Large deflection of flexible tapered functionally graded beam

In this paper the semi-analytical analyses of the flexible cantilever tapered functionally graded beam under combined inclined end loading and intermediate loading are studied.In order to derive the fully non-linear equations governing the non-linear deformation,a curvilinear coordinate system is introduced.A general non-linear second order differential equation that governs the shape of a deflected beam is derived based on the geometric nonlinearities,infinitesimal local displacements and local rotation concepts with remarkable physical properties of functionally graded materials.The solutions obtained from semi-analytical methods are numerically compared with the existing elliptic integral solution for the case of a flexible uniform cantilever functionally graded beam.The effects of taper ratio,inclined end load angle and material property gradient on large deflection of the beam are evaluated.The Adomian decomposition method will be useful toward the design of tapered functionally graded compliant mechanisms driven by smart actuators.     

Large deflection of cantilever beams with geometric non-linearity: Analytical and numerical approaches

Non-linear shooting and Adomian decomposition methods have been proposed to determine the large deflection of a cantilever beam under arbitrary loading conditions. Results obtained only due to end loading are validated using elliptic integral solutions. The non-linear shooting method gives accurate numerical results while the Adomian decomposition method yields polynomial expressions for the beam configuration. With high load parameters, occurrence of multiple solutions is discussed with reference to possible buckling of the beam-column. An example of concentrated intermediate loading (cantilever beam subjected to two concentrated self-balanced moments), for which no closed form solution can be obtained, is solved using these two methods. Some of the limitations and recipes to obviate these are included. The methods will be useful toward the design of compliant mechanisms driven by smart actuators.