Archivos Nasa Cúpulas Geodésicas

1. 4.

Report

No.

2.

Government

Accession

No.

3.

Recipient's

Catalog

No.

NASA

CR-1734
5. Report Date

Title ndSubtitle ADVANCED a STRUCTURAL GEOMETRY STUDIES PART I - POLYHEDRAL SUBDIVISION CONCEPTS FOR STRUCTURAL APPLICATIONS Joseph
Organization Name and

September
6. Performing

1971
Code

Organiza:tion

7. Author(s)
9. Performing

D. ClintonAddress

8.

Performing

Organization

Report

No.

10.

Work

Unit

No.

Southern Illinois University Carbondale, Illinois

11.

Contract

,or Gran.J No.

NGR-14-O0_-O02
13. Type of Report and Period Covered

12.

Sponsoring

Agency

Name

and Address

Contractor Space Administration
14. Sponsoring Agency

Report

National Aeronautics andWashington, D. C. 20546

Code

15.

Supplementary

Notes

16.

Abstract

A study leading to the formulation of computer-oriented mathematical models pertaining to methods of subdividing polyhedra into triangulated spherical space frames. The models perform the truncations and transformations of the polyhedral forms and calculate the geometrical properties of the generated space frames(spheres, hemispheres, and domes).

17.

Key

Words

(Selected

by Author(s))

18.

Distribution

Statement

Geodesic Structural Polyhedral Structural
19. Security Classif.

Domes Domes Subdivision Spheres,
(of this report)

Unclassified

- unlimited

Spaceframes
20. Security Classif. (of this page) 21. No. of Pages 22. Price

Unclassified

Unclassified

iii

$3.00For sale by the National Technical Information

Service, Springfield,

Virginia

22151

FOREWORD

This

final

report at under

was

prepared Illinois Contract the NASA NGR

by

the

School

of Carbondale, The contract Research

Technology Illinois was and

Southern NASA by

University, 14-008-002. of

administered Technology.

Office

Advanced

PersonnelJulian Clinton, research Michael Richard H.

participating Lauchner, prime

in principal

the

research investigator; R. Buckminster Ann B. C.

included: Joseph Fuller, Garrison, and D.

investigator; Wayne Allen

consultant; Keeling, M. Moeller,

Boo%h, Mark

Kilty,

Mabee,

computer

programmers.

iii

PART

I

POLYHEDRAL FOB

SUBDIVISION STRUCTURAL

CONCEPTSAPPLICATIONS

i.i

Introduction

.............

1-2

1.2

Polyhedron

..............

1-7

1.3

Structural

Orientation

........

I-ll

1.4

Definitions

.............

1-16

1.5

Method

of

Subdivision

........

1-18

1.6

Method

1

...............

1-36

1.7

Methods

2

&

3

............

1-76

1.8

Methods

4&

5

............

1-145

1.9

Methods

6

&

7

............

1-185

v

Computer Software and Information

Management Center

The documentation and program advanced structural geometry made available to the public

developed for the studies will be through COSMIC.

COSMIC (Computer Software Management and Information Center) was established early in 1966 at theUniversity of Georgia to collect and disseminate to the public computer software developed by government agencies. Since that time thousands of computer programs in all areas of aerospace engineering, mathematics, business, and industry have been distributed to requesters throughout the United States. The Technology Utilization Division of NASA, designed to enlarge the return on the publicinvestment in aeronautical and space activities, was the first government agency to participate formally. _In July 1968 the Atomic Energy Commission and in November 1968 the Department of Defense joined in the COSMIC endeavor. With the addition of these two major agencies, the original concept of making taxpaid developments available to the public was expanded to make COSMIC a transfer point between...