The optimization process leading to the tessellation of the first geodesic dome structure, the first Planetarium of Jena

The tessellation of the first built geodesic dome structure (the first planetarium of Jena, designed by Walther Bauersfeld, built 1922–23) has been unknown until recently. While original documentation of the tessellation has been published, the concept behind it has not been uncovered. This article presents the evolution of the final tessellation based on Bauersfeld’s hand-written notes found in the Zeiss Archives in Jena. Bauersfeld contemplated various methods of subdivision and performed detailed calculations and optimality analysis on them—preceding the theoretical studies on the tessellation of geodesic domes by almost 30 years. His key findings, relevant and comparable with later studies are highlighted. The concept of the presumably final tessellation is revealed to be the equal-area triangulation of the sphere—which has to the author’s knowledge not been considered ever since for geodesic domes. The remarkably simple algorithm applied did not result in a theoretically exact solution (well known to Bauersfeld), but as shown in this article in engineering terms it got sufficiently close. Moreover, it is concluded that the resulting tessellation excels in terms of important parameters (e.g. edge length ratio, number of different edges) compared to existing practical and theoretical solutions.

Numerical Analysis of Steel Geodesic Dome under Seismic Excitations

The paper presents the response of two geodesic domes under seismic excitations. The structures subjected to seismic analysis were created by two different methods of subdividing spherical triangles (the original octahedron face), as proposed by Fuliński. These structures are characterised by the similar number of elements. The structures are made of steel, which is a material that undoubtedly gives lightness to structures and allows large spans. Designing steel domes is currently a challenge for constructors, as well as architects, who take into account their aesthetic considerations. The analysis was carried out using the finite element method of the numerical program. The two designed domes were analysed using four different seismic excitations. The analysis shows what influence particular earthquakes have on the geodesic dome structures by two different methods. The study analysed the maximum displacements, axial forces, velocities, and accelerations of the designed domes. In addition, the Time History method was used for the analysis, which enabled the analysis of the structure in the time domain. The study will be helpful in designing new structures in seismic areas and in assessing the strength of various geodesic dome structures under seismic excitation.

TEST OF A NET DOME FRAGMENT

A geodesic or net dome, also known as a Fuller’s dome, is a spherical structure. Geodesic domes are well receptive to asymmetric loads, especially snow and wind, have high aerodynamics, increased rigidity and stability. It should be noted that the larger the diameter of the sphere, the greater its bearing capacity, and the strength of such dome slightly depends on the building materials used. With significant advantages, the design and construction of wooden net domes has not become widespread. The fact is that net domes are spatial structures with a large number of elements, which accordingly entails a large number of nodes. The elements of the dome are connected with dowels, wet film gauge, bolts, wood screws, staples, screws, nails. Adhesive connections on washers are used, also steel clamps, straps, overlays are applied. However, they all have disadvantages, the scope of each connector is different, and their cost is often comparable to the cost of the dome elements. We offer a universal connector for connecting dome parts at any angle. As a result of introduction of such technical decision of knot, we receive essential simplification of a design, reduction of quantity of components, at the same time with increase of its manufacturability. To study the operation of the joint of wooden glue-board elements of the dome with the use of a universal connector, its experimental studies were carried out. The purpose of the study: to study the actual operation of the connection of wooden parts of the dome with a universal connector in the form of rotating fasteners that rotate freely on the draw bolt, to assess its strength and deformability, to assess the possibility of using such a connection in the design of spatial structures. To solve the tasks, a full-scale fragment of the dome was tested, which includes characteristic nodes with rigid adjacency of elements to each other.

EFFECTIVE STRUCTURE OF A WOODEN RESIDENTIAL BUILDING IN THE FORM OF A GEODESIC DOME WITH A UNIVERSAL CONNECTOR

Since the middle of the twentieth century, a new architectural solution has been spherical shells broken down into elements by geodesic lines – circles with radii equal to the radius of the sphere. A geodesic dome is a dome made of a spherical polyhedron with an optimally distributed arrangement of vertices and edges tending to a perfect sphere. Using the technical capabilities of computer design, digital models of the layout and calculation of geodesic domes became available. It is possible not only to calculate multi-mesh network layouts with high accuracy, but also to automate the design. At the same time, it cannot be said that the optimal system has already been obtained and studied. The issues of optimal shaping, taking into account a simple universal connector and confirmation of theoretical results by field tests, remain not fully studied. Development of the design of a mesh wooden house in the form of a geo dome with optimal parameters of the geodetic network and nodal connections of the frame elements using a universal connector is the theme of this publication. The proposed form of division is a fullerene polyhedron describing a sphere and consisting of five and hexagonal faces. The dome polyhedron is built on the basis of the icosahedron. The number of partitions of vertices and edges that make up the split edge ‒ the frequency, is chosen equal to 3. The first class of partitioning by the "equal chords" method is adopted. The proposed universal connector for connecting parts of building structures at any angle and a method of mounting building structures using a universal connector. As a result of introduction of new technical decisions we receive essential simplification of a design, reduction of quantity of its components, at the same time increase of its manufacturability and providing an opportunity to connect details of building designs in an end face at any angle.

TRANSLATION OF GEOMETRIC MODELS OF SINGLE-CONTOUR GEODESIC DOMES FROM ARCHICAD TO A NEUTRAL STEP FORMAT

The methods of data exchange between CAD and CAE systems are described. The first method is using direct conversion, the second method is using neutral formats. The description of the modular system for designing and analysis the strength and stability of single-contour and double-contour geodesic shells GeoTran is given. The direct translation of geometric models from ArchiCAD to Patran/Nastran / Dytran has the disadvantage of having to develop translators for each data exchange scheme. It is proposed to implement the translation of geometric models in a neutral STEP format, which reduces the number of required translators. It is noted that the STEP format is recognized by various CAE systems that implement the finite element method (Autodesk Mechanical Desktop, Bentley Microstation, CATIA V4, CATIA V5, MSC Patran/Nastran, UGS PLM Solutions NX). The characteristics of the OBJ format used for storing a geometric model in the ArchiCAD CAD system and the STEP format used for data exchange with CAE systems are studied. A translator of geometric models of single-contour geodesic shells from ArchiCAD to STEP format in the Visual Basic programming language has been developed. For this purpose a syntactically oriented approach was used. The translator has a graphical user interface that makes it easier to use. The translator allows you to automate the exchange of data between the ArchiCAD CAD system and various CAE systems designed for strength analysis and supporting import from the STEP format. The applicability of the translator for the exchange of data on geometric models of single-contour geodesic domes with triangular plates between ArchiCAD and the Delcam Exchange converter program is verified. It is demonstrated that the STEP file format generated by the OBJSTEPTranslator is recognized by an external program.

The use of modern polymer materials and wood in the construction of buildings in the form of geodesic domes

Spherical structures have been used by mankind since time immemorial in religious and public buildings, as well as in engineering structures. With the development of lightweight design and construction, non-standard architectural and planning solutions are used. More and more frequently they are being successfully implemented in private home projects and becoming a fact of everyday life. This may be explained by certain advantages of the form, as well as by the opportunities offered to the construction industry by the age of new materials and technologies for the works performance. The functional and architectural-structural design of round-shaped buildings in the form of geodesic domes will allow creating comfortable, cost-effective, energy-efficient and environmentally expedient conditions for human habitation taking into account the shortage of land areas and increased demand for alternative housing options due to the environmental situation around the world. This article analyzes the experience of building spherical buildings of different types and scales. The authors present the results of research carried out in the field of the geodesic dome design improvement with the use of wood and polymer materials.

Geodesic domes for planetary exploration

Venus and the Ocean Worlds are emerging areas of interest for space exploration, as they can potentially host, or have hosted, conditions compatible with life. Landers and probes for in-situ exploration, however, must deal with very high external pressure, due to the environmental conditions, often resulting in thick and heavy structures. Robust, reinforced shell structures can provide a lightweight solution for the primary structure. In this frame, the isogrid layout is already a standard in aerospace, especially for flat panels or cylindrical shells. In this paper, isogrid-stiffened hemispherical shells, or “geodesic domes”, are described, focusing on the case of a concept of a Venus lander. Early design methods for both plain and geodesic domes subjected to external pressure are presented, providing design equations. Additive Manufacturing is identified as the key technology for fabricating metallic geodesic domes, due to the complexity of the internal features. Moreover, it allows to fabricate ports and integrated thermostructural systems in the same process, potentially resulting in improved performance or cost and schedule savings.

Two subdivision methods based on the regular octahedron for single- and double-layer spherical geodesic domes

The paper presents the topological–geometric analysis of a selected number of space frames configurations for geodesic domes which are generated from the regular octahedron. Two subdivision methods for spherical triangles, proposed by Fuliński, were used to create two families of structures. The first family consists of six single-layer and six double-layer geodesic domes shaped on the basis of the first method of subdivision, while the second family contains six single-layer and six double-layer geodesic domes shaped on the basis of the second method of subdivision. The calculated results of the geometric parameters of the analyzed structures were used to create original formulas that allow for more advanced structures to be achieved, that is, with a larger number of nodes and struts. The geometric results were also used to create nomograms showing the range of struts of the same length for double-layer geodesic domes. In both single-layer and double-layer domes, the number of groups of struts of equal lengths and the number of faces with different areas are smaller for structures created according to the first method of subdivision. The comparison of the resulting element quantities of two methods shows that the largest differences appear between the domes with a larger number of struts (up to 67%). Here, the analysis might help the designer reach a final decision on the better choice of topology, in particular, when this aspect is combined with other design goals, such as efficiency, economy, utility, and elegance in the design of the structure and the cover of large areas.

Geodesic Domes as Business Model in Hotel Management for Local Economies Development

This research aims to present the Buckminster Fuller geodesics in a contemporary context through a new hotel model, detailed by the case of the Ecocamp Hotel (CHILE), a pioneer in the construction of hotel rooms with geodetic domes incorporating aspects of local culture, sustainable development of the environment, and also, linking concepts of environmental awareness. This project was chosen for analysis because it was a great success, becoming a model for other ventures of the same segment, in other regions of the country, as well as abroad. It is important to show this case study because its model proves very promising also to be replicated in the context of the development of local economies in Brazil or in underdeveloped countries.