Smoothed numerical manifold method with physical patch‐based smoothing domains for linear elasticity
Zhijun Liu, Peng Zhang, Cong Sun, Yongtao Yang
Abstract
Abstract Smoothed finite element method with the node‐based strain smoothing domains (NS‐FEM) is remarkable for the upper‐bound feature and insensitivity to the volumetric locking. As a mesh‐based methodology, its application is limited by the burdensome meshing for which elements align with the physical domain. We extend the strain smoothing in NS‐FEM to the numerical manifold method (NMM) with unfitted meshes, and propose a novel methodology named physical patch‐based smoothed NMM. Benchmark problems demonstrate the optimal convergence, stability in term of the condition number, upper‐bound property, suppression of the volumetric locking, as well as the stress stability.
Topics & Concepts
SmoothingPolygon meshFinite element methodUpper and lower boundsConvergence (economics)Applied mathematicsBenchmark (surveying)MathematicsElasticity (physics)Stability (learning theory)Smoothed finite element methodLinear elasticityNumerical stabilityAlgorithmFeature (linguistics)Computer scienceMathematical optimizationNumerical analysisMathematical analysisGeometryStructural engineeringEngineeringBoundary knot methodPhysicsBoundary element methodEconomic growthEconomicsMachine learningPhilosophyGeographyGeodesyStatisticsThermodynamicsLinguisticsNumerical methods in engineeringAdvanced Numerical Methods in Computational MathematicsElectromagnetic Simulation and Numerical Methods