A novel numerical approach for workspace determination of parallel mechanisms

A global design methodology for supersonic air intakes is proposed. It is strongly based on numerical computations. The emphasis is especially put on the optimization of the links between the various stages of the design so as to rationalize the process and insure a good communication between the designer, the numerical computation engineer and the configuration manager. WHY IS IT IMPORTANT TO MASTER THE AIR INTAKE DESIGN IN A HIGH SPEED AEROBIC MISSILE DEVELOPPEMENT ? The design of a high-speed air-breathing vehicle is a long and delicate operation requiring the optimization of numerous design compromises interacting with each other and conditioning very widely the definition of the various constituents. The realization of these compromises is all the more difficult as we are more and more confronted with the imperative need to reduce the costs and the duration of the global cycle of development. One of the key elements of the global optimization of the aeropropulsive balance of high speed aerobic vehicles is the air intake which: Determines both the quantity and the quality of the air taken from the atmosphere (which influences directly all the tuning of the combustion chamber) Constitutes an important part of the global drag (which directly influences the fuel tank sizing) COPYRIGHT © 2001 EADS AEROSPATIALE MATRA MISSILES. Published by the American Institute of Aeronautics and Astronautics, Inc. with permission. Contributes strongly to the global lift (that participates to the global aerodynamic formula) Can be a major contributor to the radar signature (RCS) Participates substantially to the mass estimate Represents a significant part of the production cost. It is thus advisable to master and to rationalize the iterative design process of the air intake aerodynamics to be capable of: Minimizing the cost by limiting as much as possible the expensive experimental iterations; Reducing the cycle times to favour the flexibility and the reactivity of the global optimization; Estimating quickly the feasibility of beneficial shape evolutions or minimizing development and production costs or reducing the RCS. WHAT KIND OF APPROACHES ARE CLASSICALLY USED TODAY ? To establish the definition of an air intake, two approaches are possible: The experimental approach, which consists in realizing, reduced scale models and testing them in a wind tunnel; The numerical approach which consists in realizing a computation of the flow upstream and in the air intake by means of a two-, then threedimensional using, depending on the development, more and more accurate modeling of the fluid mechanics laws (Euler then NavierStokes). 1 American Institute of Aeronautics and Astronautics (c)2001 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization. THE EXPERIMENTAL APPROACH Led with skill, the experimental approach gives the surest results in terms of accessible global performances (performance curve). Even if the computation times have been reduced formidably, it remains today the most effective means to characterize an air intake in a wide flight domain in order to establish a performance serviceable for the propulsive system design, the global flight simulations, or the embarked regulation software. On the other hand, it requires heavy seed money, which consists in: Defining and realizing a model (modular able to receive various elements which allow to study configuration variants, the manufacture of which should be of very good quality precision, repeatability of the configurations, surface roughness...); Endow the of a detailed enough and precise instrumentation; Realize tests campaigns, the preparation of which being long and expensive. Besides, this experimental approach is too long if it is the only mean for the selection of the optimal air intake shape (model kit never perfectly adapted from the first tests campaign, time consuming configuration changes increasing the tests costs...). THE NUMERICAL APPROACH The numerical approach presents actually the inverse advantages and drawbacks of the experimental approach. In spite of the considerable progress realized these last ten years in the validation of the computation codes, and in spite of the precision presently obtained (of the same order as that of the tests), it will always be necessary to characterize in tests the shapes elaborated by computations, in order to definitively raise any doubt on the performances of the air intakes. Furthermore, the cost (in terms of duration) can turn out high if one wishes to perform a fine characterization requiring the computation of numerous running points. On the contrary, the numerical approach, although one endows it with effective meshing means, allows estimating in a reliable way and with a limited investment different configurations on a few flight points. Furthermore, it gives access to the detailed flow structure so yielding to understand better the physical phenomena that govern the functioning and favoring therefore the configuration desing. THE COUPLING OF THE EXPERIMENTAL AND NUMERICAL APPROACHES ALLOWS TO OPTIMIZE THE DESIGN To drive quoted rationalization process and answer more effectively the needs of the projects, we defines as objective: To establish an air intakes design methodology involving intimately both approaches to benefit of their advantages while minimizing (even eliminating) their drawbacks To obtain, thanks to this methodology, a sensitive reduction of the cost and the duration of the design cycle of an air intake To operate it according to its implementation on concrete industrial cases. GLOBAL DESIGN METHODOLOGY OF AIR INTAKES The development and the validation of internal aerodynamics computation codes being acquired, we focused on building a general design methodology for supersonic air intakes which strongly integrates the numerical approach into the traditional process based on wind-tunnel tests. Given the advantages and drawbacks described above for both experimental and numerical approaches, the best complementarity is obtained through the process described in the following scheme: American Institute of Aeronautics and Astronautics (c)2001 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization. Figure 1: coupling of numerical and experimental approaches A few of key points was identified as determining the efficiency of the process: Configuration management Simplification of the CAD / meshing interface

Numerical and empirical approach in predicting the penetration of a concrete target by an ogive-nosed projectile

Aiming at obtaining lower-mobility parallel mechanisms (PMs) in a topological and direct manner, this paper intends to propose an approach for configuration evolution of Stewart Platform and its variations. Firstly, the finite motion of Stewart Platform is described by utilizing finite screw and the motion mapping with lower-mobility PMs is formulated. Then the relationship between motion and topology is revealed in an analytical form. Following with these work, the principles for removing motions and their according topological manipulations are derived. A two-step method for configuration evolution is proposed. Finally, two examples as spatial translational and planar motion PMs are taken to show the concise process of the method and target PMs with closed-loop limbs are obtained. The principles involved in this approach are proved algebraically, but they are easy to be performed by simple topological manipulations such as synchronously driving and locking joints without any calculations even mathematic knowledge. This method facilitates the concise acquirement of lower-mobility PMs, especially 3-degree-of-freedom (DoF) PMs in the engineering.

This paper presents the analytical solution of four-component gas/oil displacements under constant pressure boundary conditions. All the previous studies in gas/oil displacement problems have been accomplished under the assumption of constant flux boundaries. In practice however, gas flooding projects are often conducted with constant injection pressure and constant producing well pressure. In this work, a novel generation of Buckley-Leverett’s classic fractional flow theory is applied to solve the problem of four-component gas/oil displacements under constant pressure boundaries. Conservation of mass in a one-dimensional, dispersion-free medium, for a four-component gas/oil displacement system leads to a set of partial differential equations. The solution of the corresponding initial value problem under constant flux boundary conditions consists of rarefaction waves, shock waves and constant states connecting the injection state to the production state. In incompressible systems with constant pressure boundaries, the total volumetric flux is a function of time and hence, the classical Buckley-Leverett theory is not valid. However, the saturation wave structure obtained from the constant flux boundary condition problem can be used in the solution of the associated problem with constant pressure boundaries by determining the flux analytically as a function of time. The solution for a four-component gas/oil displacement case study is presented. The determination of time dependent volumetric flux from the solution of the constant flux problem is demonstrated. Results are also obtained using a numerical approach and are compared to the analytical results. This indicates that the analytical solution is indistinguishable from the numerical solution as the number of grid blocks in the numerical method approaches infinity. However, a very fine grid is needed for an acceptable solution. Key Words: Gas injection, constant flux boundary condition, constant pressure boundary condition.

In practical applications, the stress status of expanded tubes is a critical parameter to control leakage and stress corrosion cracking. Therefore, it is important to study and analyze the stress distribution generated from tube expansion. Unfortunately, there are only a few theoretical approaches available for estimating the stress distribution of formed tubes, especially for cases where the expansion is achieved with spherical and oval dies. In this study, 3/8 stainless steel and copper tubes were expanded with an oval die in a designed test workbench, and the tangential and longitudinal strains were monitored during the expansion process. A new analytical approach is developed to estimate the stresses and strains in the expanded tube during the expansion process. The different expanded zones are treated using different theories. An axisymmetric finite element model as a numerical approach is used to analyze the stresses based on a multi-linear kinematic hardening behavior to validate the analytical approach. In addition, the stresses in the expanded tube and the push force of the die are also provided by the analytical, numerical and experimental approaches. Finally, the results from the three approaches are in a relatively good agreement.

Enhancing the primary efficiency of an oscillating water column wave energy converter based on a dual-mass system analogy

A numerical approach for computing standard errors (SES) of a linear equating is described. In the proposed approach, the first partial derivatives of the equating function needed to compute the SES are derived numerically. Thus, the difficulty of deriving the analytical formulas of the partial derivatives for a complicated equating method is avoided. The numerical and analytical approaches were compared using the Tucker equating method. The SES derived numerically were found to be indistinguishable from the SES derived analytically. In a computer simulation of the numerical approach using the Levine equating method, the SES based on the normality assumption were found to be less accurate than those derived without the normality assumption when the score distributions were skewed.

In recent years, the global buckling assessment of offshore pipelines in High Pressure-High Temperature (HPHT) condition become increasingly challenging since more complex pipeline system arrangement e.g. pipe(s) or cable(s) is strapped onto a larger pipeline, are rapidly utilized in many areas. Yet, the detailed guideline to assess the buckle of bundles remains unclear, therefore this study will focus to investigate on a methodical and reproducible approach to analyze in-service buckling behavior of bundled offshore pipeline system. The global buckling behavior of bundled offshore pipeline system in this study is investigated using commercial Finite Element (FE) software. Two carbon steel pipelines with different diameter are bundled and the buckling behavior is studied under the influence of buckle triggers. In the actual condition, the rogue buckle trigger is generated from OOS (out of straightness) or imperfection e.g. due to laying tolerance. Varying dimension parameter such as diameter ratio between the main pipeline and strapped pipeline are considered to understand the impact of this parameter on the buckle behavior. The study begins with a comparison of the results using numerical and analytical approaches on a straight pipeline in an unbuckled condition for validation purposes. The design parameters including wall thickness, process data, and pipe-soil interaction data, are varied since it influences the buckle behavior. In addition, some design parameter such as material properties and pipeline length will be adopted from a typical offshore pipeline project and the values are fixed so the exercise can focus on the most governing parameters. Following this, two numerical modelling methods, the equivalent properties method and the connector method, are presented in this study to simulate bundled systems. With a good agreement between the analytical and numerical approach, some buckle trigger is introduced on the numerical model of the bundled pipeline so the system is able to buckle and the behavior can be evaluated further. The strain level, lateral displacement, axial feed-in and pipe integrity shall be reported in the post-buckle conditions for both main pipe and strapped pipe as per current code and standard requirement. With more reliable results of buckling assessment for bundled pipeline system, it gives technical confidence and a major saving in both Capital Expenditure (CAPEX) and Operational Expenditure (OPEX). Industry has put serious effort through various Joint Industry Projects (JIP) to develop the global buckling assessment guideline in order to ensure long term integrity operation. Although the JIP guideline is predominantly for single pipeline system, similar assessment is demanded also for bundled pipeline system which described in this study. Key findings of the assessment are presented along with an overview of the design process and the typical mitigation techniques to be considered for similar subsea pipeline projects.

In this paper, we consider the problem of scheduling N robots interacting with a moving target. Both, the sequence of the robots and their trajectories are unknown and subject to optimization. Such type of problems appear in highly automated production plants and in the simulation of virtual factories. The purpose of the paper is to provide a mathematical model and to suggest a numerical solution approach. Our approach is based on the formulation of the problem as a bilevel optimization problem, where the lower level problem is an optimal control problem, while the upper level problem is a finite dimensional mixed-integer optimization problem. We approach the problem by exploitation of necessary optimality conditions for the lower level problem and by application of a Branch & Bound method for the resulting single level optimization problem. Two settings are taken into account. Firstly, no state constraints are assumed on the lower level problem, thus the local minimum principle applies directly. Secondly, the problem setting is augmented by pure state constraints, which are being handled by virtual controls in order to regularize the problem.

In recent years, the construction industry has seen a greater focus on the use of sustainable construction materials to reduce the environmental impact of buildings. Timber is one such material that has seen a revival in its use due to its environmental credentials coupled with advances in the manufacture of engineered wood products and connection technologies. While timber and engineered wood products have a high strength-to-weight ratio suitable for large scale construction, timber is an orthotropic material and demonstrates poorer strength when loaded perpendicular to the grain. As a result, special consideration must be given to the design of areas of support where stress perpendicular to the grain develops in timber structures. This paper describes a study which examines the use of densified wood dowels as a sustainable reinforcement against perpendicular to the grain stresses using experimental and numerical approaches. Glued laminated timber samples were reinforced with 2, 4 and 6 densified wood dowels. The experimental results show significant improvements in load-bearing capacity can be achieved. A full 3-dimensional solid finite element model has been implemented in ABAQUS/Explicit software. The numerical model utilises cohesive zone modelling (CZM) and Hill plastic yield criterion to predict the failure behaviour of specimens utilising densified wood dowel reinforcement. The examined numerical modelling approach has been shown to give good predictions of the performance of the dowel-timber interaction and load-bearing capacity of the composite system. The numerical model has been also used in a parametric study to examine the influence of dowel diameter and dowel length on the failure behaviour. A maximum dowel length-to-diameter ratio is recommended based on the numerical results

This paper carries out a comprehensive and systematic comparison study on the kinematic performance of four six degrees of freedom (6-DOF) parallel mechanisms with different topologies, i.e., 6-UPS, 3-(2-UPR)U, 3-(2-UCR)U, and 3-R(2-RPR)U. The research begins by elaborating in detail the similarities and differences among these four parallel mechanisms. By standardizing the definition of the coordinate system for each mechanism, the inverse kinematics and the Jacobian matrix of these four mechanisms are systematically derived. Employing a set of motion/force transmission indices, which are directly obtained from the Jacobian matrix, the kinematic performances of the four mechanisms are thoroughly analyzed and compared within the given workspaces while maintaining the same dimensional parameters for all cases. The comparison study of these four parallel mechanisms extends beyond local transmission indices to also include global transmission indices, covering both position and orientation workspaces, as well as assessments at both the local and global workspace levels. This comprehensive approach ensures a detailed and fair evaluation of their respective kinematic capabilities. The results indicate that the comprehensive kinematic performances of the four parallel mechanisms are similar, and providing a solid theoretical foundation for innovative design and practical guidance for selecting optimal architectures based on specific application requirements.

Linear stability analysis of plane Couette flow of a viscoelastic, upper-convected Maxwell (UCM) fluid past a deformable elastic solid is carried out in the low Reynolds number limit using both numerical and asymptotic techniques. The UCM fluid is characterized by its viscosity η, density ρ, and relaxation time τR, whereas the deformable solid is considered to be a linear elastic solid of shear modulus G. The asymptotic analysis is performed in the Re ≪ 1 limit, where Re = ρVR/μ is the Reynolds number, V is the top plate velocity, and R is the thickness of the fluid. Both asymptotic and numerical approaches are used to understand the effect of solid elasticity, represented by the dimensionless parameter Γ, and fluid elasticity, characterized by the Weissenberg number W, on the growth rate of a class of modes with high frequencies (compared to the imposed shear rate, termed high-frequency Gorodtsov-Leonov, or “HFGL” modes) in the Re ≪ 1 limit. Here, the dimensionless groups are defined as W = τRV/R and Γ = ηV/GR. The results obtained from the numerical analysis show that there is an interaction between the shear waves in the fluid and the elastic solid, which are coupled via the continuity conditions at the interface. The interaction is particularly pronounced when W = Γ, strongly reminiscent of resonance. The resonance-induced interaction leads to shear waves in the coupled system with a decay rate of ci = −1/[2k(W + Γ)]. In this case, it is not possible to differentiate the fluid and solid shear waves individually and the coupled fluid-solid system behaves as a single composite material. The leading order asymptotic analysis suggests that the growth rate of the HFGL modes is proportional to W2 for W ≪ 1. The asymptotic analysis, up to first correction, shows an oscillating behavior of ci with an increase in Γ, in agreement with the results from our numerical approach. In addition, we also carry out an asymptotic analysis in the no-flow, but nonzero inertia limits to illustrate the role played by the imposed flow in the instability of the shear waves. It is found that, at the leading order, the wave speed for the coupled fluid-solid problem is neutrally stable in the absence of flow. Thus, the unstable resonant modes in the coupled fluid-solid system are shown to be driven by the imposed flow.

Anisotropic motion laws play a key role in many applications ranging from materials science, biophysics to image processing. All these highly diversified disciplines have made it necessary to develop common math- ematical foundations and framworks to deal with anisotropy in geometric motion. The workshop brings together leading experts from various fields to address well-posedness, accuracy, and computational efficiency of the math- ematical models and algorithms.

A new simplified meta-model to evaluate the transmission of ground movements to structures integrating the elastoplastic soil behavior

Two-layer metallic sheets have wide applications in aerospace, marine, automotive and domestic industries due to their superlative characteristics. In this paper, the formability of two-layer sheet is investigated through analytical, experimental and numerical approaches. An analytical model is developed based on Marciniak-Kuczynski method associated Hill’s non-quadratic yield criterion. Forming limit diagrams are also obtained numerically based on finite element method using Bifurcation theory and ductile fracture criteria. Furthermore, experiments are carried out on Al3105-St14 two-layer sheet. Theoretical results from various methods are compared with results obtained from experiments to evaluate the competency of discussed analytical and numerical methods to predict the formability of two-layer sheets. The results show that analytical and numerical approaches discussed in this paper have good capabilities to predict the formability of two-layer sheets. However, the analytical method based on M-K model and numerical approach based on bifurcation theory are more suitable to determine the forming limit diagram of Al3105-St14 two-layer sheets.