Enhanced model for nonlinear dynamic analysis of rectangular composite plates with embedded SMA wires, considering the instantaneous local phase changes

Abstract

Realistic analysis of structures with SMA elements necessitates considering: (i) instantaneous changes of the martensite volume fraction of the SMA elements due to time variations of the stresses, (ii) various constitute equations for the successive loading and unloading events, (iii) local variations of the volume fractions of the phases due to spatial variations of the stress components, and (iv) the reverse loading. The available analyzes in literature have been simplified; so that either none or majority of the mentioned hints have not been taken into account. In the present research, all of these complexities are considered to present more realistic forced and transient vibration analyzes for composite plates with SMA wires, through presenting novel modeling and numerical solution procedures and modifying Brinson’s model to correctly trace the global and local loading and unloading events. Furthermore, nonlinear strain–displacement expressions are used to present a comprehensive research. The first-order shear-deformation plate theory and the finite element method are included in the modeling and solution process. Results reveal that the superelastic nature of the SMA wires reduces the higher transient stresses with higher rates. Furthermore, due to the material and kinematic nonlinearities, the fundamental natural frequency is both load- and time-dependent.