Analysis of materials with strain-gradient effects: A meshless local Petrov-Galerkin (MLPG) approach, with nodal displacements only

The Meshless local Petrov-Galerkin (MLPG) method was developed for materials within the Toupin-Mindlin framework of strain gradient type constitutive theory. The resultant method defines the weak form of governing equations on sub-domains, which consequently helps to evaluate integration on some well-shaped region. The remarkable accuracy in the numerical simulations shows promising characteristics of MLPG for solving generation problems of material in elasticity, where strain-gradient effects may be important.