Quasi-regional mapping for the p-version of the finite element method
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Cited by (58)
High order transition elements: The xNy-element concept, Part II: Dynamics
2021, Computer Methods in Applied Mechanics and EngineeringCurved p-version C<sup>1</sup> finite elements for the finite deformation analysis of isotropic and composite laminated thin shells in irregular shape
2021, Composite StructuresCitation Excerpt :This distinction enables the present element to be applied to shells of irregular shape where different parts are described by different parametric functions, which implies general curved mesh generation method can be used in cooperation with the present C1 elements to model problems with more complicated geometries. With this in mind, the quasi regional mapping (QRM) method originally proposed by Királyfalvi and Szabó [46] and slightly modified by the present authors is employed for the mesh generation of present work. Nevertheless, other choices of high-order curved mesh generation methods are still open as there are quite amount of works regarding to the topic of automatic high-order mesh generation.
High order transition elements: The xNy-element concept—Part I: Statics
2020, Computer Methods in Applied Mechanics and EngineeringCitation Excerpt :Gordon et al. referred to this concept as transfinite interpolation, indicating that the bivariate interpolant agrees exactly with the univariate functions at infinitely many points at the element edges. This approach is often used in the p-FEM to ensure an accurate description of the geometry of the discretized structure [1,38,82]. In the context of geometry mapping, the method is commonly referred to as blending function method.
Mass lumping techniques in the spectral element method: On the equivalence of the row-sum, nodal quadrature, and diagonal scaling methods
2019, Computer Methods in Applied Mechanics and EngineeringThe finite cell method for nearly incompressible finite strain plasticity problems with complex geometries
2018, Computers and Mathematics with ApplicationsCitation Excerpt :There are also other methods trying to integrate geometric modeling and FEM computations. Examples are Isogeometric Analysis (IGA) with NURBS-based shape functions [5] and the high-order FEM with CAD-based blending functions for geometrical mappings [6,7]. Considering zero material stiffness and zero stress outside the physical domain, the original weak form of the physical domain can be easily recovered.
The influence of geometric imperfections in cardiovascular FSI simulations
2017, Computers and Mathematics with Applications