|
| ||
|
|
||
Boundary Constraints (boundary + constraint)
Selected AbstractsSimulation of special loading conditions by means of non-linear constraints imposed through Lagrange multipliersINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 10 2002M. A. Gutiérrez Abstract This paper discusses the necessity and handling of non-linear constraint equations to describe the behaviour of properties of the loading system such as, e.g. smooth free-rotating loading platens. An exact, non-linear formulation for a smooth loading platen is derived and its incorporation into the equilibrium equations is presented. For this purpose, the Lagrange multiplier method is used. The solution of the equilibrium equations by means of a Newton,Raphson algorithm is also outlined. The proposed approach is validated on a patch of two finite elements and applied to a compression-bending test on a pre-notched specimen. It is observed that use of a linearized approximation of the boundary constraint can lead to errors in the description of the motion of the constrained nodes. Thus, the non-linear formulation is preferable. Copyright © 2002 John Wiley & Sons, Ltd. [source] Improving realism of a surgery simulator: linear anisotropic elasticity, complex interactions and force extrapolationCOMPUTER ANIMATION AND VIRTUAL WORLDS (PREV: JNL OF VISUALISATION & COMPUTER ANIMATION), Issue 3 2002Guillaume Picinbono Abstract In this article, we describe the latest developments of the minimally invasive hepatic surgery simulator prototype developed at INRIA. The goal of this simulator is to provide a realistic training test bed to perform laparoscopic procedures. Therefore, its main functionality is to simulate the action of virtual laparoscopic surgical instruments for deforming and cutting tridimensional anatomical models. Throughout this paper, we present the general features of this simulator including the implementation of several biomechanical models and the integration of two force-feedback devices in the simulation platform. More precisely, we describe three new important developments that improve the overall realism of our simulator. First, we have developed biomechanical models, based on linear elasticity and finite element theory, that include the notion of anisotropic deformation. Indeed, we have generalized the linear elastic behaviour of anatomical models to ,transversally isotropic' materials, i.e. materials having a different behaviour in a given direction. We have also added to the volumetric model an external elastic membrane representing the ,liver capsule', a rather stiff skin surrounding the liver, which creates a kind of ,surface anisotropy'. Second, we have developed new contact models between surgical instruments and soft tissue models. For instance, after detecting a contact with an instrument, we define specific boundary constraints on deformable models to represent various forms of interactions with a surgical tool, such as sliding, gripping, cutting or burning. In addition, we compute the reaction forces that should be felt by the user manipulating the force-feedback devices. The last improvement is related to the problem of haptic rendering. Currently, we are able to achieve a simulation frequency of 25,Hz (visual real time) with anatomical models of complex geometry and behaviour. But to achieve a good haptic feedback requires a frequency update of applied forces typically above 300,Hz (haptic real time). Thus, we propose a force extrapolation algorithm in order to reach haptic real time. Copyright © 2002 John Wiley & Sons, Ltd. [source] RangeModel: tools for exploring and assessing geometric constraints on species richness (the mid-domain effect) along transectsECOGRAPHY, Issue 1 2008Robert K. ColwellArticle first published online: 4 FEB 200 RangeModel is a computer application that offers animated demonstrations of the mechanism behind the mid-domain effect. The program also provides analytical tools for the assessment of geometric constraints in empirical datasets for one-dimensional domains (transects). The mid-domain effect (MDE) is the increasing overlap of species ranges towards the center of a shared, bounded domain due to geometric boundary constraints in relation to the distribution of range sizes, producing a peak or plateau of species richness towards the center of the domain. Domains may be spatial, temporal, or functional. RangeModel is a stand-alone, graphical-interface, freeware application for PC and Mac OS platforms. [source] Moving least-square interpolants in the hybrid particle methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2005H. Huang Abstract The hybrid particle method (HPM) is a particle-based method for the solution of high-speed dynamic structural problems. In the current formulation of the HPM, a moving least-squares (MLS) interpolant is used to compute the derivatives of stress and velocity components. Compared with the use of the MLS interpolant at interior particles, the boundary particles require two additional treatments in order to compute the derivatives accurately. These are the rotation of the local co-ordinate system and the imposition of boundary constraints, respectively. In this paper, it is first shown that the derivatives found by the MLS interpolant based on a complete polynomial are indifferent to the orientation of the co-ordinate system. Secondly, it is shown that imposing boundary constraints is equivalent to employing ghost particles with proper values assigned at these particles. The latter can further be viewed as placing the boundary particle in the centre of a neighbourhood that is formed jointly by the original neighbouring particles and the ghost particles. The benefit of providing a symmetric or a full circle of neighbouring points is revealed by examining the error terms generated in approximating the derivatives of a Taylor polynomial by using a linear-polynomial-based MLS interpolant. Symmetric boundaries have mostly been treated by using ghost particles in various versions of the available particle methods that are based on the strong form of the conservation equations. In light of the equivalence of the respective treatments of imposing boundary constraints and adding ghost particles, an alternative treatment for symmetry boundaries is proposed that involves imposing only the symmetry boundary constraints for the HPM. Numerical results are presented to demonstrate the validity of the proposed approach for symmetric boundaries in an axisymmetric impact problem. Copyright © 2005 John Wiley & Sons, Ltd. [source] Mid-domain models as predictors of species diversity patterns: bathymetric diversity gradients in the deep seaOIKOS, Issue 3 2005Craig R. McClain Geometric constraints represent a class of null models that describe how species diversity may vary between hard boundaries that limit geographic distributions. Recent studies have suggested that a number of large scale biogeographic patterns of diversity (e.g. latitude, altitude, depth) may reflect boundary constraints. However, few studies have rigorously tested the degree to which mid-domain null predictions match empirical patterns or how sensitive the null models are to various assumptions. We explore how variation in the assumptions of these models alter null depth ranges and consequently bathymetric variation in diversity, and test the extent to which bathymetric patterns of species diversity in deep sea gastropods, bivalves, and polychaetes match null predictions based on geometric constraints. Range,size distributions and geographic patterns of diversity produced by these null models are sensitive to the relative position of the hard boundaries, the specific algorithms used to generate range sizes, and whether species are continuously or patchily distributed between range end points. How well empirical patterns support null expectations is highly dependent on these assumptions. Bathymetric patterns of species diversity for gastropods, bivalves and polychaetes differ substantially from null expectations suggesting that geometric constraints do not account for diversity,depth patterns in the deep sea benthos. [source] Alternative Definitions of Micro,to,Macro Transitions in Particle Aggregates of Granular MaterialsPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2003Joachim Dettmar Dipl.-Ing. An alternative approach to the modelling of the overall macroscopic response of granular materials is presented based on micro,macro transitions. A homogenized macro,continuum is considered with locally attached granular microstructures. The new developments include a consistent transfer of micro,macro transitions from continuous to particle microstructures with a new overall macro,stress definition. Secondly, a new class of boundary conditions for displacements/ rotations on prescribed boundary,frame particles is presented that yields upper and lower bounds with regard to the aggregate stiffness. Thirdly, a unified implementation of the displacement/ rotation boundary constraints by a penalty method is developed that proves to be a convenient computational tool in explicit codes. [source] Tectonic Constraints on the Transformation of Paleozoic Framework of Uplift and Depression in the Ordos AreaACTA GEOLOGICA SINICA (ENGLISH EDITION), Issue 6 2006WANG Qingfei Abstract: During the Paleozoic, the Ordos area in the western North China Plate was located at the intersecting position of microplates and controlled by their interaction. The structural framework in the Ordos area, which underwent transformations in the Ordovician, the Carboniferous and the Permian respectively, was dominated by the alternation of uplift and depression. The transformations of structural framework are utilized as the clues to investigate the microplates' interacting type and its response in the Ordos area. According to the regional structural evolution, the Ordos area is simplified into an isopachous, isotropic and elastic shell model, and under proposed various boundary conditions, three series of numerical simulations corresponding to the three structural transformations are carried out to determine the detailed tectonic constraints. Numerical simulations reveal that the structure of the uplift and depression, which is similar to the actual pattern, develops only under one special boundary condition in each of the three series, indicating that the structural framework responds to the unique tectonic background. The simulation results show that in the Early Paleozoic, the L-shaped paleouplift formed nearby the southwestern corner of the Ordos area because the intensity of the compressions in the southern and western boundaries resulting from the ocean-continent collisions was similar. In the Late Paleozoic, it evolved into continent-continent (or arc-continent) interaction in the southern and northern boundaries; in the preliminary stage of the interaction, since the interface between the North China Plate and the plates on the south and north was narrow, the relative acting force was little and the regional western boundary immobile, and the structural framework in the basin was characterized by the N-S trending slender-waist,shaped uplift; as the interface between the plates expanded gradually, the extrusive force in the southern and northern boundaries of the North China Plate increased, resulting in the paleogeographic divisions showing E-W trending, and, the western boundary of the basin was extruded westward due to the intense compression inducing the local NE trending of paleogeographic division in the central area. The simulation results further reflect that the symmetry of the uplift-depression pattern is restricted by that of the boundary conditions, suggesting that the Paleozoic structural transformations of the Ordos area under boundary constraints accord with the universal physical symmetrical principle. [source] | |||||||||||||