Home About us Contact
|
Home About us Contact | ||
|
|
||
Volumetric Locking (volumetric + locking)
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] Non-locking tetrahedral finite element for surgical simulationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 7 2009Grand Roman Joldes Abstract To obtain a very fast solution for finite element models used in surgical simulations, low-order elements, such as the linear tetrahedron or the linear under-integrated hexahedron, must be used. Automatic hexahedral mesh generation for complex geometries remains a challenging problem, and therefore tetrahedral or mixed meshes are often necessary. Unfortunately, the standard formulation of the linear tetrahedral element exhibits volumetric locking in case of almost incompressible materials. In this paper, we extend the average nodal pressure (ANP) tetrahedral element proposed by Bonet and Burton for a better handling of multiple material interfaces. The new formulation can handle multiple materials in a uniform way with better accuracy, while requiring only a small additional computation effort. We discuss some implementation issues and show how easy an existing Total Lagrangian Explicit Dynamics algorithm can be modified in order to support the new element formulation. The performance evaluation of the new element shows the clear improvement in reaction forces and displacements predictions compared with the ANP element in case of models consisting of multiple materials. Copyright © 2008 John Wiley & Sons, Ltd. [source] Addressing volumetric locking and instabilities by selective integration in smoothed finite elementsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 1 2009Nguyen-Xuan Hung Abstract This paper promotes the development of a novel family of finite elements with smoothed strains, offering remarkable properties. In the smoothed finite element method (FEM), elements are divided into subcells. The strain at a point is defined as a weighted average of the standard strain field over a representative domain. This yields superconvergent stresses, both in regular and singular settings, as well as increased accuracy, with slightly lower computational cost than the standard FEM. The one-subcell version that does not exhibit volumetric locking yields more accurate stresses but less accurate displacements and is equivalent to a quasi-equilibrium FEM. It is also subject to instabilities. In the limit where the number of subcells goes to infinity, the standard FEM is recovered, which yields more accurate displacements and less accurate stresses. The specific contribution of this paper is to show that expressing the volumetric part of the strain field using a one-subcell formulation is sufficient to get rid of volumetric locking and increase the displacement accuracy compared with the standard FEM when the single subcell version is used to express both the volumetric and deviatoric parts of the strain. Selective integration also alleviates instabilities associated with the single subcell element, which are due to rank deficiency. Numerical examples on various compressible and incompressible linear elastic test cases show that high accuracy is retained compared with the standard FEM without increasing computational cost. Copyright © 2008 John Wiley & Sons, Ltd. [source] Analysis of shear locking in Timoshenko beam elements using the function space approachINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 6 2001Somenath Mukherjee Abstract Elements based purely on completeness and continuity requirements perform erroneously in a certain class of problems. These are called the locking situations, and a variety of phenomena like shear locking, membrane locking, volumetric locking, etc., have been identified. Locking has been eliminated by many techniques, e.g. reduced integration, addition of bubble functions, use of assumed strain approaches, mixed and hybrid approaches, etc. In this paper, we review the field consistency paradigm using a function space model, and propose a method to identify field-inconsistent spaces for projections that show locking behaviour. The case of the Timoshenko beam serves as an illustrative example. Copyright © 2001 John Wiley & Sons, Ltd. [source] A uniform nodal strain tetrahedron with isochoric stabilizationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2009M. W. Gee Abstract A stabilized node-based uniform strain tetrahedral element is presented and analyzed for finite deformation elasticity. The element is based on linear interpolation of a classical displacement-based tetrahedral element formulation but applies nodal averaging of the deformation gradient to improve mechanical behavior, especially in the regime of near-incompressibility where classical linear tetrahedral elements perform very poorly. This uniform strain approach adopted here exhibits spurious modes as has been previously reported in the literature. We present a new type of stabilization exploiting the circumstance that the instability in the formulation is related to the isochoric strain energy contribution only and we therefore present a stabilization based on an isochoric,volumetric splitting of the stress tensor. We demonstrate that by stabilizing the isochoric energy contributions only, reintroduction of volumetric locking through the stabilization can be avoided. The isochoric,volumetric splitting can be applied for all types of materials with only minor restrictions and leads to a formulation that demonstrates impressive performance in examples provided. Copyright © 2008 John Wiley & Sons, Ltd. [source] Smooth finite element methods: Convergence, accuracy and propertiesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2008Hung Nguyen-Xuan Abstract A stabilized conforming nodal integration finite element method based on strain smoothing stabilization is presented. The integration of the stiffness matrix is performed on the boundaries of the finite elements. A rigorous variational framework based on the Hu,Washizu assumed strain variational form is developed. We prove that solutions yielded by the proposed method are in a space bounded by the standard, finite element solution (infinite number of subcells) and a quasi-equilibrium finite element solution (a single subcell). We show elsewhere the equivalence of the one-subcell element with a quasi-equilibrium finite element, leading to a global a posteriori error estimate. We apply the method to compressible and incompressible linear elasticity problems. The method can always achieve higher accuracy and convergence rates than the standard finite element method, especially in the presence of incompressibility, singularities or distorted meshes, for a slightly smaller computational cost. It is shown numerically that the one-cell smoothed four-noded quadrilateral finite element has a convergence rate of 2.0 in the energy norm for problems with smooth solutions, which is remarkable. For problems with rough solutions, this element always converges faster than the standard finite element and is free of volumetric locking without any modification of integration scheme. Copyright © 2007 John Wiley & Sons, Ltd. [source] Smart element method II.INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2005An element based on the finite Eshelby tensor Abstract In this study, we apply the newly derived finite Eshelby tensor in a variational multiscale formulation to construct a smart element through a more accurate homogenization procedure. The so-called Neumann,Eshelby tensor for an inclusion in a finite domain is used in the fine scale feedback procedure to take into account the interactions among different scales and elements. Numerical experiments have been conducted to compare the performance and robustness of the new element to earlier formulations. The results showed that the smart element constructed via the Neumann,Eshelby tensor of a finite domain provides better numerical accuracy than that constructed via the Eshelby tensor of an infinite domain. Moreover, it can relieve volumetric locking. Copyright © 2005 John Wiley & Sons, Ltd. [source] F-bar-based linear triangles and tetrahedra for finite strain analysis of nearly incompressible solids.INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2005Part I: formulation, benchmarking Abstract This paper proposes a new technique which allows the use of simplex finite elements (linear triangles in 2D and linear tetrahedra in 3D) in the large strain analysis of nearly incompressible solids. The new technique extends the F-bar method proposed by de Souza Neto et al. (Int. J. Solids and Struct. 1996; 33: 3277,3296) and is conceptually very simple: It relies on the enforcement of (near-) incompressibility over a patch of simplex elements (rather than the point-wise enforcement of conventional displacement-based finite elements). Within the framework of the F-bar method, this is achieved by assuming, for each element of a mesh, a modified (F-bar) deformation gradient whose volumetric component is defined as the volume change ratio of a pre-defined patch of elements. The resulting constraint relaxation effectively overcomes volumetric locking and allows the successful use of simplex elements under finite strain near-incompressibility. As the original F-bar procedure, the present methodology preserves the displacement-based structure of the finite element equations as well as the strain-driven format of standard algorithms for numerical integration of path-dependent constitutive equations and can be used regardless of the constitutive model adopted. The new elements are implemented within an implicit quasi-static environment. In this context, a closed form expression for the exact tangent stiffness of the new elements is derived. This allows the use of the full Newton,Raphson scheme for equilibrium iterations. The performance of the proposed elements is assessed by means of a comprehensive set of benchmarking two- and three-dimensional numerical examples. Copyright © 2005 John Wiley & Sons, Ltd. [source] | ||||||||||