The purpose of this work is twofold. First, we demonstrate analytically that the classical Newmark family as well as related integration algorithms are variational in the sense of the Veselov formulation of discrete mechanics. Such variational algorithms are well known to be symplectic and momentum preserving and to often have excellent global energy behavior. This analytical result is verified through numerical examples and is believed to be one of the primary reasons that this class of algorithms performs so well.Second, we develop algorithms for mechanical systems with forcing, and in particular, for dissipative systems. In this case, we develop integrators that are based on a discretization of the Lagrange d'Alembert principle as well as on a variational formulation of dissipation. It is demonstrated that these types of structured integrators have good numerical behavior in terms of obtaining the correct amounts by which the energy changes over the integration run.

The purpose of this paper is to develop variational integrators for conservative mechanical systems that are symplectic and energy and momentum conserving. To do this, a space-time view of variational integrators is employed and time step adaptation is used to impose the constraint of conservation of energy. Criteria for the solvability of the time steps and some numerical examples are given.

This work develops robust contact algorithms capable of dealing with complex contact situations involving several bodies with corners. Amongst the mathematical tools we bring to bear on the problem is nonsmooth analysis, following Clarke (F.H. Clarke. Optimization and nonsmooth analysis. John Wiley and Sons, New York, 1983.). We speci®cally address contact geometries for which both the use of normals and gap functions have diculties and therefore precludes the application of most contact algorithms proposed to date. Such situations arise in applications such as fragmentation, where angular fragments undergo complex collision sequences before they scatter. We demonstrate the robustness and versatility of the nonsmooth contact algorithms developed in this paper with the aid of selected two and three-dimensional applications.

SUMMARYThe present work extends the non-smooth contact class of algorithms introduced by Kane et al. to the case of friction. The formulation speciÿcally addresses contact geometries, e.g. involving multiple collisions between tightly packed non-smooth bodies, for which neither normals nor gap functions can be properly deÿned. A key aspect of the approach is that the incremental displacements follow from a minimum principle. The objective function comprises terms which account for inertia, strain energy, contact, friction and external forcing. The Euler-Lagrange equations corresponding to this extended variational principle are shown to be consistent with the equations of motion of solids in frictional contact. In addition to its value as a basis for formulating numerical algorithms, the variational framework o ers theoretical advantages as regards the selection of trajectories in cases of non-uniqueness. We present numerical and analytical examples which demonstrate the good momentum and energy conservation characteristics of the numerical algorithms, as well as the ability of the approach to account for stick and slip conditions.

This study focused on the effect of single jersey, single pique, double pique and honeycomb structures and structural cell stitch length (SCSL) on ring and compact yarn single jersey fabric properties. Compact yarn fabrics showed better performance in all the structures and their respective SCSL. With increased SCSL, the dimensional properties like CPI, WPI, SD, grams per square meter, thickness and tightness factor decreased for all the structures, while comfort properties like air permeability and water absorbency increased. The tensile, bending and compression properties of weft knitted fabrics improved and compressional resilience and surface properties generally decreased. Total hand values improved with SCSL. Other properties, such as abrasion resistance, bursting strength and pilling resistance improved with decreased SCSL. Combination order of knit-tuck stitches played an important role in all the properties. Double pique fabric showed better performance for the summer outer wear and single jersey fabric showed better performance for summer inner wear.

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Over the past years, research has attempted to relate fiber properties with yarn prop erties, and many regression equations have been developed to accomplish this. The complexities of multiple regression equations put limits on their universal acceptance. Neural networks with better nonlinear mapping have also been used to develop such relationships. Our statistical data analysis of a few yarn properties will determine the suitability of neural networks for such textile applications.

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