Explicit Expression of the Internal Forces in a Structure
as a Function of the Element Stiffnesses
This research was performed at the
School of Mechanical Engineering
Tel Aviv University
A major obstacle in the design of structures is the need for multiple
reanalysis of the structure. Indeed, when the geometry of the structures
or the stiffnesses of its elements are modified one has to reanalyze the
structure in its new configuration in order to assess its stresses and
displacements. This is the reason for the development of
reanalysis techniques or for approximate explicit expressions for the
internal forces and displacements in terms of the design variables.
When the design variables are the cross-sectional characteristics of truss
and frame structures, this author has found the exact explicit expressions
for the internal forces in these structures in terms of the design variables.
These exact equations are rather interesting, however difficult to implement,
due to the large number of terms involved.
- M.B. Fuchs (1997),
The Exact Dependency of the Internal Forces on the Element
Stiffnesses of Framed Structures
WCSMO-2, The Second World Congress on Structural and Multidisciplinary
Optimization , Zakopane, 26-30 May.
This poster paper explains in simple steps how to construct the explicit
expressions for the internal forces N in trusses in terms of the
cross-sectional areas A of its members, and
for the internal forces M,S,N in frames in terms of the
cross-sectional areas A and the moments of inertia I
of its members. The method hinges on determining all the statically determinate
substructures which are embedded in the original structure. Having found the
internal forces in every substructure, when one applies to it the external
loads, the explicit expressions follow naturally. The problem is that there are
many determinate substructures in most engineering structures.
Last modified by
on June 19, 1997.