This paper expands on the Geometric Degrees of Freedom (GDoF) in the context of geometry-based structural form finding and emphasizes its importance in finding non-conventional architectural structures in three-dimensional space. Using GDoF allows a designer to find various iterations of a network, each representing a unique design within the state of equilibrium and explore the non-conventional solutions particularly for funicular polyhedrons of 3D graphic statics. The paper briefly explains a method to find the GDoF of a given network consisting of closed polygons in 2D or 3D and applies the same method in finding the GDoF of reciprocal polyhedral diagrams of 3D graphic statics and expands on their non-trivial geometric transformations with their planarity constraints. The paper goes beyond the GDoF and provides a method to parameterize all the members of a network by assigning weights to all edges in a network to control the design properties of the solutions. For instance, a synclastic, compression-only shell can turn into an anticlastic compression-and-tension combined shell with the same magnitude of internal forces and external loads reciprocal to the same force distribution/diagram (Fig. 1). Using this technique in the context of 3D graphic statics allows a designer to find non-conventional spatial structural solutions with both compression and tension members with planar faces for architectural/structural design purposes.

Impact: Design With All Senses: Proceedings of the Design Modelling Symposium, Berlin 2019

Geometric Degrees of Freedom and Non-conventional Spatial Structural Forms

The response of vaulted structures with dry-joints such as arches and shells can be predicted using graphical methods, limit state analysis, and rigid block analysis. However, these approaches assume material deformations are negligible. While acceptable for conventional masonry structures, there is a growing body of work investigating segmented vaulted structures where the segments comprise a large portion of the overall span. In such cases, material deformations and non-linearities can play a significant role. Typical analysis tools available are usually difficult to use and are not widely used by industry practitioners. In this paper, a modelling approach using a widely used finite element analysis package (LS-DYNA) is presented, using an ‘out-of-the-box’ approach for parameter tuning and modelling. This was then benchmarked against five experimental tests of dry-joint arches undergoing support displacements and a segmented concrete shell with large segments tested under a central point load. Crucially, the segmented shell exhibited imperfect dry-joints, with gaps occurring throughout various locations. A method of modelling and assessing such imperfections in a simple and practical manner is investigated through the use of a positive penetration allowance in the contact surfaces. The results show that the modelling approach is able to predict the collapse mechanism and failure support displacement for arches well, with further experimental tests required for 3D systems. It is envisioned that this work will add to the number of tools designers will have for analysing segmented vaulted structures with dry-joints. 

Practical finite element modelling of segmented vaulted structures with assessment of imperfect dry-joints

The effect of block geometry on structural behavior of topological interlocking assemblies

Armadillo Vault - An extreme discrete stone shell

Handle everyday research tasks with reliable, citation-backed results

Your personal Research Agent to handle research tasks with citation-backed results

Popular Tasks used by Researchers

How can I help with your research?

Meet SciSpace

Get more enhanced response by uploading the PDFs you want me to reference.

No relevant PDFs in your library

SciSpace is the AI research assistant for academics. Run systematic literature reviews on 280M+ papers, and write papers with cited sources. Trusted by 1M+ students, PhDs & researchers.

SciSpace | AI for Research

Analyze PDFs

Code & Manuscripts

Funding & Grants

Literature & Patents

Medical & Clinical Data

Systematic Review

Visualize & Present

Web & Data

Build a Google Scholar-like website for your research.

Build a website

Create charts and images for your research

Create a Chart

Write a paper for submission to a journal

Draft a manuscript

Patent Search

Design eye-catching scientific posters in minutes.

Scientific Poster Generation

Systematic Literature Review

One task is running at the moment. Your messages will be shown right after.

Drag and drop or click here to browse

Loved by <highlight>1 million+</highlight> researchers

Extract a list of specific topics and their sources from unstructured text

Topics

Compare and analyze relevant papers that matches with your search

Papers

Get insights from PDFs and bookmarked papers from your library

My library

Recent searches

Try searching for:

Catch AI-generated content in scholarly and non-scholarly content

{ai} Detector

Ai Writer

Get PDF Summaries, highlighted text explanations 

Chat with PDF

Effortlessly create in-text citations and bibliographies in APA and 2,500 other formats

Citation generator

Get explanations, summaries, and answers on academic papers

Ease up your research workflow with {scispace}'s cohort of exciting AI tools

Elevate your academic writing skills and convey your ideas the way you want

Paraphraser

Explore our range of reading and writing tools

Your file is being prepared and should be ready in a few minutes. If it's a large file, it might take a bit longer. You can close this window, and we'll email you the file when it's done.

You have reached a maximum limit of <strong>{limit}</strong> columns in the table. Remove at least <strong>1</strong> column to add or create another one.

Block Philippe

Author Tools

Chat about Author

Papers

Armadillo Vault - An extreme discrete stone shell