Nooshin H, Samavati O, Sabzali A (2016) Basics of Formian-K, Formexia
Preface: Formian is the name of a software system that is ideally suited for generation of shapes and forms of all kind. The term ?Formian? is meant to imply the ?language of form?. The software has a convenient algebraic structure and this provides a powerful basis for creation of generic (parametric) formulations that embodies all the necessary geometric details. Formian may be used for ?configuration processing? (that is, creation and processing of forms) in any discipline. In particular, Formian has been used extensively for generation and processing of spatial structural forms. The concepts on which Formian is based are evolved during the past 40 years with the concepts being further enriched continuously. This is a feature of algebraic concepts that with application they continue to grow and become more mature. There have been a number of versions of Formian used over the years, but the version that has been employed in the recent years is called Formian-2. A new version of the software is now available which is referred to as Formian-K. This new version is completely rewritten and, while providing many powerful new features, it is quite convenient to use. The material in the present document provides a concise description of the structure of Formian-K. However, regarding the description of the aspects that are similar to Formian-2, reference is often made to Formian-2 literature for detailed explanation.
Nooshin H, Samavati OA (2016) Some Morphological Aspects of Configurations, Proceedings of IASS Annual Symposia 2016
This is the second paper in a series of papers that are intended to provide a comprehensive coverage of the concepts of formex configuration processing and their applications in relation to structural configurations. In the present paper, attention is focused on the configuration processing for a number of families of space structures, namely, pyramidal forms, towers, foldable systems and diamatic domes. Also included is a section on information export as well as an Appendix on basic formex functions. The section on information export describes the manner in which the information about the details of a configuration, generated by the programming language Formian, can be exported to graphics, draughting and structural analysis packages.
This is the third paper in a series of papers that are intended to provide a comprehensive coverage of the concepts of formex configuration processing and their applications in relation to structural configurations. In the present paper, the attention is focused on structural forms that are based on hyperbolic paraboloidal, hyperboloidal and annular surfaces. It is shown that these categories of structural forms include many exciting possibilities for lattice and shell structures. The paper also includes sections on structural forms that may be obtained from combinations of simpler forms or through certain composite transformations that are called paragenic transformations.
This is the first paper in a series of papers that are intended to cover the present state of knowledge in the field of formex configuration processing. This field of knowledge has been developed during the last three decades and has now reached a level of maturity that makes it an ideal medium for configuration processing in many disciplines. In particular, it provides a rich assortment of concepts that are of great value to the engineers and architects involved in the design of space structures.
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.
Dealing with geometrical information has been an important aspect of the knowledge required for construction of a structure. In particular, data generation techniques appropriate for complex geometries are crucial for the design and construction of spatial structures. This may be referred to as ?Configuration Processing? and has been the centre of attention for some researchers in the past few decades. A main focus of this thesis is the ?regularity? in structural forms and the present research shows that the ?metric properties? of structural forms, suggested by the Author, are fundamental for the study of regularity. Metric properties refer to the geometrical information necessary for design, and in particular, construction of lattice spatial structures. To elaborate, the research addresses the following questions:
" What are the metric properties for a lattice structure and how can these be evaluated?
" What is the definition of regularity for lattice structures and how can this be quantified?
" How could the regularity of a lattice structure be improved?
The Author is an architect and structural engineer who has been involved in the design and construction of lattice spatial structures for 20 years. The experience of the actual construction over the years has shown that there are advantages in keeping the number of different types of structural components small. In another front, the study of regularity of forms for lattice structures may involve the ?visual aspects?, ?arrangements of elements? or ?structural components?. The first two aspects are subjective matters and the latter one, that is the focus of the present work, is an objective matter. The present research shows that the metric properties of structural forms are fundamental for the study of component regularity. There are considerable benefits in terms of the construction of structures which have a high degree of regular components. The benefits include savings in time and cost of construction, as well as a reduction in probability of having a wrong arrangement during assembly. In this sense, the present work could be considered as a research of fundamental importance which provides a basis for the knowledge in this field. Most of the examples in the Thesis are single layer lattice structures with straight elements and further research on other types of lattice structures is recommended.
This thesis consists of six chapters, the first of which entitled ?Introduction? provides background information about the research and discusses the research aims. Chapter 2 on the ?Literature Review? concerns the few available publications relevant to the research. The third chapter entitled ?Metric Properties? defines a number of geometrical parameters which are being used to generate the geometrical information. Also, the mathematics involved for the necessary calculations are discussed. This chapter is a major contribution of the thesis and to the available knowledge in terms of introduction a set of well defined geometrical parameters for design and construction of lattice spatial structures. Chapter 4 is dedicated to discussion of different aspects of ?Regularity? of lattice structures. To begin with, the idea of regularity is elaborated upon and then the concept of ?regularity indicators? are discussed. These indicators help to quantify regularity of components. Here again, this chapter presents a novel idea in the field of lattice spatial structures. Another major contribution of this thesis to the general knowledge is Chapter 5 entitled ?Sphere Packing?. This is a particular technique for configuration processing developed by the Author to improve the member length regularity of lattice structures. An example of the application of the technique for configuration processing of spherical domes is also discussed in details. Moreover, a comparison on the variation of the member lengths of different dome configurations is discussed which shows that around 50% of the members
Dynamic behaviour of single-layer lattice domes is complicated and fundamentally differs from conventional building structures. Their response to dynamic excitation is characterised by the contribution of several vibration modes throughout a wide range of frequencies. Furthermore, due to large deformations associated with a possible development of plasticity within the structure, seismic response of single-layer lattice domes to severe earthquakes is normally highly nonlinear. So far, in the absence of a practical equivalent static seismic loading scheme, realistic seismic response evaluation of single-layer lattice domes still relies on nonlinear dynamic time-history analysis.
Herein, a new analytical method for estimating the nonlinear seismic response of different types of single-layer lattice domes is presented, as the main contribution of this research. The method is based on ?Modal Pushover Analysis? (MPA) concept which conveniently accounts for the participation of higher vibration modes in the seismic response, and is consistent with the inherent dynamic characteristics of single-layer lattice domes. The efficiency and accuracy of the proposed method is verified through comparison between the MPA results and those obtained from a full geometrically and materially nonlinear time-history dynamic analysis. It is shown that the proposed method yields accurate results for all types of single-layer lattice domes with different geometrical properties, and effectively removes the necessity of performing nonlinear time-history earthquake response analysis.
Moreover, dynamic characteristics of single-layer lattice domes is sensitive to the geometrical particulars of the structural system. Accordingly, the importance of various geometrical particulars of single-layer lattice domes on their dynamic characteristics has been carried out by means of parametric studies, as the other contribution of this research. The particulars studied include ?span?, ?rise-to-span-ratio?, ?pattern of the configuration?, and ?relative stiffness of the supports?. It is concluded that ?rise-to-span-ratio? and ?relative stiffness of the supports? are two important parameters which significantly influence the dynamic behaviour, the effects of other properties on dynamic characteristics of single-layer lattice domes are less important.