Computer program performs stability analyses for a wide class of shells without unduly restrictive approximations. The program uses numerical integration, finite difference of finite element techniques to solve with reasonable accuracy almost any buckling problem for shells exhibiting orthotropic behavior

Almroth, B. O.

Bushnell, D.

Sobel, L. H.

English

NASA Technical Reports Server

June 1968	 Brief 68-10226 
NASA TECH BRIEF	
/& 
NASA Tech Briefs are issued to summarize specific innovations derived from the U.S. space program, 
to encourage their commercial application. Copies are available to the public at 15 cents each 
from the Clearinghouse for Federal Scientific and Technical Information, Springfield, Virginia 22151. 
Computer Program Analyzes Buckling of Shells of Revolution with Various 
Wall Constructions 
A computer program (entitled BOSOR) has been 
developed to perform stability analyses for a wide 
class of shells without unduly restrictive approxima-
tions. The program uses numerical integration and 
finite difference techniques to solve with reasonable 
accuracy a wide variety of buckling problems for shells 
of revolution which have "orthotropic" properties 
oriented with principal axes in the axial and circum-
ferential directions. For this type of shell in the pre-
buckling state, axisymmetrical loads produce axisym-
metrical displacements. The program performs a 
nonlinear axisymmetric prebuckling analysis and then 
solves an eigenvalue problem to determine buckling 
loads. 
For the geometry of the meridian, the general 
branch of the program calls for input in the form of 
cartesian coordinates for a number of points along 
the meridian. Special branches are provided for cylin-
drical, conical, spherical, and toroidal shells. 
The general branch for the shell wall stiffness data 
calls for input in the form of coefficients of the con-
stitutive equations. Special branches calling for 
simpler input data are provided for: shells with ring 
and stringer stiffening; shells with skew stiffeners; 
fiber reinforced shells; layered shells; corrugated ring 
stiffened shells; and shells with one corrugated and 
one smooth skin. The eccentricity of the stiffening is 
accounted for, but the stiffness coefficients must be 
constant along the meridian. 
The most general form of the boundary conditions 
for the prebuckling analysis is a set of 4 nonhomo-
geneous equations containing 20 coefficients. For the 
stability analysis, the homogeneous boundary condi-
tions consist of 8 equations with 64 coefficients which
are called for as input by the general branch. The 
boundary conditions can be calculated internally (with 
only control integers required as input) by several 
branches provided in the program and include force 
or displacement boundary conditions, support by 
elastic edge rings, or support by an elastic medium. 
The shell can be open or closed at the apex. When the 
program makes use of the nonlinear prebuckling 
analysis, the boundary conditions for the prebuckling 
solution are consistent with the stability analysis. 
In the first part of the analysis, the Newton—Raph-
son procedure is used to solve the set of nonlinear 
algebraic equations. These equations result from a 
finite-difference analog of the pair of nonlinear, non-
homogeneous, second-order ordinary differential 
equations governing the prebuckling state of the shell. 
The solution of the equations yields the prebuckling 
meridional rotation and meridional and circumferen-
tial stress resultants. 
The second part of the analysis solves the stability 
equations (Donnell-type formulation) which are a pair 
of linear, homogeneous, fourth-order, partial differ-
ential equations having coefficients determined from 
the prebuckling analysis. Since the dependent varia-
bles are harmonic, dependence on the circumferen-
tial coordinate can be eliminated and the resulting 
ordinary differential equations solved by the method 
of finite differences. The stability analysis is formu-
lated as an eigenvalue problem with the lowest eigen-
value of the stability equations corresponding to the 
critical load. 
Notes: 
I. This program is written in Fortran IV for use on 
the IBM 7094 computer.
(continued overleaf) 
This document was prepared under the sponsorship of the National 
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=19680000226 2020-03-12T06:07:35+00:00Z
2. Inquiries concerning this program may be made to: 
COSMIC 
Computer Center 
University of Georgia 
Athens, Georgia 30601 
Reference: B68-10226
Patent status:' 
No patent action is contemplated by NASA. 
Source: D. Bushnell, B. 0. Almroth, 
and L. H. Sobel 
of Lockheed Missiles and Space Company 
under contract to 
Langley Research Center 
(LA R- I 0290) 
Brief 68-10226	 Category 06


Computer program analyzes Buckling Of Shells Of Revolution with various wall construction, BOSOR

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