TY - JOUR A1 - Talebi, Hossein A1 - Samaniego, C. A1 - Samaniego, Esteban A1 - Rabczuk, Timon T1 - On the numerical stability and mass-lumping schemes for explicit enriched meshfree methods JF - International Journal for Numerical Methods in Engineering N2 - Meshfree methods (MMs) such as the element free Galerkin (EFG)method have gained popularity because of some advantages over other numerical methods such as the finite element method (FEM). A group of problems that have attracted a great deal of attention from the EFG method community includes the treatment of large deformations and dealing with strong discontinuities such as cracks. One efficient solution to model cracks is adding special enrichment functions to the standard shape functions such as extended FEM, within the FEM context, and the cracking particles method, based on EFG method. It is well known that explicit time integration in dynamic applications is conditionally stable. Furthermore, in enriched methods, the critical time step may tend to very small values leading to computationally expensive simulations. In this work, we study the stability of enriched MMs and propose two mass-lumping strategies. Then we show that the critical time step for enriched MMs based on lumped mass matrices is of the same order as the critical time step of MMs without enrichment. Moreover, we show that, in contrast to extended FEM, even with a consistent mass matrix, the critical time step does not vanish even when the crack directly crosses a node. KW - Angewandte Mathematik KW - Strukturmechanik Y1 - 2012 U6 - http://dx.doi.org/10.1002/nme.3275 SP - 1009 EP - 1027 ER - TY - JOUR A1 - Talebi, Hossein A1 - Zi, Goangseup A1 - Silani, Mohammad A1 - Samaniego, Esteban A1 - Rabczuk, Timon T1 - A simple circular cell method for multilevel finite element analysis JF - Journal of Applied Mathematics N2 - A simple multiscale analysis framework for heterogeneous solids based on a computational homogenization technique is presented. The macroscopic strain is linked kinematically to the boundary displacement of a circular or spherical representative volume which contains the microscopic information of the material. The macroscopic stress is obtained from the energy principle between the macroscopic scale and the microscopic scale. This new method is applied to several standard examples to show its accuracy and consistency of the method proposed. KW - Angewandte Mathematik KW - Strukturmechanik Y1 - 2012 U6 - http://dx.doi.org/10.1155/2012/526846 ER - TY - JOUR A1 - Talebi, Hossein A1 - Zi, Goangseup A1 - Silani, Mohammad A1 - Samaniego, Esteban A1 - Rabczuk, Timon T1 - A simple circular cell method for multilevel finite element analysis JF - Journal of Applied Mathematics N2 - A simple multiscale analysis framework for heterogeneous solids based on a computational homogenization technique is presented. The macroscopic strain is linked kinematically to the boundary displacement of a circular or spherical representative volume which contains the microscopic information of the material. The macroscopic stress is obtained from the energy principle between the macroscopic scale and the microscopic scale. This new method is applied to several standard examples to show its accuracy and consistency of the method proposed. KW - Finite-Elemente-Methode KW - Feststoff Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170426-31639 ER -