#### SENSITIVITY ANALYSIS OF TRUSS AND FRAME STRUCTURES WITH UNCERTAIN GEOMETRY

Alfredo Rivera

Dept. of Civil Engineering, UTEP

arivera8@miners.utep.edu
Andrzej Pownuk

Dept. of Mathematical Sciences, UTEP

ampownuk@utep.edu

Behaviour of single bar in the truss structure can be described by the following
second order differential equation

d/dx ( EA du/dx ) + n = 0, where x belongs to [0, L]

In this paper the authors are discussing sensitivity of the internal forces and
displacement of the truss structures with respect to the changes of the geometry
of the structure. Results can be applied to the calculation of the reliability
and in the optimization. Sensitivity of the solution can be calculated by using
semianalytical methods, functional derivative, topological derivative or by using
classical theory of sensitivity analysis. In order to take into account variation
of the length of the bars it is necessary to consider initial strains.
Similar theory can be applied in the case of frame structures and more complicated
problems of computational mechanics.