Analysis of Bending Deflections of Functionally Graded Beams by Using Different Beam Theories and Symmetric Smoothed Particle Hydrodynamics

Abstract

The elastostatic deformations of functionally graded beams under various boundary conditions are investigated by using different beam theories and the Symmetric Smoothed Particle Hydrodynamics (SSPH) method. The numerical calculations are performed based on the Euler-Bernoulli, Timoshenko and Reddy-Bickford beam theories. The performance of the SSPH method is investigated for the comparison of the different beam theories where the beams are composed of two different materials for the first time. For the numerical results various numbers of nodes are used in the problem domain. Regarding to the computed results for Reddy-Bickford beam theory various numbers of terms in the Taylor Series Expansions (TSEs) are employed to improve the accuracy. To validate the performance of the SSPH method, comparison studies in terms of transverse deflections are carried out with the analytical solutions by using the global L₂ error norm.

Keywords

• Meshless method, functionally graded beam, bending deflection, SSPH method, shear deformation theories

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