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Mixed MLPG Staggered Solution Procedure in Gradient Elasticity for Modeling of Heterogeneous Materials

A mixed MLPG collocation method is applied for modeling of deformation responses of heterogeneous materials in gradient elasticity. Herein, a heterogeneous material domain comprised of two isotropic homogeneous parts with different material elastic properties is considered. The solution for the entire domain is obtained by enforcing the corresponding boundary conditions along the interface of the homogeneous domains. For the approximation of the unknown field variables the Moving Least Squares (MLS) functions with interpolatory conditions are applied. The strain gradient elasticity based on the Aifantis theory with one microstructural parameter is utilized. The original fourth-order equilibrium equations of gradient elasticity are solved in a staggered manner as an uncoupled sequence of two sets of second-order differential equations. The proposed mixed meshless approach is tested and demonstrated by a representative numerical example.

Mixed meshless approach, collocation method, staggered solution procedure, heterogeneous materials

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