Elastostatic Deformation Analysis of Thick Isotropic Beams by Using Different Beam Theories and a Meshless Method

Abstract

The elastostatic deformations of thick isotropic beams subjected to various sets of boundary conditions are presented by using different beam theories and the Symmetric Smoothed Particle Hydrodynamics (SSPH) method. The analysis is 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 for the first time. For the numerical results, various numbers of nodes are used in the problem domain. Regarding to the computed results for RBT, various number of terms in the Taylor Series Expansions (TSEs) is employed. To validate the performance of the SSPH method, comparison studies in terms of transverse deflections are carried out with the analytical solutions. It is found that the SSPH method has provided satisfactory convergence rate and smaller L2 error.