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Numerical Experimentation (numerical + experimentation)
Selected AbstractsDecoupling and balancing of space and time errors in the material point method (MPM)INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2010Michael Steffen Abstract The material point method (MPM) is a computationally effective particle method with mathematical roots in both particle-in-cell and finite element-type methods. The method has proven to be extremely useful in solving solid mechanics problems involving large deformations and/or fragmentation of structures, problem domains that are sometimes problematic for finite element-type methods. Recently, the MPM community has focused significant attention on understanding the basic mathematical error properties of the method. Complementary to this thrust, in this paper we show how spatial and temporal errors are typically coupled within the MPM framework. In an attempt to overcome the challenge to analysis that this coupling poses, we take advantage of MPM's connection to finite element methods by developing a ,moving-mesh' variant of MPM that allows us to use finite element-type error analysis to demonstrate and understand the spatial and temporal error behaviors of MPM. We then provide an analysis and demonstration of various spatial and temporal errors in MPM and in simplified MPM-type simulations. Our analysis allows us to anticipate the global error behavior in MPM-type methods and allows us to estimate the time-step where spatial and temporal errors are balanced. Larger time-steps result in solutions dominated by temporal errors and show second-order temporal error convergence. Smaller time-steps result in solutions dominated by spatial errors, and hence temporal refinement produces no appreciative change in the solution. Based upon our understanding of MPM from both analysis and numerical experimentation, we are able to provide to MPM practitioners a collection of guidelines to be used in the selection of simulation parameters that respect the interplay between spatial (grid) resolution, number of particles and time-step. Copyright © 2009 John Wiley & Sons, Ltd. [source] A new shear flexible cubic spline plate element for vibration analysisINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2002B. P. Patel Abstract Here, a new cubic B-spline plate element is developed using field consistency principle, for vibration analysis. The formulation includes anisotropy, transverse shear deformation, in-plane and rotary inertia effects. The element is based on a laminated refined plate theory, which satisfies the interface transverse shear stress and displacement continuity, and has a vanishing shear stress on the top and bottom surfaces of the plates. The lack of consistency in the shear strain field interpolations in its constrained physical limits produces poor convergence and results in unacceptable solutions due to locking phenomenon. Hence, numerical experimentation for the evaluation of natural frequencies of plates is carried out to check this deficiency with a series of assumed shear strain functions, redistributed in a field consistent manner. Copyright © 2002 John Wiley & Sons, Ltd. [source] Demand and Production Management with Uniform Guaranteed Lead TimePRODUCTION AND OPERATIONS MANAGEMENT, Issue 4 2005Uday S. Rao Recently, innovation-oriented firms have been competing along dimensions other than price, lead time being one such dimension. Increasingly, customers are favoring lead time guarantees as a means to hedge supply chain risks. For a make-to-order environment, we explicitly model the impact of a lead time guarantee on customer demands and production planning. We study how a firm can integrate demand and production decisions to optimize expected profits by quoting a uniform guaranteed maximum lead time to all customers. Our analysis highlights the increasing importance of lead time for customers, as well as the tradeoffs in achieving a proper balance between revenue and cost drivers associated with lead-time guarantees. We show that the optimal lead time has a closed-form solution with a newsvendor-like structure. We prove comparative statics results for the change in optimal lead time with changes in capacity and cost parameters and illustrate the insights using numerical experimentation. [source] Meridional energy transport in the coupled atmosphere,ocean system: scaling and numerical experimentsTHE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 644 2009Geoffrey K. Vallis Abstract We explore meridional energy transfer in the coupled atmosphere,ocean system, with a focus on the extratropics. We present various elementary scaling arguments for the partitioning of the energy transfer between atmosphere and ocean, and illustrate those arguments by numerical experimentation. The numerical experiments are designed to explore the effects of changing various properties of the ocean (its size, geometry and diapycnal diffusivity), the atmosphere (its water vapour content) and the forcing of the system (the distribution of incoming solar radiation and the rotation rate of the planet). We find that the energy transport associated with wind-driven ocean gyres is closely coupled to the energy transport of the midlatitude atmosphere so that, for example, the heat transport of both systems scales in approximately the same way with the meridional temperature gradient in midlatitudes. On the other hand, the deep circulation of the ocean is not tightly coupled with the atmosphere and its energy transport varies in a different fashion. Although for present-day conditions the atmosphere transports more energy polewards than does the ocean, we find that a wider or more diffusive ocean is able to transport more energy than the atmosphere. The polewards energy transport of the ocean is smaller in the Southern Hemisphere than in the Northern Hemisphere; this arises because of the effects of a circumpolar channel on the deep overturning circulation. The atmosphere is able to compensate for changes in oceanic heat transport due to changes in diapycnal diffusivity or geometry, but we find that the compensation is not perfect. We also find that the transports of both atmosphere and ocean decrease if the planetary rotation rate increases substantially, indicating that there is no a priori constraint on the total meridional heat transport in the coupled system. Copyright © 2009 Royal Meteorological Society [source] Level-Sets fields, placement and velocity based formulations of contact-impact problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2007Hachmi Ben Dhia Abstract By introducing unknown Sign -like fields of Level-Sets type, the Signorini-Moreau dynamic contact conditions are set merely as boundary equations. From this setting, a continuous hybrid weak,strong formulation for dynamic contact between deformable solids is derived and a new Lagrangian formulation (we call stabilized) generalizing both the classical and augmented ones is obtained. Friction phenomena are treated similarly. In the global problem, the irregular Sign -like fields stand for the intrinsic contact unknown ones. This problem is discretized by means of time, space and collocation schemes. Some numerical experimentations are carried out, showing the potential of our developments. Copyright © 2006 John Wiley & Sons, Ltd. [source] | ||||||||||