The Experts below are selected from a list of 3633 Experts worldwide ranked by ideXlab platform
Samuel W. Key - One of the best experts on this subject based on the ideXlab platform.
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A transition element for uniform strain hexahedral and tetrahedral finite elements
International Journal for Numerical Methods in Engineering, 1999Co-Authors: Clark R. Dohrmann, Samuel W. KeyAbstract:A transition element is presented for meshes containing uniform strain hexahedral and tetrahedral finite elements. It is shown that the volume of the standard uniform strain Hexahedron is identical to that of a polyhedron with 14 vertices and 24 triangular faces. Based on this equivalence, a transition element is developed as a simple modification of the uniform strain Hexahedron. The transition element makes use of a general method for hourglass control and satisfies first-order patch tests. Example problems in linear elasticity are included to demonstrate the application of the element. Copyright © 1999 John Wiley & Sons, Ltd. This paper was produced under the auspices of the U.S. Government and it is therefore not subject to copyright in the U.S.
Shuo Zhang - One of the best experts on this subject based on the ideXlab platform.
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C $$_{0}$$ 0 P $$_{2}$$ 2 –P $$_{0}$$ 0 Stokes finite element pair on sub-Hexahedron tetrahedral grids
Calcolo, 2017Co-Authors: Shangyou Zhang, Shuo ZhangAbstract:This paper presents a procedure to construct stable $$C_0P_2{-}P_0$$ finite element pair for three dimensional incompressible Stokes problem. It is proved that, the quadratic-constant finite element pair, though not stable in general, is uniformly stable on a certain family of tetrahedral grids, namely some kind of sub-Hexahedron tetrahedral grids. The sub-Hexahedron tetrahedral grid is defined by refining each eight-vertex Hexahedron of a certain hexahedral grid into twelve tetrahedra with one added vertex inside the Hexahedron, while the hexahedral grid is a partition of a polyhedral domain where each (non-flat face) Hexahedron is defined by a tri-linear mapping on the unit cube with eight vertices.
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c _ 0 0 p _ 2 2 p _ 0 0 stokes finite element pair on sub Hexahedron tetrahedral grids
Calcolo, 2017Co-Authors: Shangyou Zhang, Shuo ZhangAbstract:This paper presents a procedure to construct stable $$C_0P_2{-}P_0$$ finite element pair for three dimensional incompressible Stokes problem. It is proved that, the quadratic-constant finite element pair, though not stable in general, is uniformly stable on a certain family of tetrahedral grids, namely some kind of sub-Hexahedron tetrahedral grids. The sub-Hexahedron tetrahedral grid is defined by refining each eight-vertex Hexahedron of a certain hexahedral grid into twelve tetrahedra with one added vertex inside the Hexahedron, while the hexahedral grid is a partition of a polyhedral domain where each (non-flat face) Hexahedron is defined by a tri-linear mapping on the unit cube with eight vertices.
J L Curielsosa - One of the best experts on this subject based on the ideXlab platform.
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3 d local mesh refinement xfem with variable node Hexahedron elements for extraction of stress intensity factors of straight and curved planar cracks
Computer Methods in Applied Mechanics and Engineering, 2017Co-Authors: Zhen Wang, Tinh Quoc Bui, Satoyuki Tanaka, Chuanzeng Zhang, Sohichi Hirose, J L CurielsosaAbstract:Abstract A novel local mesh refinement approach for fracture analysis of three-dimensional (3-D) linear elastic solids is developed, considering both 3-D straight and curved planar cracks. The present local mesh refinement formulation is a combination of the extended finite element method (XFEM), variable-node Hexahedron elements, and a posteriori error indicator. Our 3-D formulation using Hexahedron elements rigorously embraces a posteriori error estimation scheme, a structural coupling scale-meshes strategy and an enrichment technique. Local mesh refinement is only performed where it is needed, e.g., a vicinity of crack, through an error estimator based on the recovery stress procedure. To treat the mismatching problem induced by different scale-meshes in the domain, a structural coupling scheme employing variable-node transition Hexahedron elements based on the generic point interpolation with an arbitrary number of nodes on each of their faces is presented. The 3-D finite element approximations of field variables are enhanced by enrichments so that the mesh is fully independent of the crack geometry. The displacement extrapolation method is taken for the evaluation of linear elastic fracture parameters (e.g., stress intensity factors—SIFs). To show the accuracy and performance of our proposed 3-D formulation, six numerical examples of planar 3-D straight and curved shaped cracks with single and mixed-mode fractures and different configurations are considered and analyzed. The SIFs computed by the developed method are validated with respect to analytical solutions and the ones derived from the conventional XFEM. Associated with an adaptive process, the present 3-D formulation allows the analysts to gain a desirable accuracy with a few trials, which is suited for practices purpose.
Doo Yong Lee - One of the best experts on this subject based on the ideXlab platform.
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Adaptive surface representation based on homogeneous Hexahedrons for interactive simulation of soft tissue cutting.
Computer methods and programs in biomedicine, 2020Co-Authors: Seong Pil Byeon, Doo Yong LeeAbstract:Background and Objective Interactive simulation of cutting soft tissues is essential in simulation of surgery and medical procedures. Cutting simulation involves topological and geometrical changes of the finite elements, and requires significant additional computational burden. This problem is handled, in this paper, by approximating a small gap between the model boundaries and the volumetric finite elements. Method Deformations are computed using only the regular Hexahedrons, and the surface structure is embedded in the Hexahedrons for visualizing the objects and detecting the collisions. Cutting is handled separately for the Hexahedrons and the surface structure. The intersected Hexahedrons are duplicated in the cutting without geometrical changes, and the surface structure is conformed to the cutting path to represent the cut surfaces faithfully. A method of using partial elements is introduced to compensate for inaccuracies due to the gap between the cut surface and the Hexahedron. Result Simulation results show that the additional computation burden of the proposed method is reduced to 34% and 37.12% of the previous method in the literature. The theoretical range of additional arithmetic operations for each method is derived, showing the superiority of the proposed method. Conclusion The proposed method improves the real-time performance of the simulation through an adaptive approximation of the cut surface.
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Method for real-time simulation of haptic interaction with deformable objects using GPU-based parallel computing and homogeneous hexahedral elements
Computational Mechanics, 2020Co-Authors: Seong Pil Byeon, Doo Yong LeeAbstract:This paper proposes a method for simulating real-time haptic interaction with deformable objects. The deformable model consists of regular Hexahedrons of a single type. This homogeneity is exploited to improve the efficiency in deformation computations. Model boundaries are approximated using a moving-least-squares function reflecting the deformation results of the Hexahedrons. A method for adaptively approximating the model boundaries is presented for efficient collision handling in the haptic loop. The proposed method can simulate a model of 16,481 nodes in less than 1 ms, which is a significant improvement over the previous methods in the literature. Small gap between the model boundary and the Hexahedrons can cause errors in the proposed method. Numerical examples considering the characteristics of human tissues show that the errors are less than just-noticeable difference of human.
Clark R. Dohrmann - One of the best experts on this subject based on the ideXlab platform.
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A transition element for uniform strain hexahedral and tetrahedral finite elements
International Journal for Numerical Methods in Engineering, 1999Co-Authors: Clark R. Dohrmann, Samuel W. KeyAbstract:A transition element is presented for meshes containing uniform strain hexahedral and tetrahedral finite elements. It is shown that the volume of the standard uniform strain Hexahedron is identical to that of a polyhedron with 14 vertices and 24 triangular faces. Based on this equivalence, a transition element is developed as a simple modification of the uniform strain Hexahedron. The transition element makes use of a general method for hourglass control and satisfies first-order patch tests. Example problems in linear elasticity are included to demonstrate the application of the element. Copyright © 1999 John Wiley & Sons, Ltd. This paper was produced under the auspices of the U.S. Government and it is therefore not subject to copyright in the U.S.