Large De ection of Functionally Graded Cantilever Flexible Beam with Geometric Non-Linearity: Analytical and Numerical Approaches

Abstract

Analytical and Adomian decomposition methods have been developed to determine the large de ection of a functionally graded cantilever beam under inclined end loading by fully accounting for geometric nonlinearities, and by incorporating the physical properties of functionally graded materials, and have also been solved. The large de ection problem will also be solved by using an FEA solver. Results obtained only due to end loading are validated using a developed analytical solution. The Adomian decomposition method yields polynomial expressions for the beam con guration. The equilibrium equation of a functionally graded cantilever beam actuated through self-balanced moments has been derived and solved using the Adomian decomposition method and the FEA solver for which no closed form solution can be obtained. Some of the limitations and recipes to obviate these are included. The Adomian decomposition method will be useful toward the design of functionally graded compliant mechanisms driven by smart actuators.