AuthorXiaojuan Luo
TitleAn Automatic Adaptive Directional Variable P-Version Method in 3D Curved Domains
SchoolSchool of Engineering
InstitutionRensselaer Polytechnic Institute
AbstractRealization of the full benefits of p-version finite elements for general 3D curved domains requires (i) careful construction and control of the mesh layout and geometric approximation, (ii) effective three dimensional adaptive control, and (iii) efficient numerical methods for high order method. This thesis addresses the first two issues in solving linear elliptic problems in general 3D curved domains.

An automatic p-version mesh generation procedure to construct near optimal p-version meshes is presented. Starting from a surface triangulation, the process automatically isolates and meshes the singular model features and thin sections with structured cylindrical graded meshes and one layer prismatic thin section meshes respectively. A p-version mesh curving procedure with gradation and thin section mesh control curves all the mesh entities on the model boundaries. Controlled curved local mesh modifications are applied to correct the invalid mesh entities caused by curving the mesh entities. Examples demonstrated that the curved p-version meshes produced by this procedure save 15% to 40% fewer elements comparing to the curved meshes generated by curving without gradation and thin section control. The simulation results presented further demonstrate these meshes provide superior simulation results with less computational effort.

The performance of the p-version meshes are investigated in the p-version analysis software StressCheck and Trellis. Trellis takes advantage of a topology based high order hierarchic shape function structure to allow the assignment of different p-order for the independent coordinates of the mesh entities in the adaptive analysis. A directional correction indicator is derived from the computation of the elemental residual error estimator such that the p-orders are adaptively enriched in the appropriate directions. Linear elasticity examples demonstrate that the p-version meshes, particular in the adaptive directional p-version analysis, can achieve the same level of solution as conventional p-version method with substantially fewer degrees of freedom.

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