Mode-displacement method for structural dynamic analysis of bio-inspired structures: a palm-tree stem subject to wind effects

Biological materials (orthotropic materials), like wood, can offer good mechanical properties with a minimum amount of material, making their internal structure the suitable one to be applied on bio-inspired structures. The knowledge of the exceptional structural performance of palm trees, and specially its response to different loading conditions, provides useful information when lightweight structures with high slenderness ratio are desired. Recent researches focused on the analysis of palm trees subject to static loading conditions, ignoring the fluctuating nature of the wind speed. The purpose of this study is to simulate in a computational efficient way the effect of dynamic loading conditions applied on palm trees. Using the mode displacement method, the number of degrees of freedom of a dynamic finite element analysis can be drastically reduced with a minimal loss of accuracy. It was applied to simulate the behavior of structures comprised of an orthotropic material subject to a stochastic dynamic load. The influence of the number of selected degrees of freedom has also been studied. In addition, an exponential integration method is proposed to perform the time integration procedure. The results obtained show that a properly reduced model suitably represents the full finite element model without any appreciable loss of accuracy; it is also shown that computational cost can be drastically reduced. This method could give an appropriate computational representation of the behavior of orthotropic structures, and it could be used for studying more complex bio-inspired structures.