Using a coarse time discretisation for saving calculation effort will induce non-uniform heat input within thermal-transient analyses which include translational rigid body motions by the technique of discrete displacement adjustment. We are going to show, why these non-uniformities are generally unavoidable and how a suitable choice of time step size pre-minimizes their consequences. Afterwards, the amount and location of the remaining load-bumps are analytical deduced for an arbitrary motion. With this information, we develop a correction method based on arithmetic calculations to avoid these numerical caused errors. For practical use, the correction is applied as an algorithm to the solution process of analyses with spatial discretized motion partners. We finish by demonstrating the performance of the correction.

In this paper a new method for achieving isotropic compliance at the contact point is applied to a manipulator for packaging operation. Two different manipulators are considered, namely, PR and PPR. The paper discloses some different strategies for stiffness control, with the purpose of contact force optimization. The control system acts on the controlled joint stiffness in such a way that the contact force, in the Cartesian Space, will be parallel to the displacement of the contact point. Such feature minimizes friction and wear during packaging operations and minimize tangential reactions.

Schoenflies ( X ) motion is a 4D displacement Lie group including a spatial translation and any rotation whose axis is parallel to a given direction. Delassus parallelogram has four parallel screw (H) pairs with related pitches and the isosceles triangle is a special HHHP. After merging these two chains, an HHH-//-HHH generator of 2-DoF translation along a right helicoid is derived. It produces a 2-DoF motion mathematically modeled by a 2D submanifold of a 4D group of X -motion. Because of the product closure in an X -group, the 4-DoF generator with HHH-//-HHH loop serving as a subchain is revealed by adding two H pairs with axes parallel to fixed H axes. Parallel arrangement of two generators of the same X motion results in a new Schoenflies-motion manipulator with hybrid topology for 4-DoF pick-and-place operations. Four fixed H pairs (two double Hs) can actuate this manipulator and the two coaxial Hs must have distinct pitches. In addition, the possible design choices of special architectures are introduced for practical applications. Computer simulations of the new parallel manipulator with Schoenflies motion verify the effectiveness.

This study addresses in-plane thermal residual stresses in two-dimensional functionally graded plates under a constant in-plane heat flux. The plate material properties vary with a power law along two in-plane directions not through the plate thickness. The transient heat conduction and Elasticity’s Navier equations describing the two-dimensional thermo-elastic problem were discretized using the finite-difference method, and the set of linear equations was solved using the pseudo singular value method. The in-plane transient distributions of temperature, displacement, stress and strain components were determined, and the two-dimensional exponents and directions of compositional gradient were investigated in terms of their effects on the stress and strain distributions in both plates. The exponent and direction of the compositional gradient affected the peak in-plane strain and stress levels; therefore, the stress and strain distributions can be relieved by arranging the exponent and directions of the compositional gradient.

Functionally graded materials (FGMs) are multi-phase inhomogeneous composites, possessing smooth spatial variations in certain physical properties of the constituents. Depending on the types of the constituent materials used in the processing of orthotropic FGMs, the influences of thermal and hygroscopic loadings could be rather significant. This study is directed towards developing a new computational fracture analysis technique for orthotropic FGMs that are under mixed-mode hygrothermal loading. The method is based on the use of the J -integral in conjunction with the asymptotic crack tip displacement fields. Developed computational technique is integrated into a finite element analysis software. Parametric analyses are carried out by considering an inclined edge crack in an orthotropic FGM layer that is subjected to the influence of hygrothermal loading. In order to be able to verify the proposed method, obtained results are compared to those computed via displacement correlation technique (DCT). Comparisons demonstrate that proposed technique leads to numerical results of high accuracy. Further results are provided to illustrate the influences of crack inclination angle and geometry on the temperature and the specific moisture concentration fields; and the modes I and II stress intensity factors.

This work presents a closed form investigation on the effect of temperature gradient on the buckling resistance of functionally graded material (FGM) shallow arches. The constituents are assumed to vary smoothly through the thickness of the arch according to the power law distribution and they are assumed to be temperature dependent. The arches subjected to the both uniform distributed radial load and central concentrated load and both boundary supports are supposed to be pinned. The temperature field is approximated by one-dimensional linear gradient through the thickness of the arch and the displacement field approximated by classical arches model. Also, Donnell type kinematics is utilized to extract the suitable strain-displacement relations for shallow arches. Adjacent equilibrium criterion is used to buckling analysis, and, critical bifurcation load is obtain in the complete presence of pre-buckling deformations. Results discloses the usefulness of using the FGM shallow arches in thermal environment because the temperature gradient enhances the buckling resistance of these structures when they are subjected to a lateral mechanical load.

In this study non-linear thermal buckling of circular shallow arches made of functionally graded materials subjected to a linear temperature gradient is investigated. For this purpose, a functionally graded circular shallow arch is considered that its strain-displacement relation follows the Donnells nonlinear shallow shell theory. The material properties are varied smoothly through the arch thickness according to the power law distribution of the volume fraction of constituent materials. Also, material properties are considered temperature-dependent. The classical single layer theory assumptions that are reasonable for slender arches are implemented. To investigate the large deformations of such arch, the von-Karman type geometrical nonlinearity is utilized that is suitable for moderately large class of rotations. The virtual displacement principle and calculus of variation are employed to derive the governing equilibrium equations and complete set of boundary conditions of the FGM arch. The adjacent equilibrium criterion is employed for the stability analysis of the FGM arch. An analytical approach is accomplished and a closed-forms solution for thermal bifurcation points of the FGM shallow arches is presented. Also critical bifurcation loads corresponding to the critical temperatures with the presence of non-linear pre-buckling deformations is obtained. Illustrative results examine the effect of various involved parameters such as power law index, opening angle, geometric parameter (or otherwise length to thickness ratio). Obtained numerical results represent that, in most cases, thermal bifurcation for the FGM arches occurs in the high temperatures and the critical buckling temperatures are approximately high even for slender FGM arches. Also effective of ceramic or metal rich area at the bottom surface of the FGM arch is investigated and results are presented for both cases and are compared together. Varieties between this two cases due to contrast between material and structural stretching-bending coupling effect. Results presented illustrative the ceramic rich area at the bottom surface cause the higher critical buckling temperatures for the FGM arches.

In this paper a vibration isolated design of the Coriolis Mass-Flow Meter (CMFM) is proposed, by introducing a compliant connection between the casing and the tube displacement sensors with the intention to obtain a relative displacement measurement of the fluid conveying tube, dependent on the tube actuation and mass-flow, but independent of casing excitations. Analyses are focussed on changing the transfer function of support excitations to the relative displacement measurement. The influence of external vibrations on a compliant sensor element and the tube are made equal by tuning the resonance frequency and damping of the compliant sensor element and therefore the influence on the relative displacement measurement is minimised. Based on simulation results, a prototype is built and validated. The validated design show a 20dB reduction of the influence of external vibrations on the mass-flow measurement value of a CMFM, without affecting the sensitivity for mass-flow.

This paper reports experimental measurements of film thickness for continuous fluid flow within a spinning cone. The results are compared to analytical theory for thin film flow and found to be in good agreement. Spinning cones are used in various industrial process machines, including spinning cone distillation columns, centrifugal film evaporators and continuous centrifugal filters. In each case a fluid is fed continuously into the centre of a conical vessel which spins about a vertical axis with the cone apex pointing downwards. The fluid acquires the angular velocity of the cone and migrates up the internal wall of the cone under centrifugal force. Knowledge of the film thickness and flow velocity is often important in order to understand other performance parameters of the process such as evaporation or filtration rates. This paper aims to aid the design of new process machines by providing a mathematical model for film thickness that is validated by experimental results. Experiments have been conducted in which the angle of cone, angular velocity and input flow rate were all varied. Film thickness measurements were obtained via a novel optical method based on photographing the displacement of a projected grid on the surface of the flow within the cone. The method has the advantages of not disturbing the flow in any way and can provide thickness measurements over the whole cone depth. Measurements are also made insensitive to any transients by use of relatively long photographic exposures. Measurements are compared to analytical theory for axisymmetric, steady state, free-surface laminar flow of a Newtonian fluid in a spinning cone. The theory assumes the flow is thin but takes account of gravity. The theoretical model is found to be in good agreement with the experimental results.

In synchronous belt drives, transmission error is generated due to resonance of the belt spanning the driving and driven pulleys when the transverse natural frequency of the belt approaches the meshing frequency of the belt and the pulley teeth. The behavior of the transmission error caused by resonance has been assumed to be dependent on the installation tension. In the present study, the influence of installation tension on the transmission error in a synchronous belt drive was experimentally investigated for a case in which first mode vibration due to resonance was induced in both the upper and lower spans. In addition, an analysis of the transmission error based on the experimental results was carried out. A transmission error contains two components: one with a period equal to the pitch of the pulley, and the other with a period of half the pulley pitch. Good agreement was found between the calculation and experimental results, thus confirming the validity of the analysis method. For a fixed pulley speed, the transmission error was largest when the installation tension was applied at a position where the displacement of the upper span was equal to that of the lower span. When the installation tension was varied and the pulley speed was adjusted so that the belt experienced resonance, the transmission error decreased with an increase in installation tension.

Digital Displacement (DD) fluid power machines utilizes electronically controlled seat valves connected to pressure chambers to obtain variable displacement with high operational efficiency and high bandwidth. To achieve high efficiency, fast valve switching is essential and all aspects related to the dynamic behaviour of the seat valves must be considered to optimize the machine efficiency. A significant effect influencing the valves switching performance is the presence of oil stiction when separating the contact surfaces in valve opening movement. This oil stiction force is limited by cavitation for low pressure levels, e.g. valves connected to the low pressure manifold, however for valves operated at higher pressure levels, the oil stiction force is dominating when the separating surfaces are close to contact. This paper presents an analytic solution to the oil stiction force for annular seat valves suitable for DD applications based on the Reynolds equation and considers contact surface curvature and attack angle. A dynamic cavitation zone is included in the stiction model, and cavitation is found to be present even for seat valves surrounded by high pressure levels.

To perform 3D inspection, the most common digitizing system is a coordinate measuring machine (CMM) equipped with a touch trigger probe. Because of their large time consuming, a large number of industrial digitizing systems presenting different characteristics have recently emerged, but collected data quality strongly depends on the sensor technology combined with the associated displacement system. The works presented here focus on a novel approach that help users to select the most appropriate digitizing system in regard of the specification to be verified. This selection is performed in two steps: an ability selection that removes non convenient systems and a performance selection to select the system that provides sufficient data quality in the minimum time. This quality can be noise, trueness, density, depending on the specification to be verified. To store all necessary information, databases that contain intrinsic and qualified information have been developed. An example with GPS specifications is treated.

Knee orthotic devices are widely proposed by physicians and medical practitioners for preventive or therapeutic objectives in relation with their effects, usually known as to stabilize joint or restrict ranges of motion. The objectives of this work are to characterize the mechanical performance of knee orthoses using a Finite Element Model of a braced human leg. The interface properties of the model are calibrated against experimental data measured by full-field measurements of 3D displacement over the surface of a patient’s leg. The results show that the mechanical action of knee braces is essentially limited by skin/fabric and skin/muscles sliding. Finally, the model leads to a better understanding of the knee/brace interaction, and of the role of the brace components on the stability of the injured knee. Thanks to this computational tool, novel brace designs can be tested and evaluated for an optimal mechanical efficiency of the devices.

Graded materials, also known as functionally graded materials (FGMs), are multiphase composites mainly composed of a ceramic and a metal; thus, they exploit the heat, oxidation and corrosion resistance typical of ceramics, and the strength, ductility and toughness typical of metals. These materials are mainly used as heat barriers. In addition, many of the present and potential applications of FGMs involve contact problems. On the other hand, the production process of FGMs is somewhat complex and leaves some defects in the produced structure. One of the most important defects in such structures is surface cracks. Here, the combination of the contact and crack problems is investigated in a functionally graded rectangular plate containing a semi–elliptic surface crack indented by a frictionless rigid spherical indenter. The plate is simply supported and the crack is located in the middle of the plate surface in the tension part. The crack surface is parallel to one of the plate edges. The gradient of mechanical properties variation is considered through the thickness of the plate and the volume fraction distribution of the constituting phases is modeled by a polynomial function and the Poisson’s ratio is kept constant. The analyzing of the problem is divided into two steps. At the first step, for an uncracked plate the equations of equilibrium are derived in terms of the displacement field and are solved numerically to find the contact rule. As the second step in studying the problem, the contact problem of a cracked plate is modeled by using ABAQUS finite element package. The aim of this step is to find the effect of the presence of the crack on the contact rule. The optimum mesh for the ABAQUS model is found by using the results of the first step. In order to do so, an ABAQUS model is created for the uncracked plate. The analytical results and the obtained results from ABAQUS for specified plate and indenter dimensions and material properties are compared. After finding the optimum mesh, a crack is added to the ABAQUS model of the plate under contact loading. The effects of gradient changes and indenter dimensions on the contact rule and stress distribution at the crack tip are then investigated by using the obtained ABAQUS model. The acquired results show that the influence of the material nonhomogeneity on the stress distribution around the crack tip and in the plate (uncracked and cracked) and contact rule can be quite significant. In general, increasing the overall volume fraction of the metal phase increases the load carrying capacity in an uncracked plate. In a cracked plate, the changes in material distribution as well as the changes of the indenter diameter does not affect the results that much.

A series of biaxial experiments are performed to investigate the yield envelope of high-density polyethylene (HDPE). An Arcan apparatus is achieved in order to load a newly-designed flat specimen “butterfly specimen” to various combinations of tensile/compressive and shear loading. It subjected a central section of the specimen to a uniform state of plane stress. The stresses have local maxima at the central section, thus ensuring that yielding occurs there. The yield stresses are determined from the load-displacement curves and plotted in two-dimensional principal stress. The experimental results are compared with a predicted yield envelope based upon a pressure modified von Mises criterion, which accounts for the difference in tensile and compressive yield stress; additionally the hydrostatic pressure on yielding is also considered. Good agreement is found.

This paper presents the development of Meshless Methods based on Moving Least Square Approximation (MLSA) [3][10][14]. In the case of solid mechanics, the shape displacement functions are computed for each node with a centered scheme approximation [3][12] associated with a specific weight function [10]. Both interpolated and approximated weight functions are studied [10][9][15]. We propose to build a new C 1 weight function based on a 2d boundary line. The Galerkin Method is used to solve the mechanical equilibrium balance problems [14]. A 2-dimensional example is presented to validate the Meshless Method.

3D discrete dislocation dynamic (DDD) simulations are performed to simulate stage-I fatigue crack initiation and propagation along the surface, in the primary grain and its neighbouring grain, in 316L stainless steel. The scenario of crack propagation in primary grain and the evolution of dislocation structure ahead of crack tip are discussed, and in addition crack tip sliding displacement is estimated. Probable mechanisms of crack propagation from primary grain to neighbouring grain are evaluated. In this process, surface relief in the neighbouring-grain under the influence of crack stress field in the primary grain is studied for varying neighbouring-grain orientations. An enhanced evolution of surface extrusions in the neighbouring grain, are observed in the presence of heterogeneous stress field (i.e., in the presence of crack in the primary grain), compared to that in the case of homogeneous stress field. In addition, influence of crack stress field on prior cyclic-deformed substructure is presented.

In redundant manipulation systems the end-effector path does not completely determine the trajectories of all the individual degrees of freedom (dof). The redundancy is used in this paper to minimize energy consumption. A full electromechanical model is used, and the invested energy is calculated explicitly. The optimization includes also displacement limits via penalty functions that are included in the cost function. The solution is based on separating the system and the input into two parts. One that is completely determined by the end-effector path and the other that is driven by it, yet free for optimization. The boundary conditions are resolved in a similar manner, where the physical values are translated to the scaled down system by using a specific projection. Simulation results show that even with limited joint motion, the redundancy can lead to a considerable saving in energy.

A digital electromagnetic actuator having two displacement directions and four discrete positions is presented. These discrete positions are located at each corner of a closed square bracket where a mobile magnet moves due to Lorentz force generated with a driving current through a wire. An optimized design of this actuator is presented, modeled and tested. At first, plane displacements are presented which proves the ability of the actuator to realize this type of displacement. Second, comparisons between the experimental and modeled displacements are carried out which show a good agreement from dynamic point of view and finally, the measured positioning repeatability errors in discrete position are given.

The objective of this paper is to present the Spectral Element Method (SEM) as an accurate and efficient design tool for static and dynamic simulations of cantilever based MEMS devices. The microcantilever under consideration is modeled as a Timoshenko beam and discretized using the spectral element formulation that accounts for fringing field and the nonlinearity arising from the electrostatic driving force. The static analysis has been carried out using Picard’s iteration method and the static pull-in displacement and voltage have been calculated. An eigenvalue analysis of this beam is also carried out to determine its natural frequencies. In addition, the dynamics of this cantilever is studied using the explicit Newmark predictor-corrector method to generate the time history. In all cases, the results have been compared to the one-dimensional Finite Element Method and three-dimensional finite element method (implemented through the commercial package COMSOL Multiphysics) to examine the accuracy and computational speed of the proposed SEM. The results of the simulations were also compared to those obtained by experiments in the existing scientific literature. These comparisons lead to the inference that the SEM is able to reproduce the static and dynamic response of the beam to a high degree of accuracy. It was also found that several numerical features inherent in the SEM lead to a significantly faster computation than the corresponding finite element method for equivalent degrees of freedom. This advantage was verified by using the SEM to carry out static and dynamic simulations of variable width microcantilevers. We therefore propose that the SEM is a viable tool for the MEMS community to accurately and quickly determine the static and dynamic pull-in parameters, frequency eigenvalues, and static and dynamic behavior at the design stage.