projected initial geometry

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Figure 8. Possibilities in the integration of CAD and CAE interfaces

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Figure 9. Workflow driven from parameter and design rules with integrated feedback between the design steps

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Figure 10. Software architecture of BATS

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Figure 11. BATS data model

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Figure 12. Linear and surface patch for cable and membrane members

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Figure 13. Definition of surface strips. A surface strip contains the assembled and flattened geometry and its topological reference to the main surface patch

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Figure 14. Flowchart of the communication between BATScore and BATS++

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Figure 15. Benchmark of function implemented using third-party linear algebra libraries, native C++ arrays, and AceGen generated code

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Figure 16. BATS Solvers flowchart. Green represents actions using parallelism and yellow actions computed in a single thread

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Figure 17. Parametric workflow for design and analysis of tensile structure implemented using BATS Grasshopper plug-in

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Figure 18. Model definition and solutions from the form-finding component for different vertical displacement of the supports and different ratio between the membrane and cable stresses

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Figure 19. Patterning and re-meshing of the defined shape into different number of strips and remapping of the stress field to the new mesh. First principal stress field displayed in Pa

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Figure 20. Flattening process generates the production strips of the fabric, which can be used for the further assembly analysis to find the real stress field resultant from the assembly.First principal stress field of the assembled fabric is displayed in Pa

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Figure 21. Load response analysis of a wind pressure of 800Pa. From left to right: first principal stress (Pa), second principal stress (Pa), and displacement fields (m)

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Figure 22. Example of conoid with torsioned strips. At the top from left to right: a) Geometry and first principal stress obtained from form-finding (Pa), b) Patterned geometry, c) First principal stress from real assembly (Pa). At the bottom: Flattened strips with residual stress with legend omitted for simplicity

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Figure 23. Example of multi-patch membrane. At the top from left to right: a) Geometry and first principal stress obtained from form-finding (Pa), b) Patterned geometry, c) First principal stress from real assembly (Pa). At the bottom: Flattened strips with residual stress with legend omitted for simplicity

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