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

2021 ◽  
pp. 095605992110641
Author(s):  
Orsolya Gáspár
Keyword(s):  
Exact Solution ◽  
Simple Algorithm ◽  
Edge Length ◽  
Optimization Process ◽  
Length Ratio ◽  
Theoretical Studies ◽  
Equal Area ◽  
Geodesic Domes ◽  
Dome Structure ◽  
Geodesic Dome

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.

Projecting Stars, Triangles and Concrete

Architectura ◽  
2019 ◽  
Vol 47 (1-2) ◽  
pp. 92-114 ◽  
Author(s):  
Martino Peña Fernández-Serrano ◽  
José Calvo López
Keyword(s):  
20Th Century ◽  
Building Construction ◽  
The Other ◽  
Technical Object ◽  
Geodesic Domes ◽  
Buckminster Fuller ◽  
Scientific Technical ◽  
Art And Architecture ◽  
Walter Gropius ◽  
Geodesic Dome

AbstractSometimes scientific-technical objects can be given an extended meaning as cultural icons and be received in art and architecture. To this end, the object must be detached from its original context and viewed from different, new perspectives.In 1922 Walter Bauersfeld constructed one of the first geodesic domes for testing projection devices in Jena. Walter Gropius and Lázló Moholy-Nagy were among the first to visit the Jena Planetarium; Moholy-Nagy received the dome in his book ›Von Material zu Architektur‹. Richard Buckminster Fuller further developed Bauersfeld’s concept from the 1940s and patented the construction principle of a geodesic dome under the name ›Building Construction‹ in 1954. His patent bears resemblances to the Bauersfeld Planetarium in Jena, which can be demonstrated by manuscripts by Bauersfeld from the Zeiss Archive in Jena. Fuller, on the other hand, also used the geodesic dome to explain his theory as Synergetic. The article traces the transformation of the technical object conceived by Bauersfeld via Moholy-Nagy and Fuller into a cultural icon of the 20th century.

Effect of Length Ratio on Heat Exchange Rate by a Triangular Heat Generating Conductive Body Inside an Enclosure

2018 ◽  
Vol 10 (5) ◽  
Author(s):  
Mohammad Ahmad ◽  
Harish Chandra Thakur
Keyword(s):  
Heat Exchange ◽  
Numerical Analysis ◽  
Simple Algorithm ◽  
Length Ratio ◽  
Convective Term ◽  
Square Enclosure ◽  
Numerical Investigations ◽  
Discrete Equations ◽  
Conjugate Heat Exchange ◽  
Triangular Block

This paper presents a numerical analysis of the conjugate heat exchange inside a square enclosure full of a copper-water nanofluid. The enclosure also contains a heat-generating solid triangular block (a source of heat) at the center. While the horizontal walls of the enclosure are viewed as adiabatic, its perpendicular walls are operated at a consistently low temperature. The second order upwind scheme is used for the convective term and SIMPLE algorithm, to lead the numerical analysis and solve the discrete equations using the commercial software FLUENT 15.0. The consequences of the numerical investigations are then used to clear up the effect of length-ratio and transfer of heat. As per observations, the expansion in the length-ratio influences the rate of heat transfer.

scholarly journals AN EQUAL-AREA METHOD FOR SCALAR CONSERVATION LAWS

2011 ◽  
Vol 53 (2) ◽  
pp. 156-170
Author(s):  
MARJETA KRAMAR FIJAVŽ ◽  
MITJA LAKNER ◽  
MARJETA ŠKAPIN RUGELJ
Keyword(s):  
Conservation Law ◽  
Simple Algorithm ◽  
Characteristic Surface ◽  
Scalar Conservation Laws ◽  
Equal Area ◽  
One Dimensional ◽  
Scalar Conservation ◽  
The One ◽  
Integral Version ◽  
Class Of Functions

AbstractWe study the one-dimensional conservation law. We use a characteristic surface to define a class of functions, within which the integral version of the conservation law is solved in a simple and direct way. A simple algorithm for computing the unique solution is developed. The method uses the equal-area principle and yields the solution for any given time directly.

scholarly journals ANALISIS PENGARUH PEMODELAN SAMBUNGAN TITIK BUHUL PADA STRUKTUR KUBAH GEODESIK

2021 ◽  
Vol 4 (2) ◽  
pp. 503
Author(s):  
Rivven Meilvin ◽  
Leo S. Tedianto
Keyword(s):  
Axial Force ◽  
Joint Modeling ◽  
Internal Force ◽  
Cross Sectional ◽  
Axial Forces ◽  
Translational Displacement ◽  
Single Structure ◽  
Dome Structure ◽  
Internal Forces ◽  
Geodesic Dome

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.

scholarly journals A possible theory for the interaction between convective activities and vortical flows

2011 ◽  
Vol 18 (5) ◽  
pp. 779-789
Author(s):  
N. Zhao ◽  
X. Y. Shen ◽  
Y. H. Ding ◽  
M. Takahashi
Keyword(s):  
Exact Solution ◽  
Equations Of Motion ◽  
Basic Flow ◽  
Vortical Flow ◽  
Dynamical Instability ◽  
Theoretical Studies ◽  
Initial Condition ◽  
Balanced Flow ◽  
Nonlinear Equations Of Motion ◽  
Balance Property

Abstract. Theoretical studies usually attribute convections to the developments of instabilities such as the static or symmetric instabilities of the basic flows. However, the following three facts make the validities of these basic theories unconvincing. First, it seems that in most cases the basic flow with balance property cannot exist as the exact solution, so one cannot formulate appropriate problems of stability. Second, neither linear nor nonlinear theories of dynamical instability are able to describe a two-way interaction between convection and its background, because the basic state which must be an exact solution of the nonlinear equations of motion is prescribed in these issues. And third, the dynamical instability needs some extra initial disturbance to trigger it, which is usually another point of uncertainty. The present study suggests that convective activities can be recognized in the perspective of the interaction of convection with vortical flow. It is demonstrated that convective activities can be regarded as the superposition of free modes of convection and the response to the forcing induced by the imbalance of the unstably stratified vortical flow. An imbalanced vortical flow provides not only an initial condition from which unstable free modes of convection can develop but also a forcing on the convection. So, convection is more appropriately to be regarded as a spontaneous phenomenon rather than a disturbance-triggered phenomenon which is indicated by any theory of dynamical instability. Meanwhile, convection, particularly the forced part, has also a reaction on the basic flow by preventing the imbalance of the vortical flow from further increase and maintaining an approximately balanced flow.

The Optimization Process of Elimination Sediment from the Pipe by Impact Load

2004 ◽  
Vol 9 (3) ◽  
pp. 219-232
Author(s):  
V. Doroševas ◽  
V. Volkovas
Keyword(s):  
Heterogeneous System ◽  
Impact Load ◽  
Homogeneous System ◽  
Transformation Process ◽  
Optimization Process ◽  
Shock Load ◽  
Theoretical Studies ◽  
Shock Impact ◽  
Functional Purpose

The article deals with dynamics of a heterogeneous system of two cylindrical surfaces with different physical and mechanical qualities, which are impacted by shock load. An effective method was suggested for optimization process of elimination sediment from pipe as the result of theoretical studies. This method allows transforming a heterogeneous system of pipe into a homogeneous system, which preserves its functional purpose. Shock impact is applied for transformation, which is optimized according to the suggested qualitative criteria of the transformation process and removing sediment from pipe.

scholarly journals Be water my friend: mesh assimilation

2021 ◽  
Author(s):  
Dennis R. Bukenberger ◽  
Hendrik P. A. Lensch
Keyword(s):  
Point Cloud ◽  
Simple Algorithm ◽  
Edge Length ◽  
Single Parameter ◽  
High Quality ◽  
Shrink Wrapping ◽  
Mesh Topology ◽  
Fine Detail ◽  
Shape Approximation ◽  
Surface Reconstructions

AbstractInspired by the ability of water to assimilate any shape, if being poured into it, regardless if flat, round, sharp, or pointy, we present a novel, high-quality meshing method. Our algorithm creates a triangulated mesh, which automatically refines where necessary and accurately aligns to any target, given as mesh, point cloud, or volumetric function. Our core optimization iterates over steps for mesh uniformity, point cloud projection, and mesh topology corrections, always guaranteeing mesh integrity and $$\epsilon $$ ϵ -close surface reconstructions. In contrast with similar approaches, our simple algorithm operates on an individual vertex basis. This allows for automated and seamless transitions between the optimization phases for rough shape approximation and fine detail reconstruction. Therefore, our proposed algorithm equals established techniques in terms of accuracy and robustness but supersedes them in terms of simplicity and better feature reconstruction, all controlled by a single parameter, the intended edge length. Due to the overall increased versatility of input scenarios and robustness of the assimilation, our technique furthermore generalizes multiple established approaches such as ballooning or shrink wrapping.

THEORETICAL STUDIES OF MODEL COMPOSITES

1993 ◽  
Vol 07 (12) ◽  
pp. 849-856 ◽  
Author(s):  
K.K. MON
Keyword(s):  
Exact Solution ◽  
Sound Velocity ◽  
Power Law ◽  
Direct Method ◽  
Continuum Approximation ◽  
Theoretical Studies ◽  
Model Composite ◽  
Number Of Components ◽  
The Continuum

We study the application and convergence of the continuum approximation to discret composite as a function of the number of Fourier components. A discret model composite with alternating parallel slabs of different constituents and exact solution is considered. The direct method of solving the related eigensystem problem is used to calculate the sound velocity. We show that rather accurate results can be obtained from the continuum approximation with only a small number of Fourier components. The dependence on the number of components is consistent with a power law. Our model results also confirm recent arguments that the sound velocity is independent of density modulations.

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