Formex algebra adaptation into parametric design tools and rotational grids

This paper describes the adaptation of the formex configuration processing to the computer program Grasshopper 3D and focuses on the applied mathematical solutions. Formex algebra is a mathematical system, primarily used for planning structural systems like truss-grid domes and vaults, together with the programming language Formian. The goal of the research is to allow architects to plan truss-grid structures easily with parametric design tools based on the versatile formex algebra mathematical system. To produce regular structures, coordinate system transformations are used. Owing to the abilities of the parametric design software, it is possible to apply further modifications on the structures and gain special forms. The paper covers the basic dome types, and it introduces additional dome-based structures using special coordinate-system solutions based on a spherical coordinate system, vault structures and their modifications based on a cylindrical coordinate system and circular structures and their modifications based on polar coordinates. Moreover two rotational grid tools are introduced, which uses coordinate system transformations on a unique way to create surfaces of revolutions based on the given generating curve and create grid structures on these surfaces. It also describes the solution technique to implement the triangular grid version of every one of these tools based on diamatic domes. The adaptation of formex algebra and the parametric workflow of Grasshopper together give the possibility of quick and easy design and optimization of special truss-grid domes.

Formex configuration processing: A young branch of knowledge

The term ‘configuration’ refers to an arrangement of parts. For example, the elements of a structure constitute a configuration and so do the atoms of a molecule and the components of an electrical network. The most common usage of the term configuration is in reference to geometric compositions that consist of points, lines, surfaces and so on. The term ‘configuration processing’ refers to the skill of dealing with creation and manipulation of configurations. In particular, the term ‘formex configuration processing’ implies configuration processing with the aid of ‘formex algebra’. Formex algebra is evolved to perform processes needed for configuration processing, just as the ordinary algebra is evolved to perform operations needed for creation and manipulation of numerical models. The term ‘formex’ is derived from the word ‘form’ and it is meant to imply a ‘representation of form’. This article has two main objectives. The first objective is to provide a general feeling of how the elements of formex algebra perform configuration processing. This objective is achieved through simple examples, without involvement in too many details. It will be seen that working with parameters is a natural characteristic of formex configuration processing. Thus, a formex solution is, normally, for a class of problems rather than an individual one. This would allow consideration of different variants of a configuration by simply changing the values of the parameters. It will also be seen the ease with which freeforms can be created. The coverage also includes information about ‘Formian’ which is the name of the computer software for formex configuration processing. The second objective of this article is to record the story of the development of formex algebra from the beginnings in the mid-1970s to the middle of the second decade of the 21st century, covering some 40 years of development. Formex configuration processing is an effective and elegant conceptual tool for generation and manipulation of forms. However, there are also other approaches to configuration processing. In particular, there are now a number of highly successful software systems for configuration processing using various tactics. Formex algebra will be a natural complement for these systems.

Formex Formulation of Transmission Tower Structures

The formex formulation of the topological configuration, geometry, load and support conditions of self-supporting or free-standing transmission towers is presented. In the formulation, a natural normat coordinate system is used. The tower topology is formulated according to member types and orientations within the tower. The formex formulation is implemented as a preprocessor for a general elasto-plastic nonlinear large displacement analysis program for transmission tower structures. The data generated from the formex formulation is transformed into an AutoLISP file that can be loaded and used by AutoCAD. Throughout the paper, it is assumed that the readers are familiar with the basic concept and terminology used in formex algebra.

A Formex Formulation for Substructure Analysis of Open Web Grids

In this work, a formex procedure is presented in order to provide a conceptually consistent method of formex formulation in the context of substructure analysis. Grids composed of beams with multiple web openings are treated for which substructuring is well suited. An open web beam can be regarded as an assembly of typical units. Formex formulations are produced for such typical units and for the whole assembly. The concepts of plenices are also employed in order to organise a suitable system for a formex representation of partitioned configurations. Also, a formex function is introduced which makes it possible to generate some distorted configurations from regular patterns. A reader with no familiarity with formex algebra may wish to consult Ref. 2 or Ref. 6 for a brief sketch of formex algebra and Ref. 7 for a quick reference on plenices.