engleski

Mixed Meshless Analysis of Heterogeneous Structures Using Staggered Gradient Elasticity

The numerical solution of fourth order problems arising in non-classic theories requires a high order of approximation functions. Hence, using FEM for solving this type of problems is not a wise choice since standard formulations need to possess C1 continuity, which leads to complicated shape functions with large number of nodal degrees of freedom, even if mixed elements are utilized. Therefore, these procedures are considered to be highly numerically inefficient. The required C1 continuity is easily obtainable in the meshless methods since the approximation functions of arbitrary order can be formulated without increasing the nodal number of unknowns. In this contribution, the fourth order equilibrium equations of gradient elasticity are solved as an uncoupled sequence of two sets of the second order differential equations. The application of the staggered solution scheme and the mixed meshless approach should result in a more stable numerical formulation. The proposed computational strategy can be extended on the modeling of material localization phenomena, and it can be used for the modeling of deformation responses on the macro as well as microlevel in the frame of multiscale computational procedures.

meshless method; gradient elasticity; heterogeneous material

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