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Hexahedral Elements (hexahedral + element)
Selected AbstractsAccurate eight-node hexahedral elementINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6 2007Magnus Fredriksson Abstract Based on the assumed strain method, an eight-node hexahedral element is proposed. Consistent choice of the fundamental element stiffness guarantees convergence and fulfillment of the patch test a priori. In conjunction with a ,-projection operator, the higher order strain field becomes orthogonal to rigid body and linear displacement fields. The higher order strain field in question is carefully selected to preserve correct rank for the element stiffness matrix, also for distorted elements. Volumetric locking is also removed effectively. By considerations of the bending energy, improved accuracy is obtained even for coarse element meshes. The choice of local co-ordinate system aligned with the principal axes of inertia makes it possible to improve the performance even for distorted elements. The strain-driven format obtained is well suited for materials with non-linear stress,strain relations. Several numerical examples are presented where the excellent performance of the proposed eight-node hexahedral is verified. Copyright © 2007 John Wiley & Sons, Ltd. [source] Analysis of 3D problems using a new enhanced strain hexahedral elementINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2003P. M. A. Areias Abstract The now classical enhanced strain technique, employed with success for more than 10 years in solid, both 2D and 3D and shell finite elements, is here explored in a versatile 3D low-order element which is identified as HIS. The quest for accurate results in a wide range of problems, from solid analysis including near-incompressibility to the analysis of locking-prone beam and shell bending problems leads to a general 3D element. This element, put here to test in various contexts, is found to be suitable in the analysis of both linear problems and general non-linear problems including finite strain plasticity. The formulation is based on the enrichment of the deformation gradient and approximations to the shape function material derivatives. Both the equilibrium equations and their variation are completely exposed and deduced, from which internal forces and consistent tangent stiffness follow. A stabilizing term is included, in a simple and natural form. Two sets of examples are detailed: the accuracy tests in the linear elastic regime and several finite strain tests. Some examples involve finite strain plasticity. In both sets the element behaves very well, as is illustrated in numerous examples. Copyright © 2003 John Wiley & Sons, Ltd. [source] Polynomial basis functions on pyramidal elementsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 12 2008M. J. Bluck Abstract Pyramidal elements are necessary to effect the transition from tetrahedral to hexahedral elements, a common requirement in practical finite element applications. However, existing pyramidal transition elements suffer from degeneracy or other numerical difficulties, requiring, at the least, warnings and care in their use. This paper presents a general technique for the construction of nodal basis functions on pyramidal finite elements. General forms for basis functions of arbitrary order are presented. The basis functions so derived are fully conformal and free of degeneracy. Copyright © 2007 John Wiley & Sons, Ltd. [source] Fully-automated hex-dominant mesh generation with directionality control via packing rectangular solid cellsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 15 2003Soji Yamakawa Abstract A new fully automatic hex-dominant mesh generation technique of an arbitrary 3D geometric domain is presented herein. The proposed method generates a high-quality hex-dominant mesh by: (1) controlling the directionality of the output hex-dominant mesh; and (2) avoiding ill-shaped elements induced by nodes located too closely to each other. The proposed method takes a 3D geometric domain as input and creates a hex-dominant mesh consisting mostly of hexahedral elements, with additional prism and tetrahedral elements. Rectangular solid cells are packed on the boundary of and inside the input domain to obtain ideal node locations for a hex-dominant mesh. Each cell has a potential energy field that mimics a body-centred cubic (BCC) structure (seen in natural substances such as NaCl) and the cells are moved to stable positions by a physically based simulation. The simulation mimics the formation of a crystal pattern so that the centres of the cells provide ideal node locations for a hex-dominant mesh. Via the advancing front method, the centres of the packed cells are then connected to form a tetrahedral mesh, and this is converted to a hex-dominant mesh by merging some of the tetrahedrons. Copyright © 2003 John Wiley & Sons, Ltd. [source] On the stability of bubble functions and a stabilized mixed finite element formulation for the Stokes problemINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2009D. Z. Turner Abstract In this paper we investigate the relationship between stabilized and enriched finite element formulations for the Stokes problem. We also present a new stabilized mixed formulation for which the stability parameter is derived purely by the method of weighted residuals. This new formulation allows equal-order interpolation for the velocity and pressure fields. Finally, we show by counterexample that a direct equivalence between subgrid-based stabilized finite element methods and Galerkin methods enriched by bubble functions cannot be constructed for quadrilateral and hexahedral elements using standard bubble functions. Copyright © 2008 John Wiley & Sons, Ltd. [source] Mechanical implications of estrogen supplementation in early postmenopausal womenJOURNAL OF BONE AND MINERAL RESEARCH, Issue 6 2010Felix W Wehrli Abstract Whereas the structural implications of drug intervention are well established, there are few data on the possible mechanical consequences of treatment. In this work we examined the changes in elastic and shear moduli (EM and SM) in a region of trabecular bone in the distal radius and distal tibia of early postmenopausal women on the basis of MRI-based micro-finite-element (µFE) analysis. Whole-section axial stiffness (AS) encompassing both trabecular and cortical compartments was evaluated as well. The study was conducted on previously acquired high-resolution images at the two anatomic sites. Images were processed to yield a 3D voxel array of bone-volume fraction (BVF), which was converted to a µFE model of hexahedral elements in which tissue modulus was set proportional to voxel BVF. The study comprised 65 early postmenopausal women (age range 45 to 55 years), of whom 32 had chosen estrogen supplementation (estradiol group); the remainder had not (control group). Subjects had been scanned at baseline and 12 and 24 months thereafter. At the distal tibia, EM and SM were reduced by 2.9% to 5.5% in the control group (p,<,.05 to <.005), but there was no change in the estradiol subjects. AS decreased 3.9% (4.0%) in controls (p,<,.005) and increased by 5.8% (6.2%) in estradiol group subjects (p,<,.05) at 12 (24) months. At the distal radius, EM and SM changes from baseline were not significant, but at both time points AS was increased in estradiol group subjects and decreased in controls (p,<,.005 to <.05), albeit by a smaller margin than at the tibia. EM and SM were strongly correlated with BV/TV (r2,=,0.44 to 0.92) as well as with topologic parameters expressing the ratio of plates to rods (r2,=,0.45 to 0.82), jointly explaining up to 96% of the variation in the mechanical parameters. Finally, baseline AS was strongly correlated between the two anatomic sites (r2,=,0.58), suggesting that intersubject variations in the bone's mechanical competence follows similar mechanisms. In conclusion, the results demonstrate that micro-MRI-based µFE models are suited for the study of the mechanical implications of antiresorptive treatment. The data further highlight the anabolic effect of short-term estrogen supplementation. © 2010 American Society for Bone and Mineral Research [source] | ||||||||||