Computer program on axisymmetric response of shells with other meridional geometries and response of shells subjected to asymmetric loads is described. Description of theory, method of solution, instructions for preparing input data, and two sample problems to illustrate data preparation and output format are included

Ball, R. G.

English

A digital computer program known as SATANS (static and transient analysis, nonlinear, shells) for the geometrically nonlinear static and dynamic response of arbitrarily loaded shells of revolution is presented. Instructions for the preparation of the input data cards and other information necessary for the operation of the program are described in detail and two sample problems are included. The governing partial differential equations are based upon Sanders' nonlinear thin shell theory for the conditions of small strains and moderately small rotations. The governing equations are reduced to uncoupled sets of four linear, second order, partial differential equations in the meridional and time coordinates by expanding the dependent variables in a Fourier sine or cosine series in the circumferential coordinate and treating the nonlinear modal coupling terms as pseudo loads. The derivatives with respect to the meridional coordinate are approximated by central finite differences, and the displacement accelerations are approximated by the implicit Houbolt backward difference scheme with a constant time interval. The boundaries of the shell may be closed, free, fixed, or elastically restrained. The program is coded in the FORTRAN 4 language and is dimensioned to allow a maximum of 10 arbitrary Fourier harmonics and a maximum product of the total number of meridional stations and the total number of Fourier harmonics of 200. The program requires 155,000 bytes of core storage

Ball, R. E.

NASA Technical Reports Server

A computer program for the geometrically nonlinear static and dynamic analysis of arbitrarily loaded shells of revolution, theory and users manual

Computer program on axisymmetric response of shells with other meridional geometries and response of shells subjected to asymmetric loads is described. Description of theory, method of solution, instructions for preparing input data, and two sample problems to illustrate data preparation and output format are included.Approved for public release; distribution is unlimited

Ball, R.G.

Calhoun, Institutional Archive of the Naval Postgraduate School

Geometrically nonlinear static and dynamic analysis of arbitrarily loaded shells of revolution

August 1972	 CORRECTED COPY
	 B72-10504 
NASA TECH BRIEF 
Langley Research Center 
NASA Tech Briefs announce new technology derived from the U.S. space program. They are issued to encourage 
commercial application. Tech Briefs are available on a subscription basis from the National Technical Information 
Service, Springfield, Virginia 22151. Requests for individual copies or questions relating to the Tech Brief program may 
be directed to the Technology Utilization Office, NASA, Code KT, Washington, D.C. 20546. 
Geometrically Nonlinear Static and Dynamic Analysis of

Arbitrarily Loaded Shells of Revolution 
The problem: 
The design of many shell structures is influenced by 
the geometrically nonlinear response of the shell when 
subjected to static and/or dynamic loads. As a conse-
quence, a number of investigations have been devoted 
to the study of the buckling phenomenon exhibited by 
shells. Most early works examine the behavior of the 
shallow spherical cap, the truncated cone, and the 
cylinder under axisymmetric loads. 
The solution: 
A computer program was developed for the geo-
metrically nonlinear static and dynamic response of 
arbitrarily loaded shells of revolution. It was developed 
due to the lack of information on the axisymmetric 
response of shells with other meridional geometries and 
on the response of shells subjected to asymmetric loads. 
How it's done: 
The program can be used to analyze any shell of 
revolution for which the following conditions hold: 
1. The geometric and material properties of the shell 
are axisymmetric, but may vary along the shell 
meridian. 
2. The applied pressure and temperature distributions 
and initial conditions are symmetric about a datum 
meridional plane. 
3. The shell material is isotropic, but the modulus of 
elasticity may vary through the thickness. Poisson's 
ratio is Constant. 
4. The boundaries of the shell may be closed, free, fixed, 
or elastically restrained. 
The governing partial differential equations are based 
upon Sanders' nonlinear thin shell theory for the condi-
tion of small strains and moderately small rotations. 
At each load or time step, an estimate of the solution 
is obtained by extrapolation from the solutions at the
previous load or time steps. The sets of algebraic equa-
tions are repeatedly solved using Potter's form of 
Gaussian elimination, and the pseudo loads are re-
computed, until the solution converges. 
An automatic variable load incrementing routine is 
included in the program for the static analysis. Post-
buckling behavior cannot be determined in the static 
analysis because of the method of solution employed. 
The documentation contains a description of the 
theory, the method of solution, instructions for pre-
paring the input data, and two sample problems to 
illustrate the data preparation and output format. 
Notes: 
1. This program is written in FORTRAN IV Level H to 
be used on the IBM-360/67 computer with 150K 
bytes of core. The program has also been success-
fully compiled on the CDC-6400 computer. 
2. The dynamic analysis capability of this program is 
a recent extension of a program developed for the 
non-linear static analysis of arbitrarily loaded shells 
of revolution. 
(Reference computer program LAR- 10736) 
3. Inquiries concerning this program should be directed 
to:
COSMIC 
112 Barrow Hall 
University of Georgia 
Athens, Georgia 30601 
Reference: LAR-1 1109 
Source: Robert E. Ball of

U.S. Naval Postgraduate School

under contract to

Langley Research Center

(LAR-1 1109) 
Category 09 
This document was prepared under the sponsorship of the National
	 Government assumes any liability resulting from the use of the 
Aeronautics and Space Administration. Neither the United States
	 information contained in this document, or warrants that such use Government nor any person acting on behalf of the United States
	 will be free from privately owned rights.
https://ntrs.nasa.gov/search.jsp?R=19720000503 2020-03-17T03:34:25+00:00Z


NASA Contractor Report prepared for Langley Research CenterA digital computer program known as SATANS Static and Transient Analysis, Nonlinear, Shells, for the geometrically nonlinear static and dynamic response of arbitrarily loaded shells of revolution is presented...National Aeronautics and Space Administratio

Geometrically nonlinear static and dynamic analysis of arbitrarily loaded shells of revolution

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Calhoun, Institutional Archive of the Naval Postgraduate School