Chou Y.

Large amplitude vibrations introduce a geometrical type of nonlinearity that influences the dynamic behavior of a structure. The geometrically nonlinear vibrations of isotropic, straight beams are studied using smoothed particle hydrodynamics (SPH). First-order shear deformation theory is followed, and both the longitudinal displacements and inertia are taken into account. SPH is used to transform the complex partial differential equations into their corresponding ordinary differential equations by construction of integral equations with a kernel function. Using the ghost particle method, consistent estimation of near-boundary corrections for system variables is also accomplished. The nonlinear equations of motion are solved in the time domain by Newmark¡¦s method. The influence of parameters like the thickness and the configuration on the beams nonlinear dynamics is studied. Periodic and non-periodic motions are found. To verify this numerical procedure, the comparison between the SPH results and the exact solution for the 1D case, together with the numerical solution obtained via finite element method. These efforts will eventually enhance the application of the SPH and extend to analyze the complex structural problems.