Semi-Analytical Solution for The Static Analysis of Functionally Graded Beams Resting on Two Parameter Elastic Foundation

Two-dimensional elasticity solution is presented for static analysis of functionally graded beams with various end conditions and resting on elastic foundation, using the semi-analytical approach, which makes use of the state space method and differential quadrature method. The beams are assumed to be transversely isotropic, with Young's modulus varying exponentially along the thickness, while Poisson's ratio remaining constant. The state space method (SSM) is adopted to obtain analytically the thickness variation of the elastic field and, approximate solution in the longitudinal direction can be obtained using the one dimensional differential quadrature method (DQM). The convergence and accuracy of the present approach is then validated by comparing the numerical results with the exact solutions for the case of simply support functionally graded beam. The influence of material gradient index, coefficient of elastic foundation and the ratio of thickness to length on the behavior of functionally graded beams are finally investigated