Abstract
Based on our proposed adaptivity strategy for the vibration of Reissner–Mindlin plate, we develop it to apply for the vibration of Kirchhoff plate. The adaptive algorithm is based on the Geometry-Independent Field approximaTion (GIFT), generalized from Iso-Geometric Analysis (IGA), and it can characterize the geometry of the structure with NURBS (Non-Uniform Rational B-Splines), and independently apply PHT-splines (Polynomial splines over Hierarchical T-meshes) to achieve local refinement in the solution field. The MAC (Modal Assurance Criterion) is improved to locate unique, as well as multiple, modal correspondence between different meshes, in order to deal with error estimation. Local adaptivity is carried out by sweeping modes from low to high frequency. Numerical examples show that a proper choice of the spline space in solution field (with GIFT) can deliver better accuracy than using NURBS solution field. In addition, for vibration of heterogeneous Kirchhoff plates, our proposed method indicates that the adaptive local h-refinement achieves a better solution accuracy than the uniform h-refinement.
Highlights
Isogeometric analysis (IGA) was proposed in [1] to assemble analysis in Computer Aided Engineering (CAE) and Computer Aided Design (CAD)
(3) Based on our established adaptive method for the vibration of thick plate problem [27], we extend to the adaptivity for thin plate vibration by sweeping the mode driven by a-posteriori error estimation, with the help of Modal Assurance Criterion (MAC) method to recognize the correspondence between two different mesh spaces
In this article, based on our proposed adaptivity strategy in the framework of Geometry-Independent Field approximaTion (GIFT) paradigm utilized for vibration of Reissner–Mindlin plate, it is developed to investigate the error-driven adaptivity for structural vibration of Kirchhoff plate
Summary
Isogeometric analysis (IGA) was proposed in [1] to assemble analysis in Computer Aided Engineering (CAE) and Computer Aided Design (CAD). In [14], authors consider NURBS local prolongation operators which are based on multigrid principles This approach needs to construct an operator by marking some extra elements for refinement, thereby, the resulting adaptive mesh is not the most efficient one. Since PHTsplines are polynomial functions, they are not able to exactly represent the geometry of shapes with conic sections, e.g., circles, ellipsoids, and spheres, which typically arise in engineering design and analysis To tackle with this limitation, rational splines over hierarchical T-meshes (RHTsplines) have been recently introduced in [25]. Though the continuity of C1 is sufficient for the analysis of many engineering problems, for the description of geometry requiring higher continuity, RHT-splines will suffer from the geometry inexactness To weaker this tight coupling between geometry and simulation, a new approach called Geometry-Independent Field approximaTion (GIFT) has been proposed [26]. These results using GIFT approach show two major achievements: (1) Despite a poor geometric parameterization, an accurate numerical approximation can be obtained by adopting an appropriate parameterization in solution field. (2) When structural vibration is localized, the proposed adaptive refinement delivers a better convergence rate than the uniform refinement
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