Finite-element computer program solves for nodal point displacements in an axisymmetric solid. The options in the program include plane stress analysis, axisymmetric solids analysis, nonlinear /plastic/ analysis, and equivalent stress and strain

Wilson, E. L.

English

NASA Technical Reports Server

July 1969	 Brief 69-10238 
•
ICY C
AEC-NASA TECH BRIEF 
FES
AEC-NASA Tech Briefs describe innovations resulting from the research and development program 
of the U.S. AEC or from AEC-NASA interagency efforts. They are issued to encourage commercial 
application. Tech Briefs are published by NASA and may be purchased, at 15 cents each, from 
the Clearinghouse for Federal Scientific and Technical Information, Springfield, Virginia 22151. 
Finite Element Analysis of Compressible Solids
with Nonlinear Material Properties 
The potential widespread use of this program should 
be of interest to many engineers since the procedure 
used may be applied to structures of many different 
materials of practically any geometry. 
The problem: 
To solve for the state of stress and strain in a revolv-
ing solid which may have arbitrary geometry, loading, 
or boundary conditions. The analysis should extend 
into the plastic region. 
The solution: 
Using the direct stiffness approach, a finite-element 
computer program is written which solves for nodal 
point displacements in an axisymmetric solid. 
How it's done: 
The finite-element method is applied to the deter-
mination of displacements and stresses within plane 
or axisymmetric solids with linear or nonlinear ma-
terial properties. 
The continuous body is replaced by a finite number 
of discrete triangular or quadrilateral elements inter-
connected at joints or nodal points. Approximations 
are developed relative to the behavior of any one 
element and applied to the solution of the continuous 
structure. Equilibrium equations, in terms of unknown 
nodal point displacements, are developed at each 
nodal point and the solution of this set of equations 
constitutes a solution to the system. 
The stress in the solid is found from the displace-
ments at the nodes. The options in the program in-
clude axisymmetric solids analysis, plane stress analy-
sis, nonlinear (plastic) analysis, and equivalent stress 
and strain (according to the Von Mises yield condi-
tion). 
Advantages of the finite-element method compared 
to other numerical approaches include the following:
I) The method is completely general with respect 
to geometry and material properties. 
2) Complex bodies composed of many different 
materials are easily represented. 
3) Since anisotropic materials are automatically 
included in the formulation, filament structures are 
readily handled. 
4) Displacement or stress boundary conditions may 
be specified at any nodal point within the finite-
element system. 
5) Arbitrary thermal, mechanical, and accelera-
tional loads are possible. 
6) In addition, the finite-element approach provides 
equilibrium equations which produce a symmetric, 
positive-definite matrix which may be placed in a 
band form and solved with a minimum of computer 
storage and time. 
Notes: 
1. This program is written in FORTRAN H for use on 
the IBM 360/65 system. 
2. Inquiries should be made to: 
COSMIC 
Computer Center 
University of Georgia 
Athens, Georgia 30601 
Reference: B69-10238 
Patent status: 
No patent action is contemplated by NASA. 
Source: E. L. Wilson of 
Aerojet-General Corporation 
under contract to 
AEC--NASA Space Nuclear Propulsion Office 
(NUC- 10342) 
Category 06 
This document was prepared under the sponsorship of the Atomic 
Energy Commission and/or the National Aeronautics and Space 
Administration. Neither the United States Government nor any per-
son 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 the use of any information, apparatus, 
method, or process disclosed in this document may not infringe pri-
vately owned rights.
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Finite element analysis of compressible solids with nonlinear material properties

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