Contents:
INSTITUTE FOR LIGHTWEIGHT STRUCTURES (IL)
THE EXPERIMENTAL DETERMINATION OF MINIMAL NETS
A study of the IL by Ekkehard Bertram, Berthold Burkhardt,
Rainer Gaupp, Eberhard Haug, Gernot Minke, Frei Otto,
Jochen Schilling, Gunther Schisfl.
Frei Otto
MINIMAL NETS
Gernot Minke, Gunther Schofl
THE EXPERIMENTAL DETERMINATION OF MINIMAL NETS
INTRODUCTION
1.13
1.2
1.3
1.4
15
Preface
The Problem
Definition
Different Path Configuration for the Same Point Constellation
Experimental Solution to the Problem by Soap Film Strips
DETERMINATION OF THE MINIMAL NET USING SOAP
ZILMS
>reliminary Tests
Test Instrument
Adjustment
Defining the Point Constellation
Formation of the Film Strips
2.
2.2
2.3
2.4
2.5
3
DIFFERENT MINIMAL NETS FOR THE SAME
CONSTELLATIONS
Different Configurations for the Same Sum Length
Irregularities in the Formation of the Minimal Nets
3.1
3 2
SYSTEMS AND THEIR DEFINITIONS
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4 3
Definitions of the Elements
Primary Systems
Secondary Systems
3.
PRINCIPLE POSSIBILITIES FOR THE UNION OF FIGURES
5.1 Union of Primary Figures
5.2 Union of Secondary Figures
10
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I
12
A
or
a
20
20
21
23
23
23
23
25
25
25
.. CONSTELLATIONS INVESTIGATED EXPERIMENTALLY
6.1 Band Constellations
5.2 Grid Constellations
6.3 Constellations of Regular Polygons
6.4 Group Constellations
MEASUREMENTS TECHNIQUES
Measurement Errors
Conirol of the Measuring Accuracy when Using Regular
Polygons
MINIMAL NETS OF IRREGULAR CONNECTIONS
8.1 Irregular Change of the Field Value
8.2 Minimal Nets for Continually Changing Field Value
THREE-DIMENSIONAL MINIMAL NETS
27
27
31
33
35
39
39
10
{
4 |
14
APPLICATION OF THE ANALOGY PROCEDURE TO
MINIMIZE THE NET LENGTH
10.1 Introduction
10.2 Superposition of Minimal Nets
10.3 Hierarchy of Minimal Nets
10.4 Changes of Minimal Nets
10.5 Traffic Nets with Minimal Total Length
Ekkehard Bertram
11, GEOMETRICAL CONSTRUCTION AND LENGTH OF
MINIMAL NETS
11.1 Conditions
11.2 Construction possibilities for secondary figures of the first and
second grade
Length calculation for secondary figures of the first and second
grade
4A
46
46
46
47
40
50
50
51
51
PROJECTS AT THE INSTITUTE FOR LIGHT WEIGHT STRUCTURES (IL) 54
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