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.

ANALISIS PENGARUH PEMODELAN SAMBUNGAN TITIK BUHUL PADA STRUKTUR KUBAH GEODESIK

The geodesic dome consists of steel rod elements joined together to form a single structure. Generally, these geodesic domes are analyzed by assuming the joints of the gusset points are joints and only receive axial forces on the rods. However, in reality, it is not easy to apply gusset joints as pure joints in construction. This research will analyze the geodesic dome by modeling the joints of the gusset points as joints where there is only axial force arising on the rods and modeling the rigid gusset points where there will also be moments and shear on the rods. The analysis will only be carried out by comparing the value of the displacement at each gusset joint modeling and checking the cross-sectional dimensions of the internal forces that arise with the help of the MIDAS GEN program in modeling the geodesic dome structure which has a diameter of 20000 mm and a height of 10000 mm with the type of steel profile. used is a pipe profile using two types of geodesic dome, namely type 2V and 3V. For loads that are calculated, namely dead load, live load, and wind load. The results showed a relatively small difference in translational displacement and the axial force was relatively the same in the internal force analysis, so it is better if the analysis by modeling the gusset connection as rigid.ABSTRAKKubah geodesik terdiri dari elemen batang baja yang disambung menjadi satu kesatuan struktur. Umumnya kubah geodesik ini dianalisis dengan menganggap sambungan titik buhulnya berupa sendi dan hanya menerima gaya aksial saja pada batang - batangnya. Namun pada kenyataannya untuk mengaplikasikan sambungan titik buhul sebagai sendi murni pada konstruksi tidaklah mudah. Penelitian ini akan menganalisis kubah geodesik dengan memodelkan sambungan titik buhulnya sebagai sendi dimana hanya ada gaya aksial saja yang timbul pada batang - batangnya dan memodelkan titik buhulnya rigid dimana akan terjadi juga momen dan geser pada batang tersebut. Analisis hanya akan dilakukan dengan membandingkan nilai dari perpindahan pada setiap pemodelan sambungan titik buhul dan pengecekan dimensi penampang terhadap gaya – gaya dalam yang timbul dengan bantuan program MIDAS GEN dalam memodelkan struktur kubah geodesik yang mempunyai diameter 20000 mm dan tinggi 10000 mm dengan jenis profil baja yang digunakan adalah profil pipa dengan menggunakan dua tipe kubah geodesik yaitu tipe 2V dan 3V. Untuk beban yang diperhitungkan yaitu beban mati, beban hidup, dan beban angin. Hasil penelitian menunjukkan nilai perbedaan yang relatif kecil pada perpindahan translasi dan diperoleh gaya aksial yang relatif sama pada analisis gaya dalam yang timbul, sehingga sebaiknya analisis dengan pemodelan sambungan titik buhul sebagai rigid.

Passive Strategies to Improve the Comfort Conditions in a Geodesic Dome

Non-conventional thermal zones are low-cost and ecology friendly alternatives to the housing needs of populations in various situations, such as surviving natural disasters or addressing homelessness. However, it is necessary to guarantee thermal comfort for occupants, while aiming to minimize energy consumption and wastage in refrigeration systems. To reduce the cooling requirements in non-conventional thermal zones it is necessary to model the structure and analyze the principal factors contributing to internal temperature. In this paper, a geodesic dome is modellingusing the lumped parameter technique. This structure is composed of a wooden skeleton and wooden floor, with a canvas surface as its exterior. The mathematical model was tuned using experimental data, and its parameters were classified using Monte Carlo sensitivity analysis. The mathematical model was used to evaluate the impact on internal temperature and occupants’ comfort when two strategies are considered. The results obtained indicatee internal temperature reductions down to a range of 7% to 11%; this result is reflected directly in the energy used to refrigerate the thermal zone, contributing to the objective of providing houses with lower energy consumption.

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.