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Reference Configuration (reference + configuration)
Selected AbstractsStabilized updated Lagrangian corrected SPH for explicit dynamic problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2007Y. Vidal Abstract Smooth particle hydrodynamics with a total Lagrangian formulation are, in general, more robust than finite elements for large distortion problems. Nevertheless, updating the reference configuration may still be necessary in some problems involving extremely large distortions. However, as discussed here, a standard updated formulation suffers the presence of zero-energy modes that are activated and may completely spoil the solution. It is important to note that, unlike an Eulerian formulation, the updated Lagrangian does not present tension instability but only zero-energy modes. Here a stabilization technique is incorporated to the updated formulation to obtain an improved method without any mechanisms and which is capable to solve problems with extremely large distortions. Copyright © 2006 John Wiley & Sons, Ltd. [source] Remarks on tension instability of Eulerian and Lagrangian corrected smooth particle hydrodynamics (CSPH) methodsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2001Javier Bonet Abstract The paper discusses the problem of tension instability of particle-based methods such as smooth particle hydrodynamics (SPH) or corrected SPH (CSPH). It is shown that tension instability is a property of a continuum where the stress tensor is isotropic and the value of the pressure is a function of the density or volume ratio. The paper will show that, for this material model, the non-linear continuum equations fail to satisfy the stability condition in the presence of tension. Consequently, any discretization of this continuum will result in negative eigenvalues in the tangent stiffness matrix that will lead to instabilities in the time integration process. An important exception is the 1-D case where the continuum becomes stable but SPH or CSPH can still exhibit negative eigenvalues. The paper will show that these negative eigenvalues can be eliminated if a Lagrangian formulation is used whereby all derivatives are referred to a fixed reference configuration. The resulting formulation maintains the momentum preservation properties of its Eulerian equivalent. Finally a simple 1-D wave propagation example will be used to demonstrate that a stable solution can be obtained using Lagrangian CSPH without the need for any artificial viscosity. Copyright © 2001 John Wiley & Sons, Ltd. [source] Medial collateral ligament insertion site and contact forces in the ACL-deficient kneeJOURNAL OF ORTHOPAEDIC RESEARCH, Issue 4 2006Benjamin J. Ellis Abstract The objectives of this research were to determine the effects of anterior cruciate ligament (ACL) deficiency on medial collateral ligament (MCL) insertion site and contact forces during anterior tibial loading and valgus loading using a combined experimental-finite element (FE) approach. Our hypothesis was that ACL deficiency would increase MCL insertion site forces at the attachments to the tibia and femur and increase contact forces between the MCL and these bones. Six male knees were subjected to varus,valgus and anterior,posterior loading at flexion angles of ,0° and 30°. Three-dimensional joint kinematics and MCL strains were recorded during kinematic testing. Following testing, the MCL of each knee was removed to establish a stress-free reference configuration. An FE model of the femur,MCL,tibia complex was constructed for each knee to simulate valgus rotation and anterior translation at 0° and 30°, using subject-specific bone and ligament geometry and joint kinematics. A transversely isotropic hyperelastic material model with average material coefficients taken from a previous study was used to represent the MCL. Subject-specific MCL in situ strain distributions were used in each model. Insertion site and contact forces were determined from the FE analyses. FE predictions were validated by comparing MCL fiber strains to experimental measurements. The subject-specific FE predictions of MCL fiber stretch correlated well with the experimentally measured values (R2,=,0.95). ACL deficiency caused a significant increase in MCL insertion site and contact forces in response to anterior tibial loading. In contrast, ACL deficiency did not significantly increase MCL insertion site and contact forces in response to valgus loading, demonstrating that the ACL is not a restraint to valgus rotation in knees that have an intact MCL. When evaluating valgus laxity in the ACL-deficient knee, increased valgus laxity indicates a compromised MCL. © 2006 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res [source] Coherence of Structural Optimization and Configurational MechanicsPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2006Daniel Materna This contribution is concerned with the similarities of structural optimization and configurational mechanics. In structural optimization sensitivity analysis is used to obtain the sensitivity of continuum mechanical functions with respect to variations of the material body, i.e. the reference configuration. In the same manner in configurational mechanics we are interested in changes of the material body, e.g. crack propagation or phase transition problems. Consequently, variational design sensitivity analysis and the numerical techniques from structural optimization are applicable to problems fromconfigurational mechanics. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Multireference coupled-cluster methods for ground and low-lying excited states.INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 15 2010A benchmark illustration on CH + potentials Abstract Multireference (MR), general-model-space (GMS), state-universal (SU) coupled-cluster (CC) method that considers singly (S) and doubly (D) excited cluster amplitudes relative to the reference configurations spanning the model space (GMS SU CCSD), as well as its externally corrected (ec) version (N,M)-CCSD that uses N -reference MR CISD as an external source of higher-than-pair cluster amplitudes in a M -reference GMS CCSD, are used to investigate low-lying states of the CH+ ion. Relying on a simple ab initio model that enables a comparison with the exact full configuration interaction energies, the performance of the GMS-based methods is assessed in the whole relevant range of internuclear separations. It is shown that the ec (N,M)-CCSD version provides best results for both the singlet and the triplet states considered. For triplets, the use of high-spin (MS = 1) references is to be preferred. The GMS-based MR SU CC results for the ten low-lying states of CH+ clearly indicate the usefulness and reliability of these approaches. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2010 [source] | ||||||||||