A stabilized quasi and bending consistent meshfree Galerkin formulation for Reissner

TSUNG-HUI HUANGWei, Yen LingYen LingWei2025-09-242025-09-242022https://www.scopus.com/inward/record.uri?eid=2-s2.0-85137048475&doi=10.1007%2Fs00466-022-02222-6&partnerID=40&md5=e736753360f31c5935a1c1bf488868e0https://scholars.lib.ntu.edu.tw/handle/123456789/732529The state-of-the-art locking-free meshfree Galerkin formulation for modeling the Reissner–Mindlin plate problems is plagued by the following issues: (1) the requirement of a large enough kernel support size in avoiding kernel instability because of the quadratic basis in meeting the Kirchhoff mode reproducing condition, as well as (2) the tedious construction of the conforming representative domains and the smoothed strain in the stabilized conforming integration scheme. This study introduces an efficient and stabilized approach that circumvents the above-mentioned issues. A quasi-consistent reproducing kernel approximation is first developed to enable a smaller kernel support size to be used without the moment matrix singularity issue under a controllable loss of completeness; thus, the approximation construction is accelerated. Then, a bending consistent nodal integration method is proposed where the bending consistency in Galerkin formulation is achieved via an assumed strain approach without using the conforming cell. A variational multiscale stabilization method from our earlier research is implemented to avoid low energy instability while maintaining the locking-free property. The performance of the present formulation is validated in several benchmark problems.Quasi-consistent ApproximationReissner–mindlin PlateReproducing Kernel Particle MethodStabilized Bending Consistent Nodal IntegrationBenchmarkingGalerkin MethodsIntegrationLocks (fasteners)Galerkin FormulationLocking-freeMeshfreeNodal IntegrationsQuasi-consistent ApproximationReissner-mindlin Plate ProblemReissner/mindlin PlateReproducing Kernel Particle MethodStabilized Bending Consistent Nodal IntegrationState Of The ArtMindlin Plates[SDGs]SDG13A stabilized quasi and bending consistent meshfree Galerkin formulation for Reissner–Mindlin platesjournal article10.1007/s00466-022-02222-62-s2.0-85137048475