Mathematical formulation, suitable for analytical design of structural networks with uniform local stability, yields idealized solutions for specific two-family networks

Hedgepeth, J. M.

Preiswerk, P.

Scheurch, H. U.

English

NASA Technical Reports Server

32 
November 1971
	 Brief 71-10446 
NASA TECH BRIEF 
NASA Pasadena Office	
_ilv 
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Axisymmetric and Cylindrical Isostable Structures: A Concept 
A mathematical formulation, suitable for the ana-
lytical design of structural networks with uniform 
local stability, has yielded idealized solutions for 
specific two-family networks. However, much work 
remains to be done before idealized structures such 
Axisymrnetric, Gravity-Loaded Isostabiloid: Side and Top View 
as that shown in the figure can be reduced to prac-
tice. For example, the effects of multiple loading 
and of unavoidable imperfections found in real 
construction materials remain to be considered. 
Nevertheless, such configurations may eventually be 
used in the design of practical structures.
A structure that uses the minimum amount of 
material is frequently described theoretically by spe-
cifying that each structural component fail simul-
taneously under a unique ultimate tensile load. 
Examples of such structures, called " isotensoids," 
are uniformly stressed Maxwell-Michell networks, 
isotropically stressed structural "soap-film" mem-
branes, and uniformly stressed filamentary structures. 
Uniformly compressed structures analogous to the 
isotensoids can also be found. However, these "iso-
compressoids" may fail because of buckling, at a 
point well below their maximum compressive 
strength. 
The referenced report is a first attempt to treat 
isocompressoid structures. It avoids the complex 
effects of general instability, matrix support, and ar-
ticulate loading by constraining each element of the 
structure to buckle as an Euler column upon reach-
ing its ultimate compressive load. The term "isosta-
biloid" is used to describe structures which satisfy 
this condition. The report gives particular attention 
to the existtiice of closed-dome isostabiloids, be-
cause such structures appear to have the greatest 
practical value. 
The differential equations for the geometry of 
compression-loaded, two-family filamentary struc-
tures are established. The analytical formulation 
requires that failure due to local instability occurs 
simultaneously in the whole structure. Solutions 
such as the one illustrated are obtained for the par-
ticular case where the structure's own weight, under 
earth gravity, is the only load. For this case, the 
shape of the meridian and the cross section are de-
termined, as well as the pattern of the filaments. 
(continued overleaf) 
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Aeronautics and Space Administration. Neither the United States 
Government nor any person acting on behalf of the United States
Government assumes any liability resulting from the use of the 
information contained in this document, or warrants that such use 
will be free from privately owned rights.
https://ntrs.nasa.gov/search.jsp?R=19710000443 2020-03-17T02:30:37+00:00Z
Patent status: 
No patent action is contemplated by NASA. 
Source: P. Preiswerk, J.M. Hedgepeth,

and H.U. Scheurch of

Astro Research Corp.

under contract to

NASA Pasadena Office

(N P0-12049) 
Note: 
Requests for further information may be directed 
to
Technology Utilization Officer 
NASA Pasadena Office 
4800 Oak Grove Drive 
Pasadena, California 91103 
Reference: TSP7I-10446
Brief 71-10446	 Category 06


Axisymmetric and cylindrical isostable structures - A concept

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