An improved meshless method for analyzing the time dependent problems in solid mechanics

In this paper, the local radial point interpolation method (LRPIM) is developed for the investigation of time dependent problems in solid mechanics. By a new integration scheme considered for the obtained meshless weak form, integrands are approximated up to the second order of the Taylor series and the integrals are evaluated on some points, which are located inside the local quadrature domains, called integration points. In order to show the efficiency of the suggested method, some time dependent mechanical problems are considered for the engineering structures such as beams and plates, which are subjected to dynamical loads, the deflections and stresses are evaluated. Finally, it has been shown that using the proposed method greatly reduces the number of integration points without affecting the accuracy of the results.

► In this paper, LRPIM is developed for the solving of time dependent problems in mechanics.
► A new integration scheme is used for obtaining the meshless weak-forms.
► Integrals are approximated up to the second order of the Taylor series.
► Using this method greatly reduces the number of integration points without losing the accuracy.