Large deflection of adaptive multilayered Timoshenko beams

The paper deals with the formulation of the nonlinear equations governing the mechanical behavior of anisotropic, laminated Timoshenkobeams having any number of arbitrarily positioned and orientated actuator and/or sensor layers. Use is made of the von Karman nonlinear strain-displacement relations. Subsequently, the static stability equations for the initial (bifurcation) buckling under transverse and compressive loads are formulated via the Euler method of the adjacent equilibrium configurations. The present analysis is quite general in that no assumptions are made on the placements of the active layers, their symmetry, and their constitutive relations. The only assumptions pertain to the behavior of the adaptivemultilayered beam as one equivalent, linear elastic, anisotropic beam (smeared laminate model). Numerical results deal with the nonlinear flexural response of unsymmetrically laminated beams under transverse and compressive axial loads. It is concluded that the effectiveness of the control depends on the boundary conditions, mechanisms of activation and lay-ups.