الفهرس 
FINITE ELEMENT MODELLING OF TRUSSESOnly 14 pages are availabe for public view
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Abstract
Most of the research works dedicated to the size optimization of trusses subject to dynamic loading
have been devoted to the maximization of the fundamental frequency of the truss (i.e. increasing
rigidity and/or reducing its mass). Much less work considered the dynamic stresses resulting from
actual dynamic loading. In practice, most truss designers are interested in the mass minimization
of the truss while constraining the stresses to a certain limit to safely sustain the loads. This
does not necessarily correspond to the maximization of the fundamental frequency of the truss.
In the present work, the sizing optimization problem of undamped trusses subjected to dynamic
loading is investigated, aiming to minimize the truss mass while maintaining the dynamic stresses
to certain appropriate safe limits. The Finite Element Method is utilized for modelling the
mechanical behaviour of trusses. The investigation aim is achieved by comparing three optimization
models which are proposed and examined by two simple examples. The first model is the minimization
of the truss mass while maintaining the dynamic stresses within specific limits. The second is the
minimization of the absolute value of the dynamic compliance while its mass is constrained to the
mass of the optimal truss obtained in the solution of the first model. The third is the
minimization of the maximum overall dynamic strain energy while its mass is constrained to the mass
of the optimal truss obtained in the solution of the first model. The results have shown that the
first model achieves the objective in relatively long time due to the large number of constraints
which is equal to twice the number of the truss bars. Based on this outcome, an optimization
procedure, aiming to minimizing the truss mass is proposed. This procedure starts with finding an
improved initial solution either by the second or the third model, and then the first model is
used. The proposed optimization procedure is applied by numerical examples involving plane and
space trusses up to 582 bars. Numerical examples revealed that the truss mass is minimized with
remarkable reduction in the computational costs by implementing the proposed procedure.
Also in this work, a mathematical model for sizing optimization of undamped trusses subjected to
varying load leading to fatigue is proposed. The combined effect of static and dynamic loading is
considered. An optimization model is developed to maximize of the safety factor by changing the
configuration of the truss bars cross-sectional areas. A new quantity ‘Equivalent Fatigue Strain
Energy’ combining the effects of static and dynamic stresses is proposed. This quantity is used as
a global measure of how far fatigue failure is. This assumption is verified through two simple
examples.
The predictions of the presented Finite Element model are verified experimentally through
measurements on a real simple truss. The truss is subjected to different static loads and the
deflections are measured and compared to those predicted by the Finite Element model. Results show
a fair agreement between the experiments and the model and deviations are justifiable.
Maintaining the same stress levels for the given dynamic loads within the safe limits, the proposed
optimization model is used to optimize the design of the tower of a wind turbine as a case study
for structures subjected to dynamic loading. The resulting optimized structure is almost 60% less
in mass than tubular towers.