Projection methods in flexible multibody dynamics. Part I: Kinematics

In this paper a recursive projection method for the dynamic analysis of open-loop mechanical systems that consist of a set of interconnected deformable bodies is presented. The configuration of each body in the system is identified using a coupled set of reference and elastic co-ordinates. The absolute velocities and accelerations of leaf or child bodies in the open-loop system are expressed in terms of the absolute velocities and accelerations of the parent bodies and the time derivatives of the relative co-ordinates of the joints between the bodies. The dynamic differential equations of motion are developed for each link using the generalized Newton-Euler equations. The relationship between the actual joint reactions and the generalized forces combined with the kinematic relationships and the generalized Newton-Euler equations are used to develop a system of loosely coupled equations which has a sparse matrix structure. Using matrix partitioning and recursive projection techniques based on optimal block factorization an efficient solution for the system accelerations and joint reaction forces is obtained. This solution technique yields a much smaller operations count and can more effectively exploit vectorization and parallel processing. It also allows a systematic procedure for decoupling the joint and elastic accelerations.     

Dynamics of an elastic multibody chain: Part C—Recursive dynamics

In multibody dynamics, and particularly in the robotics field, there are essentially two problems to consider: inverse dynamics and simulation dynamics. In the former problem, the desired trajectory is specmed and me necessary control forces and torques must be determined, the latter is the converse problem and the one of greater interest for elastic multibody systems

Just as the formulation of motion equations for multibody systems can take numerous paths, so too can their solution. The 'standard' approach to inverse and simulation dynamics is to write the equations of motion in toto for the entire system. However, the topological nature of chains can be exploited using the notion of recursion. Recursive methods allow the chain to be considered on a body-by-body basis rather than on a 'global$apos; level. The attractive feature of recursive algorithms is their computational cost, which varies linearly with the number of bodies in the chain. Global methods, on the other hand, are typically cubic in the number of coordinates

In this paper, which builds on the foundation of the inaugural paper in this series, we develop a recursive simulation algorithm for chains of general elastic bodies having arbitrary (rotational and/or translational) interbody constraints     

Dynamics of an elastic multibody chain: Part B—Global dynamics

In this the second paper in a series describing the dynamics of an arbitrary multibody system, the global dynamics of a topological chain of elasticbodies is considered in detail. The direct-path approach is used in the assignment of coordinate systems, interbody position vectors, connection matrices, and in the handling of mass properties, all in conjunction with a Newton-Euler, finite-element formulation. Nonlinear inertial effects, which can be important during rapid manoeuvres, are also identified.

The equations are first collected in a form appropriate to a chain with unconstrained joints—a full six degrees of freedom are permitted at each interbody joint. Constraints are then selectively introduced and the associated constraint forces calculated using the concept of projection matrices. The associated control forces (to carry out robotics tasks, for example) are also calculated. Finally, a compact form of the motion equations is presented for a multibody chain with constrained-controlled interbody joints.     

Stability analysis of constraints in flexible multibody systems dynamics

Automated algorithms for the dynamic analysis and simulation of constrained multibody systems assume that the constraint equations are linearly independent. During the motion, when the system is at a singular configuration, the constraint Jacobian matrix possesses less than full rank and hence it results in singularities. This occurs when the direction of a constraint coincides with the direction of the lost degree of freedom. In this paper the constraint equations for deformable bodies are modified for use in the neighborhood of the singular configuration to yield the system inertia matrix which is nonsingular and also to take the actual generalized constraint forces into account. The procedures developed are applicable to both the augmented approach and the coordinate reduction methods. For the modeling of the constrained flexible multibody systems, a general recursive formulation is developed using Kane's equations, finite element method and modal analysis techniques. The system may contain revolute, prismatic, spherical or other types of joints, as well as geometrical nonlinearities; the rotary inertia is also automatically included. Simulation of a two-link flexible manipulator is presented at a singular configuration to demonstrate the utility of the method.     

Dynamics of an elastic multibody chain: Part D—Modelling of joints

In the three previous papers in this series on the dynamics of a topological chain of arbitrary elastic bodies, rotational and translational displacements of arbitrary magnitude were allowed at all interbody joints. While this degree of generahty lends relevance withrespect to a diverse range of robotics applications, a careful specification of the displacement and force components at each joint becomes mandatory. In the present analysis, from one to six degrees of freedom are permitted at each joint, as reflected in the number of columns in its joint projection matrix. The special but practically important cases ofrotational (revolute) joints with one, two or three degrees of freedom are considered in detail, including physical interpretations for the coefficient matrices in the equations of motion. With robotics applications in mind, the many possibilities for sensors and actuators at the joints are catalogued and the four most important classes of ‘sensactor’ (a colocated sensor/actuator pair) are identified and their implications for the system equations presented.     

A Lagrangian approach to the non-causal inverse dynamics of flexible multibody systems: The three-dimensional case

This paper addresses the problem of end-point trajectory tracking in flexible multibody systems through the use of inverse dynamics. A global Lagrangian approach is employed in formulating the system equations of motion, and an iterative procedure is proposed to achieve end-point trajectory tracking in three-dimensional, flexible multibody systems. Each iteration involves firstly, a recursive inverse kinematics procedure wherein elastic displacements are determined in terms of the rigid body co-ordinates and Lagrange multipliers, secondly, an explicit computation of the inverse dynamic joint actuation, and thirdly, a non-recursive forward dynamic analysis wherein generalized co-ordinates and Lagrange multipliers are determined in terms of the joint actuation and desired end-point co-ordinates. In contrast with the recursive methods previously proposed, this new method is the most general since it is suitable for both open-chain and closed-chain configurations of three-dimensional multibody systems. The algorithm yields stable, non-casual actuating joint torques and associated Lagrange multipliers that account for the constraint forces between flexible multibody components.     

A non-recursive Lagrangian solution of the non-causal inverse dynamics of flexible multibody systems: The planar case

A technique is presented for solving the inverse dynamics of flexible planar multibody systems. This technique yields the non-causal joint efforts (inverse dynamics) as well as the internal states (inverse kinematics) that produce a prescribed nominal trajectory of the end effector. A non-recursive Lagrangian approach is used in formulating the equations of motion as well as in solving the inverse dynamics equations. Contrary to the recursive method previously presented, the proposed method solves the inverse problem in a systematic and direct manner for both open-chain as well as closed-chain configurations. Numerical simulation shows that the proposed procedure provides an excellent tracking of the desired end effector trajectory.     

Dynamics of rotating paramagnetic particles simulated by lattice Boltzmann and particle dynamics methods

Novel biochemical sensors consisting of rotating chains of microscale paramagnetic particles have been proposed that would enable convenient, sensitive analyte detection. Predicting the dynamics of these particles is required to optimise their design. The results of lattice Boltzmann (LB) and particle dynamics (PD) simulations are reported, where the LB approach provides a verified solution of the complete Navier-Stokes equations, including the hydrodynamic interactions among the particles. On the other hand, the simpler PD approach neglects hydrodynamic interactions, and does not compute the fluid motion. It is shown that macroscopic properties, like the number of aggregated particles, depend only on the drag force and not on the total hydrodynamic force, making PD simulations yield reasonably accurate predictions. Relatively good agreement between the LB and PD simulations, and qualitative agreement with experimental data, are found for the number of aggregated particles as a function of the Mason number. The drag force on a rotating cylinder is significantly different from that on particle chains calculated from both simulations, demonstrating the different dynamics between the two cases. For microscopic quantities like the detailed force distributions on each particle, the complete Navier-Stokes solution, here represented by the LB simulation, is required.     

Simulation of growth dynamics in atomic layer deposition. Part II. Polycrystalline films from cubic crystallites

The growth dynamics of polycrystalline thin films by the atomic layer deposition (ALD) technique has been simulated for randomly oriented and randomly positioned seed objects. Cubic crystals with the shape of cubes, octahedra, and truncated cubes have been used to exemplify the dynamics of polycrystalline growth of films with columnar structures. We have reproduced the non-linear growth in the initial stages of ALD preparation of polycrystalline films according to type-2 substrate-inhibited growth. The dependences of topography roughness, surface object density, and selection of angles on terminating surfaces on the film thickness are demonstrated. The topography and cross sections of the simulated films are also shown for the different crystal shapes considered. Means to control the topography to obtain either smooth or rough films are discussed. A possible reduction of surface roughness by the use of different types of precursors is exemplified for growth of crystal objects combining cube and octahedron shapes.     

Higher derivative explicit one step methods for non-linear dynamic problems. Part II: Practical calculations and comparisons with other higher order methods

A generalized explicit one step alogorithm developed in Part I of this paper is presented in the form of a predictor–corrector scheme suitable for arbitrary non-linear analyses of structural dynamics problems. Convergence results are checked through practical calculations on linear and non-linear systems. The generalized algorithm proposed is compared with other recently developed higher order one step algorithms. The slight amount of additional computational effort compared to second order methods pays off in linear and weakly non-linear systems. The behaviour of the methods is also tested on extreme stiffening and softening systems to investigate reliability and robustness of the algorithm.     

The dynamics of avalanches of granular materials from initiation to runout. Part II. Experiments

Summary This paper describes a model to predict the flow of an initially stationary mass of cohesionsless granular material down a rough curved bed and checks it against laboratory experiments that were conducted with two different kinds of granular materials that are released from rest and travel in a chute consisting of a straight inclined section, a curved segment that is followed by a straight horizontal segment. This work is of interest in connection with the motion of landslides, rockfalls and ice and dense flow snow avalanches. Experiments were performed with two different granular materials, nearly spherical glass beads of 3 mm nominal diameter, Vestolen particles (a light plastic material) of lense type shape and 4 mm nominal diameter and 2,5 mm height. Piles of finite masses of these granular materials with various initial shapes and weight were released from rest in a 100 mm wide chute with the mentioned bent profile. The basal surface consisted of smooth PVC, but was in other experiments also coated with drawing paper and with sandpaper. The granular masses under motion were photographed and partly video filmed and thus the geometry of the avalanche was recorded as a function of position and time. For the two granular materials and for the three bed linings the angle of repose and the bed friction angle were determined. The experimental technique with which the laboratory avalanches were run are described in detail as is the reliability of the generated data. We present and use the depth-averaged field equations of balance of mass and linear momentum as presented by Savage and Hutter [28]. These are partial differential equations for the depth averaged streamwise velocity and the distribution of the avalanche depth and involve two phenomenological parameters, the internal angle of friction, ø, and a bed friction angle, , both as constitutive properties of Coulomb-type behaviour. We present the model but do not derive its equations. The numerical integration scheme for these equations is a Lagrangian finite difference scheme used earlier by Savage and Hutter [27],[28]. We present this scheme for completeness but do not discuss its peculiarities. Comparison of the theoretical results with experiments is commenced by discussing the implementation of the initial conditions. Observations indicate that with the onset of the motion a dilatation is involved that should be accomodated for in the definition of the initial conditions. Early studies of the temporal evolution of the trailing and leading edges of the granular avalanche indicate that their computed counterparts react sensitively to variations in the bed friction angle but not to those of the internal angle of friction. Furthermore, a weak velocity dependence of the bed friction angle, , is also scen to have a small, but negligible influence on these variables. We finally compare the experimental results with computational findings for many combinations of the masses of the granular materials and bed linings. It is found that the experimental results and the theoretical predictions agree satisfactorily. They thus validate the simple model equations that were proposed in Savage and Hutter [28].     

Linear thermoviscoelasticity. Part II: Energy balances

Summary Based on the functional thermoviscoelastic model developed by the authors in the preceding paper of this issue, energy balances are drawn up (dissipation vs internal work production) for a material under thermomechanical loading. By classifying the thermomechanical processes involved, we show how delayed phenomena can appear on the energy balance for processes ending with an equilibrium state. Under cyclic loading, the characteristics of the energy phenomena are found to differ between the transient period and the established periodic mode. Lastly in the case of a null trace strain, methods of modelling the relaxation kernels are proposed with which it is possible to draw up energy balances of the kind using mechanical data.     

Quality and exposure control in semiconductor manufacturing. Part II: Evaluation

The purpose of this article is to test the performance of a heuristic algorithm that computes a quality control plan. The objective of the tests reported in this paper is twofold: (1) to compare the proposed heuristic algorithm (HA) to an optimal allocation (OA) method; and (2) to analyse the behaviour and limitations of the proposed HA on a scale-1 test with a before/after test. The method employed to evaluate this algorithm is based on comparisons: 1. The first test illustrates the method and its sensitivity to internal parameters. It is based on a simplified case study of a product from the semiconductor industry. The product is made up of 1000, 800 and 1200 wafers incorporating three different technologies. The production duration is 1 week, and three tools were involved in this test. The behaviour of the proposed algorithm is checked throughout the evolution of the model parameters: risk exposure limit (R_L ) and measurement capacity (P). The quality control plan for each tool and product are analysed and compared to those from a one stage allocation process (named C ⁰) that does not take into account risk exposure considerations. A comparison is also performed with OA.

2. The second scale-1 test is based on three scenarios of several months of regular semiconductor production. Data were obtained from 23 etching and 12 photolithographical tools. The outputs provided by the HA are used in the sampling scheduler implemented at this plant. The resulting samples are compared against three indicators.

The results of these comparisons show that, for small instances, OA is more relevant than the HA method. The HA provides realistic limits that are suitable for daily operations. Even though the HA may provide far from optimal results, it demonstrates major MAR improvement. In terms of the maximum inhibit limit, the HA achieves better performances than C ⁰, and they are strongly correlated to R_L and to the control capacity. The article concludes that the proposed algorithm can be used to plan controls and to guide their scheduling. It can also improve the insurance design for several levels of acceptance of risk.     

An elasticity microscope. Part II: Experimental results

For pt.I see ibid., vol.44, no.6, pp.1304-19 (1997). Initial experimental results from a 50 MHz elasticity microscope are shown. Using methods discussed previously, we present measured displacement and normal axial strain fields from a tissue mimicking phantom. Results from this homogenous gel are compared to a finite element simulation of the deformation experiment. The spatial resolution is estimated to be approximately 52 μm for axial displacements, and 71 μm for normal axial strains. These estimates were further tested by imaging a phantom containing a hard cylindrical inclusion with cross-sectional diameter of 265 μm. By examining the strain transition between regions in this image, the spatial resolution of the normal axial strain was verified to be at most 88 μm. A typical experiment produces peak normal axial strain around 3%. These experiments demonstrate the potential of high frequency ultrasound as a means for elasticity microscopy. Preliminary deformation experiments are presented on porcine epidermis     

Polyglycolide: Degradation and drug release. Part II: Drug release

This paper considers drug release from a polyglycolide (PGA) matrix and is divided into two sections. The first investigates the effects on the degradation of the polymer of incorporating a model drug, theophylline, into the polymer. Small and wide angle X-ray scattering, and mass loss and water uptake measurements indicate that the presence of this drug does not affect the time scale of the degradation process. However, the dissolved theophylline molecules affect the extent to which the polymer crystallizes during degradation. In the second section, theophylline release profiles, obtained using UV-spectrophotometry, show that the erosion of the polymer controls the release of the drug. The drug release results add further evidence to support the four stage degradation process which was described in Part I. © 2001 Kluwer Academic Publishers     

Transformation toughening in the γ-TiAl–β-Ti–Vsystem: Part II A molecular dynamics study

Molecular dynamics simulations of the evolution of materials in a region surrounding a crack tip were carried out for the case of a crack in a γ-TiAl phase impinging at a right angle onto the interface between a γ-TiAl phase and a metastable Ti–15V (at %) phase. The corresponding linear anisotropic solutions for the singular stress and displacement fields were used to both generate the crack in the original crystal and to prescribe the boundary conditions applied to the computational crystal during the molecular dynamics simulation runs. The atomic interactions were accounted for using appropriated embedded atom method (EAM) type interatomic potentials. The crack-tip behaviour for the two-phase γ–β material was ultimately compared with the one in the corresponding single-phase material, i.e. to the one in pure γ and the one in pure β crystals. The simulation results showed that under the same applied level of external stress, the crack tip became blunt and the crack stopped propagating in the γ-TiAl–β-Ti–15V bicrystal and in the single β-phase crystal while the crack extended by brittle cleavage in the single-phase γ crystal. The blunting process was found to be controlled by the martensitic transformation that took place in the β-phase ahead of the crack tip. Depending on the local stress conditions the crystal structure of martensite was found to be either hexagonal close packed (h.c.p.), body centred orthorhombic (b.c.o.) and/or face centred orthorhombic (f.c.o.). Finally the implications of crack tip martensitic transformation on the toughness of the materials are analysed in quantitative terms using the concept of Eshelby's conservation integral, i.e. the energy release rate. This revised version was published online in November 2006 with corrections to the Cover Date.     

Some questions on the corrosion of steel in concrete. Part II: Corrosion mechanism and monitoring,service life prediction and protection methods

This second part addresses some important issues that remain controversial despite the vast amounts of work devoted to investigating corrosion in concrete-embedded steel. Specifically, these refer to: 1) the relative significance of galvanic macrocouples and corrosion microcells in reinforced concrete structures; 2) the mechanism by which reinforcements corrode in an active state; 3) the best protective methods for preventing or stopping reinforcement corrosion; 4) the possiblity of a reliable prediction of the service life of a reinforced concrete structure; and 5) the best corrosion measurement and control methods. The responses provided are supported by experimental results, most of which were obtained by the authors themselves.     

Evaluation of impact assessment methodologies. Part I: Applied methods

The present paper is the first part of a comparative evaluation of two methodologies for the analysis of damage in composites. The subject of the investigation is low-velocity impact and residual compression strength of monolithic composite panels. One of the methodologies is implemented in the tool CODAC, which is a stand-alone software that aims to be a fast tool and works with specialized finite element (FE) and material models. The other methodology IDAT parametrically generates the FE models by using MSC.Patran and performs the analysis by the FE code ABAQUS/Standard. The evaluation in regard to accuracy and efficiency is performed by comparing and judging the models and techniques, which are applied for stress analysis, failure detection, material degradation and time integration. Part I of the paper describes the applied methodologies. In Part II, the methodologies are validated by comparing computational results against experimental results.     

Practical Productivity Analysis for Management: Part II. Measurement and Interpretation

In Part I, a framework for the analysis and measurement of productivity was provided, along with a sample of some empirical findings obtained with this framework. In this paper, the array of factors which must be examined in order to account for the observed findings is reviewed. Problems encountered in the application of this framework in different kinds of plants are discussed, including problems with the development of managerial ability to interpret the results of the analysis.