Efficient smoothed particle hydrodynamics method for the analysis of planar structures undergoing geometric nonlinearities

In the present investigation, a new modified smoothed particle hydrodynamics (SPH) method particularly adapted for the analysis of planar structures undergoing geometric nonlinearities is introduced and discussed. The problem of inconsistency which is often encountered in the classical SPH method is alleviated by introducing modifications of the kernel function and its derivatives using an explicit polynomial feature representation based on the Taylor series expansion. Tensile instabilities arising in the Eulerian-based SPH formulation which appear due to large deformations are attenuated by the introduction of a total Lagrangian formulation which is robust for large displacements/rotations. The resulting nonlinear problem is solved using the explicit dynamics time integration scheme. The validity of the proposed approach is demonstrated through two numerical applications involving geometrical nonlinearities, where the obtained results are compared to those obtained using the standard finite element method.