Analysis of isotropic tapered beams by using symmetric smoothed particle hydrodynamics method

The Symmetric Smoothed Particle Hydrodynamics (SSPH) method is applied to solve elastostatic deformations of isotropic tapered beams subjected to different sets of boundary conditions. Governing equations are presented by using either the Euler-Bernoulli and Timoshenko beam theories. The performance of the SSPH method is evaluated by using different numbers of nodes in the problem domain and employing different beam theories for the numerical solutions of the iostropic tapered beam problems. To validate the performance of the SSPH method, comparison studies in terms of transverse deflections and axial stresses are carried out with the analytical solutions of Euler Bernoulli Beam Theory. Since there is no available closed form solutions of the problems based on the Timoshenko Beam Theory, the analytical solutions obtained by the Euler Beam Theory are used for the comparison purposes. It is observed that the SSPH method has the conventional convergence properties and yields smaller L2 error.