Elastostatic analysis of two-directional functionally graded beams using various beam theories and Symmetric Smoothed Particle Hydrodynamics method

The elastostatic behaviour of two-directional functionally graded beams (FGBs) subjected to various sets of boundary conditions are investigated for the first time by using the Euler-Bernoulli, Timoshenko and Reddy-Bickford beam theories and the Symmetric Smoothed Particle Hydrodynamics (SSPH) method. To validate the developed code, a simply supported conventional FGB problem is studied and the comparison studies are performed along with the analytical solutions and the results from previous studies. The numerical calculations in terms of maximum dimensionless transverse deflections, dimensionless axial and transverse shear stresses are performed based on different beam theories with varying gradation exponents (power-law index), different aspect ratios (L/h) and sets of boundary conditions.