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The work herein proposes the use of the data-driven Loewner-framework for reduced order modeling as applied to dynamic Finite Element Models (FEM) of thermally morphing structures. The Loewner-based modeling approach is computationally efficient and accurately constructs reduced models using analytical output data from a FEM. This paper details the two-step process proposed in the Loewner approach. First, a random vibration FEM simulation is used as the input for the development of a Single Input Single Output (SISO) data-based dynamic Loewner state space model. Second, an SVD-based truncation is used on the Loewner state space model, such that the minimal, dynamically representative, state space model is achieved. For this second part, varying levels of reduction are generated and compared. The work herein can be extended to model generation using experimental measurements by replacing the FEM output data in the first step and following the same procedure. This method will be demonstrated on two thermally morphing structures, a rigidly fixed hexapod in multiple geometric configurations and a low mass anisotropic morphing boom. This paper is working to detail the method and identify the benefits of the reduced model methodology. [ABSTRACT FROM AUTHOR]

Highlights • Accurate and efficient numerical simulation of granular flow. • Two regularized models of the μ (I) -rheology. • Application of the PFEM to frictional material simulation. • Validation against 3D experimental tests. Abstract This paper proposes two regularized models of the μ (I) -rheology and shows their application to the numerical simulation of 3D dense granular flows. The proposed regularizations are inspired by the Papanastasiou and Bercovier–Engleman methods, typically used to approximate the Bingham law. The key idea is to keep limited the value of the apparent viscosity for low shear rates without introducing a fixed cutoff. The proposed techniques are introduced into the Particle Finite Element Method (PFEM) framework to deal with the large deformations expected in free-surface granular flows. After showing the numerical drawbacks associated to the standard μ (I) -rheology, the two regularization strategies are derived and discussed. The regularized μ (I) -rheology is then applied to the simulation of the collapse of 2D and 3D granular columns. The numerical results show that the regularization techniques improve substantially the conditioning of the linear system without affecting the solution accuracy. A good agreement with the experimental tests and other numerical methods is obtained in all the analyzed problems. [ABSTRACT FROM AUTHOR]

Abstract Conventionally, the dynamic modeling of H-type gantry stage(HGS) assumes that the stiffness of mid-beam is extremely high so that its deformation is ignorable. This assumption apparently simplifies the study, but unavoidably compromises the modeling precision as it is not consistent with the real working status especially at high frequency motion. Comparing with similar studies on moving mass problems, the beam vibration of HGS is excited not only by the moving mass and system acceleration but also by the non-synchronized motion of the two moving ends of mid-beam. Therefore, the objective of this paper is to propose an assumed mode method based on simplified mode shapes(AMM-SMS) by simultaneously considering the lateral flexibility and the motion of the ends of mid-beam. The proposed AMM-SMS adopts the mode shapes of a simplified system, which has the same geometry boundary condition(BC) with the investigated system, to discretize the nonlinear kinematic equations of the proposed system. This method improves the modeling precision with low complexity, and can be applied in different BCs of FHGS. The proposed method is verified by various comparisons with the finite element method. Based on the AMM-SMS, the first three natural frequencies and mode shapes are studied. The open-loop responses of the system are obtained to analyze the effects of different BCs, of the motion of end-effector and of the external exciting force on the vibratory behavior. [ABSTRACT FROM AUTHOR]

This paper constitutes our initial effort in developing sparse grid discontinuous Galerkin (DG) methods for high-dimensional partial differential equations (PDEs). Over the past few decades, DG methods have gained popularity in many applications due to their distinctive features. However, they are often deemed too costly because of the large degrees of freedom of the approximation space, which are the main bottleneck for simulations in high dimensions. In this paper, we develop sparse grid DG methods for elliptic equations with the aim of breaking the curse of dimensionality . Using a hierarchical basis representation, we construct a sparse finite element approximation space, reducing the degrees of freedom from the standard O ( h − d ) to O ( h − 1 | log 2 ⁡ h | d − 1 ) for d -dimensional problems, where h is the uniform mesh size in each dimension. Our method, based on the interior penalty (IP) DG framework, can achieve accuracy of O ( h k | log 2 ⁡ h | d − 1 ) in the energy norm, where k is the degree of polynomials used. Error estimates are provided and confirmed by numerical tests in multi-dimensions. [ABSTRACT FROM AUTHOR]

The detection and localization of damage in metallic structures using acoustic emission (AE) monitoring and artificial intelligence technology such as deep learning has been widely studied. However, a current challenge of this approach is the difficulty of obtaining sufficient labeled historical AE signals for the training process of deep learning models. This problem can be approached through the implementation of transfer learning. The innovation of this paper lies in the development of a transfer learning approach for AE source localization on a stainless-steel structure when no historical labeled AE signals are available for training. A finite element model is developed to generate numerical AE signals for the training. Unsupervised domain adaptation (UDA) technology is utilized to reduce the distribution difference between the numerical and the realistic AE signals and to derive the localization results of the unlabeled realistic AE signals. The results suggest that the proposed approach is capable of localizing AE signals with high accuracy in the absence of labeled training data. [ABSTRACT FROM AUTHOR]

Understanding thermal effects on the vibration of local (cable-dominant) modes in multi-cable structures is a complicated task. The main difficulty lies in the modification by temperature change of cable tensions, which are then undetermined. This paper applies a finite element procedure to investigate the effects of thermal loads on the linear dynamics of prestressed self-weighted multi-cable structures. Provided that boundary conditions are carefully handled, the discretization of cables with nonlinear curved beam elements can properly represent the thermoelastic behavior of cables as well as their linearized dynamics. A three-step procedure that aims to replace applied pretension forces with displacement continuity conditions is used. Despite an increase in the computational cost related to beam rotational degrees of freedom, such an approach has several advantages. Nonlinear beam finite elements are usually available in commercial codes. The overall method follows a thermoelastic geometrically non-linear analysis and hereby includes the main sources of non-linearities in multi-cable structures. The effects of cable bending stiffness, which can be significant, are also naturally accounted for. The accuracy of the numerical approach is assessed thanks to an analytical model for the vibration of a single inclined cable under temperature change. Then, the effects of thermal loads are investigated for two cable bridges, highlighting how natural frequencies can be affected by temperature. Although counterintuitive, a reverse relative change of natural frequency may occur for certain local modes. This phenomenon can be explained by two distinct mechanisms, one related to the physics intrinsic to cables and the other related to the thermal deflection of the superstructure. Numerical results show that cables cannot be isolated from the rest of the structure and the importance of modeling the whole structure for a quantitative analysis of temperature effects on the dynamics of cable bridges. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to develop a fast and efficient local meshless method for solving shallow water equations in one- and two-dimensional cases. The mentioned equation has been classified in category of advection equations. The solutions of advection equations have some shock, thus, especial numerical methods should be employed for example discontinuous Galerkin and finite volume methods. Here, based on the proper orthogonal decomposition approach we want to construct a fast meshless method. To this end, we consider shallow water models and obtain a suitable time-discrete scheme based on the predictor-corrector technique. Then by applying the proper orthogonal decomposition technique a new set of basis functions can be built for the solution space in which the size of new solution space is less than the original problem. Thus, by employing the new bases the CPU time will be reduced. Some examples have been studied to show the efficiency of the present numerical technique. [ABSTRACT FROM AUTHOR]

This paper gives the finite-length analysis of a spectrum estimation method for the case that the samples are obtained at a rate lower than the Nyquist rate. The method is referred to as the averaged correlogram for undersampled data. It is based on partitioning the spectrum into a number of segments and estimating the average power within each spectral segment. This method is able to estimate the power spectrum density of a signal from undersampled data without essentially requiring the signal to be sparse. We derive the bias and the variance of the spectrum estimator, and show that there is a tradeoff between the accuracy of the estimation, the frequency resolution, and the complexity of the estimator. A closed-form approximation of the estimation variance is derived, which clearly shows how the variance is related to different parameters. The asymptotic behavior of the estimator is also investigated, and it is proved that in the case of a white Gaussian process, this spectrum estimator is consistent. Moreover, the estimation made for different spectral segments becomes uncorrelated as the signal length tends to infinity. Finally, numerical examples and simulation results are provided, which approve the theoretical conclusions. [ABSTRACT FROM AUTHOR]

Abstract: FE model updating techniques are used to update dynamic FE models of structures in the light of modal test data. Iterative methods of model updating that update a set of chosen parameters of the model, so as to reduce the difference between the natural frequencies and the mode shapes of the FE model and the corresponding quantities obtained through a modal test on the structure, are probably the most widely used methods. Once experimental modal data has been identified, a necessary prior step, before updating can be carried out, is that of establishing the correspondence between the FE model modes and the experimentally identified modes. It is however experienced that, many a times a situation is encountered where not all of the modes identified through an experiment can be correlated with certainty with those predicted by the FE model and some experimental modes may be left uncorrelated. There could be several reasons for this lack of correlation as identified in the paper. But the consequence is that such uncorrelated modes cannot be used in FE model updating using existing iterative methods based on modal data even when they form valid known pieces of information about the structure. This is a disadvantage since it reduces the quantity of experimental data available for model updating and hence makes the updating process less effective in yielding an updated model that is a closer representation of the structure. This paper identifies this as a limitation of the existing iterative methods of model updating based on modal data and puts forward a notion of FE model updating using uncorrelated modes. The paper proposes a solution to overcome this limitation in the form of a new method of FE model updating that accepts both correlated as well as uncorrelated modes for updating. This is in contrast to all the current iterative modal data based methods of model updating that are based on the assumption of availability of correlated mode pairs and hence cannot use uncorrelated mode shapes and corresponding natural frequencies in the updating process. Formulation of the proposed method is described followed by a couple of numerical examples based on a beam structure to validate the method. The robustness of the method in the presence of simulated noise is also studied. Another numerical example of a more complex F-shape structure is also presented. The method is then validated though an experimental study. The proposed method is found to successfully update an FE model yielding correct estimates of the updating parameters in the presence of uncorrelated modes. [Copyright &y& Elsevier]

Abstract: In this paper, mode shapes of a cracked beam with a rectangular cross section beam are analysed using finite element method. The 3D beam element is applied for this finite element analysis. The influence of the coupling mechanism between horizontal bending and vertical bending vibrations due to the crack on the mode shapes is investigated. Due to the coupling mechanism the mode shapes of a beam change from plane curves to space curves. Thus, the existence of the crack can be detected based on the mode shapes: when the mode shapes are space curves there is a crack in the beam. Also, when there is a crack, the mode shapes have distortions or sharp changes at the crack position. Thus, the position of the crack can be determined as a position at which the mode shapes exhibit such distortions or sharp changes. While in previous studies using 2D beam element, distortions in the mode shapes caused by a small crack could not be detected, these distortions in the case using the 3D beam element can be amplified and inspected clearly by using the projections of the mode shapes on appropriate planes. The quantitative analysis is also implemented to relate the size and position of the crack with the observed coupled modes. These results can be applied for crack detection of a beam. In this paper, the stiffness matrix of a cracked element obtained from fracture mechanics is presented and numerical simulations of three case studies are provided. [Copyright &y& Elsevier]

Abstract: In this paper the closed form expression of the exact dynamic stiffness matrix of an Euler–Bernoulli beam in the presence of an arbitrary number of concentrated cracks is derived. The procedure adopted for the evaluation of the dynamic stiffness matrix is based on the availability of the exact closed form solution of the vibration modes of the multi-cracked beam, derived by the same authors in a previous paper. The knowledge of the exact explicit dynamic stiffness matrix of the multi-cracked beam makes the direct evaluation of the exact global dynamic stiffness matrix of damaged frame structures possible. Furthermore, it allows the exact evaluation of the frequencies and the corresponding vibration modes, consistent with the distributed parameter model, through the application of the well-known Wittrick–Williams algorithm. Some numerical applications, relative to the evaluation of frequencies and the corresponding mode shapes of multi-cracked framed structure, are reported. Furthermore, the closed-form solution has been validated by comparing with some exact results available in the literature, for a simple single cracked frame. Finally, further new results for a multi-cracked frame have been compared with those obtained by a finite element simulation. [Copyright &y& Elsevier]

The present paper is dedicated to the post-processing analysis of the time pressure signals when a weakly-compressible Smoothed Particle Hydrodynamics (SPH) model is used to simulate free-surface flows. Indeed, it is well known in literature that this particle model is characterized by the occurrence of high-frequency acoustic noise making the pressure signals unusable for engineering applications. This non-physical pressure noise is both linked to the weakly-compressible approach and to numerical inaccuracies. To reduce the latter, different enhanced SPH models have been developed in recent years. Nonetheless, even using accurate and stable SPH schemes when simulating water impacts, acoustic signals can be generated and, since the speed of sound used in the model is not the real one, these acoustic components need to be filtered in a suitable way. Indeed, for low Mach number regime the solution of the compressible Navier-Stokes equation can be decomposed in an incompressible solution plus an acoustic perturbation. In this work, a filtering technique based on Wavelet Transform is presented. In the proposed procedure the acoustic frequencies are individuated through a preliminary analysis which takes into account: the adopted speed of sound, the spatial resolutions and the fluid domain configuration. The filtering technique to remove the acoustic components is finally applied to several test-cases ranging from prototype problems to more practical applications such as a violent sloshing flow. [ABSTRACT FROM AUTHOR]

Model-based damage detection entails the calibration of damage-indicative parameters in a physics-based computer model of an undamaged structural system against measurements collected from its damaged counterpart. The approach relies on the premise that changes identified in the damage-indicative parameters during calibration reveal the structural damage in the system. In model-based damage detection, model calibration has traditionally been treated as a process, solely operating on the model output without incorporating available knowledge regarding the underlying mechanistic behavior of the structural system. In this paper, the authors propose a novel approach for model-based damage detection by implementing the Extended Constitutive Relation Error (ECRE), a method developed for error localization in finite element models. The ECRE method was originally conceived to identify discrepancies between experimental measurements and model predictions for a structure in a given healthy state. Implementing ECRE for damage detection leads to the evaluation of a structure in varying healthy states and determination of discrepancy between model predictions and experiments due to damage. The authors developed an ECRE-based damage detection procedure in which the model error and structural damage are identified in two distinct steps and demonstrate feasibility of the procedure in identifying the presence, location and relative severity of damage on a scaled two-story steel frame for damage scenarios of varying type and severity. [ABSTRACT FROM AUTHOR]

An imprecise probability approach based on evidence theory is proposed for squeal instability analysis of uncertain disc brakes in this paper. First, the squeal instability of the finite element (FE) model of a disc brake is investigated and its dominant unstable eigenvalue is detected by running two typical numerical simulations, i.e., complex eigenvalue analysis (CEA) and transient dynamical analysis. Next, the uncertainty mainly caused by contact and friction is taken into account and some key parameters of the brake are described as uncertain parameters. All these uncertain parameters are usually involved with imprecise data such as incomplete information and conflict information. Finally, a squeal instability analysis model considering imprecise uncertainty is established by integrating evidence theory, Taylor expansion, subinterval analysis and surrogate model. In the proposed analysis model, the uncertain parameters with imprecise data are treated as evidence variables, and the belief measure and plausibility measure are employed to evaluate system squeal instability. The effectiveness of the proposed approach is demonstrated by numerical examples and some interesting observations and conclusions are summarized from the analyses and discussions. The proposed approach is generally limited to the squeal problems without too many investigated parameters. It can be considered as a potential method for squeal instability analysis, which will act as the first step to reduce squeal noise of uncertain brakes with imprecise information. [ABSTRACT FROM AUTHOR]

Abstract: We develop in this paper a model for the numerical simulation of free surface debris- and mudflows, described as a mixture of two viscous phases. A Lagrangian approach with finite element approximation and regular remeshing is adopted in this paper. The proposed model solves the equations of motion in both phases, coupled with conservation of volume of the mixture, implicitly; volume fractions are computed explicitly at the end of each iteration. A one-step trapezoidal scheme is used for time integration. The resulting model combines simplicity, robustness and versatility and provides a novel and unified algorithmic framework for a large spectrum of applications. It is also easily extensible to three spatial dimensions, more complex constitutive models and coupling with geomechanical models. Application to sedimentation and to impact on an obstacle shows the effectiveness of the approach. [Copyright &y& Elsevier]

Abstract: In this paper we present a novel discretization technique for the simulation of premixed combustion based on a locally enriched finite element method (FEM). Use is made of the G-function approach to premixed combustion in which the domain is divided into two parts, one part containing the burned and another containing the unburned gases. A level-set or G-function is used to define the flame interface separating burned from unburned gases. The eXtended finite element method (X-FEM) is employed, which allows for velocity and pressure fields that are discontinuous across the flame interface. Lagrange multipliers are used to enforce the correct essential interface conditions in the form of jump conditions across the embedded flame interface. A persisting problem with the use of Lagrange multipliers in X-FEM has been the discretization of the Lagrange multipliers. In this paper the distributed Lagrange multiplier technique is adopted. We will provide results from a spatial convergence analysis showing good convergence. However, a small modification of the interface is required to ensure a unique solution. Finally, results are presented from the application of the method to the problems of moving flame fronts, the Darrieus–Landau instability and a piloted Bunsen burner flame. [Copyright &y& Elsevier]

Optimal sensor placement technique plays a key role in structural health monitoring of spatial lattice structures. This paper considers the problem of locating sensors on a spatial lattice structure with the aim of maximizing the data information so that structural dynamic behavior can be fully characterized. Based on the criterion of optimal sensor placement for modal test, an improved genetic algorithm is introduced to find the optimal placement of sensors. The modal strain energy (MSE) and the modal assurance criterion (MAC) have been taken as the fitness function, respectively, so that three placement designs were produced. The decimal two-dimension array coding method instead of binary coding method is proposed to code the solution. Forced mutation operator is introduced when the identical genes appear via the crossover procedure. A computational simulation of a 12-bay plain truss model has been implemented to demonstrate the feasibility of the three optimal algorithms above. The obtained optimal sensor placements using the improved genetic algorithm are compared with those gained by exiting genetic algorithm using the binary coding method. Further the comparison criterion based on the mean square error between the finite element method (FEM) mode shapes and the Guyan expansion mode shapes identified by data-driven stochastic subspace identification (SSI-DATA) method are employed to demonstrate the advantage of the different fitness function. The results showed that some innovations in genetic algorithm proposed in this paper can enlarge the genes storage and improve the convergence of the algorithm. More importantly, the three optimal sensor placement methods can all provide the reliable results and identify the vibration characteristics of the 12-bay plain truss model accurately. [Copyright &y& Elsevier]

Abstract: This paper presents a numerical scheme for computer simulation of microstructural evolution of porous polycrystalline materials at elevated temperatures. The scheme is then applied to study the sintering behaviour of polycrystalline solid containing elongate pores. In a previous paper [J. Comput. Phys. 196 (2004) 724], we presented a set of finite element formulations to model surface diffusion, grain-boundary diffusion and grain-boundary migration, and their interactions. A range of numerical examples were provided for which analytical solutions are available to verify the finite element formulations. All these examples had to be simple and contained at most two grains for the analytical solutions to be possible. In this paper, we complete the numerical scheme and address the numerical issues which have to be resolved when applying the finite element formulations to material models consisted of many grains and pores. In particular, we demonstrate how the joining conditions at triple junctions are achieved in the finite element solution and how the microstructure is updated according to the velocities obtained from the finite element solution. The numerical scheme is then used to study the problem of anisotropic sintering. A series of computer simulations were carried out to study microstructural evolution around an elongate pore. The numerical results show that an elongate pore leads to anisotropic shrinkage and that the shrinkage is always larger in the direction of the longer axis of the pore. The numerical results also show that the shrinkage anisotropy can be controlled by manipulating the ratios between the kinetic mobilities of surface diffusion, grain-boundary diffusion and grain-boundary migration. Increasing the grain-boundary migration mobility increases the shrinkage anisotropy. Increasing the surface diffusion mobility, on the other hand, reduces the shrinkage anisotropy. These numerical findings are not obvious and remain to be verified by future experiment. [Copyright &y& Elsevier]

A new set of finite element formulations are presented in this paper to model surface diffusion, grain-boundary diffusion, grain-boundary migration and their interaction. The new formulations use the classical cubic splines both to represent material interface and to act as shape functions for the migration velocity of the interface. The smoothness of the interface is enforced such that the second order derivatives of the migration velocity is continuous anywhere on the interface. This is achieved by using the cubic spline shape functions and by introducing two new Lagrange terms in the variational principle. The work presented here is a new development to the finite element scheme which was previously developed by Pan, Cocks and their co-workers [Comput. Mater. Sci. 18 (2000) 76; Comput. Mater. Sci. 1 (1993) 95; Acta Mater. 43 (1995) 1395; Proc. Roy. Soc. London A 453 (1997) 2161] for modelling microstructural evolution of materials. The cubic spline elements provide a numerically efficient alternative to the linear elements used by Pan et al. [Proc. Roy. Soc. London A 453 (1997) 2161]. The finite element formulations are verified using a series of test cases for which analytical solutions exist in the literature. A further demonstration case of the co-sintering of two particles of different sizes is provided. The new finite element scheme has made it possible to carry out computer simulations of microstructural evolution using sophisticated and more realistic material models than ever before. The over-simplifications in various existing material models can lead to incorrect predictions. This is dramatically demonstrated in a separate paper in which the finite element scheme is used to investigate the sintering behaviour of large pores [Mech. Mater. (2003)]. [Copyright &y& Elsevier]

In this paper, the natural frequencies and mode shapes of a rotating disk submerged and totally confined inside a rigid casing, have been obtained. These have been calculated analytically, numerically and experimentally for different axial gaps disk-casing. A simplified analytical model to analyse the dynamic response of a rotating disk submerged and confined, that has been used and validated in previous researches, is used in this case, generalised for arbitrary axial gaps disk-casing. To use this model, it is necessary to know the averaged rotating speed of the flow with respect to the disk. This parameter is obtained after an analytical discussion of the motion of the flow inside the casing where the disk rotates, and by means of CFD simulations for different axial positions of the disk. The natural frequencies of the rotating disk for the different axial confinements can be calculated following this method. A Finite Element Model has been built up to obtain the natural frequencies by means of computational simulation. The relative velocity of the flow with respect to the disk is also introduced in the simulation model in order to estimate the natural frequencies of the rotating disk. Experimental tests have been performed with a rotating disk test rig. A thin stainless steel disk (thickness of 8 mm, ( h / r <5%) and mass of 7.6 kg) rotates inside a rigid casing. The position of the disk can be adjusted at several axial gaps disk-casing. A piezoelectric patch (PZT) attached on the rotating disk is used to excite the structure. Several miniature and submergible accelerometers have measured the response from the rotating frame. Excitation and measured signals are transmitted from the rotating to the stationary frame through a slip ring system. Experimental results are contrasted with the results obtained by the analytical and numerical model. Thereby, the influence of the axial gap disk-casing on the natural frequencies of a rotating disk totally confined and surrounded by a heavy fluid is determined. [ABSTRACT FROM AUTHOR]

The aim of the paper is the evaluation and the prediction of the perceived quality of engine sounds, which is predicted in the design process by numerical simulations. Periodic combustion sounds of the operating engine are synthesized with the help of an overall numerical simulation approach before a real prototype exists. The perceived quality of the sound is rated in hearing tests using the method of relative comparison and absolute judgment. Results are transferred into an interval scaled ranking of the stimuli. Based on the data, a psychoacoustic model for sound quality is developed using psychoacoustic parameters. Predictions of this model are used to evaluate the sound quality of several technical design modifications, for example, different engine encapsulations. The results are visualized to allow a simple qualitative analysis of the sound perception. This results in an impartial and objective decision regarding the final design of an acoustic encapsulation with a higher perceived sound quality. [ABSTRACT FROM AUTHOR]

This paper deals with the dynamic response of pump-turbine impellers. A pump-turbine impeller is a complex structure attached to a rotor and rotating inside a casing full of water with very small clearances between the rotating and the stationary parts. The dynamic response of this type of structures is very complex and it is very much affected by the connection to the rotor as well as by the added mass and boundary conditions. As a consequence its calculation presents several uncertainties. First, the dynamic response of pump-turbine impellers is introduced. Second an experimental investigation in a real impeller attached to the rotor and inside the machine was carried out. For this investigation, the impeller of an existing pump-turbine unit with an installed power of 110 MW and a diameter of 2.87 m was studied. For a better analysis of the experimental results a numerical model using FEM was also built-up. Frequencies and mode-shapes were identified numerically and experimentally and the characteristics of the structural response analyzed. To determine the influence of the rotor and supporting structures on the impeller response the results were compared with the ones obtained with the same impeller but suspended (non-connected to the rotor). Experimental and numerical simulation were also used for this case. The changes in the dynamic response due to the rotor connection were determined. Finally the results obtained are compared with the results from other pump-turbine impellers of different designs and general conclusions about the dynamics of this type of structures are given. [ABSTRACT FROM AUTHOR]

In this paper, we construct a combined finite element and oversampling multiscale Petrov–Galerkin method (FE-OMsPGM) to solve the multiscale problems which may have singularities in some special portions of the computational domain. For example, in the simulation of subsurface flow, singularities lie in the porous media with channelized features, or in near-well regions since the solution behaves like the Green function. The basic idea of FE-OMsPGM is to utilize the traditional finite element method (FEM) directly on a fine mesh of the problematic part of the domain and using the Petrov–Galerkin version of oversampling multiscale finite element method (OMsPGM) on a coarse mesh of the other part. The transmission condition across the FE-OMsPG interface is treated by the penalty technique. The FE-OMsPGM takes advantages of the FEM and OMsPGM, which uses much less DOFs than the standard FEM and may be more accurate than the OMsPGM for problems with singularities. Although the error analysis is carried out under the assumption that the oscillating coefficients are periodic, our method is not restrict to the periodic case. Numerical examples with periodic and random highly oscillating coefficients, as well as the multiscale problems on the L-shaped domain, and multiscale problems with high contrast channels or well-singularities are presented to demonstrate the efficiency and accuracy of the proposed method. [ABSTRACT FROM AUTHOR]

Concurrently coupled numerical simulations using heterogeneous solvers are powerful tools for modeling multiscale phenomena. However, major modifications to existing codes are often required to enable such simulations, posing significant difficulties in practice. In this paper we present a C++ library, i.e. the Multiscale Universal Interface (MUI), which is capable of facilitating the coupling effort for a wide range of multiscale simulations. The library adopts a header-only form with minimal external dependency and hence can be easily dropped into existing codes. A data sampler concept is introduced, combined with a hybrid dynamic/static typing mechanism, to create an easily customizable framework for solver-independent data interpretation. The library integrates MPI MPMD support and an asynchronous communication protocol to handle inter-solver information exchange irrespective of the solvers' own MPI awareness. Template metaprogramming is heavily employed to simultaneously improve runtime performance and code flexibility. We validated the library by solving three different multiscale problems, which also serve to demonstrate the flexibility of the framework in handling heterogeneous models and solvers. In the first example, a Couette flow was simulated using two concurrently coupled Smoothed Particle Hydrodynamics (SPH) simulations of different spatial resolutions. In the second example, we coupled the deterministic SPH method with the stochastic Dissipative Particle Dynamics (DPD) method to study the effect of surface grafting on the hydrodynamics properties on the surface. In the third example, we consider conjugate heat transfer between a solid domain and a fluid domain by coupling the particle-based energy-conserving DPD (eDPD) method with the Finite Element Method (FEM). [ABSTRACT FROM AUTHOR]

Abstract: The validity domain of Energy Finite Element Analysis (EFEA) is studied in this paper. The validity region and criterion of EFEA are studied theoretically from the formation of reverberant plane wave field, one of the main assumptions of EFEA. The studies are acquired by virtue of the equation of radiative energy transfer method, a similar wave method that can express the direct field and its conversion relationship with reverberant field exactly. The result shows that the SEA criterion of diffuse field derived by Le Bot can be used as a good indicator for the EFEA validity. Numerical simulations on a rectangular plate with different physical parameters are applied to validate the criterion. The validity region and the diagrams of validity of EFEA are assessed and discussed. Some noteworthy conclusions about EFEA are drawn. [Copyright &y& Elsevier]

Abstract: The numerical simulation of the deformation of vesicle membranes under simple shear external fluid flow is considered in this paper. A saddle-point approach is proposed for the imposition of the fluid incompressibility and the membrane inextensibility constraints, through Lagrange multipliers defined in the fluid and on the membrane respectively. Using a level set formulation, the problem is approximated by mixed finite elements combined with an automatic adaptive mesh procedure at the vicinity of the membrane boundary. Numerical experiments show that this combination of the saddle-point and adaptive mesh method enhances the robustness of the method. The effect of inertia on the stability of the vesicle in a shear flow is also investigated. [Copyright &y& Elsevier]

Abstract: In this paper, we present a parallel Image-to-Mesh Conversion (I2M) algorithm with quality and fidelity guarantees achieved by dynamic point insertions and removals. Starting directly from an image, its implementation is capable of recovering the isosurface and meshing the volume with tetrahedra of good shape. Our tightly-coupled shared-memory parallel speculative execution paradigm employs carefully designed contention managers, load balancing, synchronization and optimizations schemes. These techniques are shown to boost not only the parallel but also the single-threaded efficiency of our code. Specifically, our single-threaded performance is faster than both CGAL and TetGen, the state of the art sequential open source meshing tools we are aware of. The effectiveness of our method is demonstrated on Blacklight, the Pittsburgh Supercomputing Center’s cache-coherent NUMA machine. We observe a more than 82% strong scaling efficiency for up to 64 cores, and a more than 82% weak scaling efficiency for up to 144 cores, reaching a rate of more than 14.3 million elements per second. This is the fastest 3D Delaunay mesh generation and refinement algorithm, to the best of our knowledge. [Copyright &y& Elsevier]

Abstract: In this paper, we consider a one-dimensional fully nonlinear weakly dispersive Green–Naghdi model for shallow water waves over variable bottom topographies. Such model describes a large spectrum of shallow water waves, and it is thus of great importance to design accurate and robust numerical methods for solving it. The governing equations contain mixed spatial and temporal derivatives of the unknowns. They also have still-water stationary solutions which should be preserved in stable numerical simulations. In our numerical approach, we first reformulate the Green–Naghdi equations into balance laws coupled with an elliptic equation. We then propose a family of high order numerical methods which discretize the balance laws with well-balanced central discontinuous Galerkin methods and the elliptic part with continuous finite element methods. Linear dispersion analysis for both the (reformulated) Green–Naghdi system and versions of the proposed numerical scheme is performed when the bottom topography is flat. Numerical tests are presented to illustrate the accuracy and stability of the proposed schemes as well as the capability of the Green–Naghdi model to describe a wide range of shallow water wave phenomena. [Copyright &y& Elsevier]

Abstract: This paper presents a three-dimensional implementation of the so-called rheology to accurately and efficiently compute steady-state dense granular flows. The tricky pressure dependent visco-plastic behaviour within an incompressible flow solver has been overcome using a regularisation technique along with a complete derivation of the incremental formulation associated with the Newton–Raphson algorithm. The computational accuracy and efficiency of the proposed numerical model have been assessed on two representative problems that have an analytical solution. Then, two application examples dealing with actual lab experiments have also been considered: the first one concerns a granular flow on a heap and the second one deals with the granular flow around a cylinder. In both configurations the obtained computational results are in good agreement with available experimental data. [Copyright &y& Elsevier]

Abstract: In this paper we propose a locally conservative Galerkin (LCG) finite element method for two-phase flow simulations in heterogeneous porous media. The main idea of the method is to use the property of local conservation at steady state conditions in order to define a numerical flux at element boundaries. It provides a way to apply standard Galerkin finite element method in two-phase flow simulations in porous media. The LCG method has all the advantages of the standard finite element method while explicitly conserving fluxes over each element. All the examples presented show that the formulation employed is accurate and robust, while using less CPU time than finite volume method. [Copyright &y& Elsevier]

Abstract: Numerical simulation of multiphase compositional flow in fractured porous media, when all the species can transfer between the phases, is a real challenge. Despite the broad applications in hydrocarbon reservoir engineering and hydrology, a compositional numerical simulator for three-phase flow in fractured media has not appeared in the literature, to the best of our knowledge. In this work, we present a three-phase fully compositional simulator for fractured media, based on higher-order finite element methods. To achieve computational efficiency, we invoke the cross-flow equilibrium (CFE) concept between discrete fractures and a small neighborhood in the matrix blocks. We adopt the mixed hybrid finite element (MHFE) method to approximate convective Darcy fluxes and the pressure equation. This approach is the most natural choice for flow in fractured media. The mass balance equations are discretized by the discontinuous Galerkin (DG) method, which is perhaps the most efficient approach to capture physical discontinuities in phase properties at the matrix-fracture interfaces and at phase boundaries. In this work, we account for gravity and Fickian diffusion. The modeling of capillary effects is discussed in a separate paper. We present the mathematical framework, using the implicit-pressure-explicit-composition (IMPEC) scheme, which facilitates rigorous thermodynamic stability analyses and the computation of phase behavior effects to account for transfer of species between the phases. A deceptively simple CFL condition is implemented to improve numerical stability and accuracy. We provide six numerical examples at both small and larger scales and in two and three dimensions, to demonstrate powerful features of the formulation. [Copyright &y& Elsevier]

Abstract: The paper is concerned with the analysis of dynamic behavior of elastic cylindrical shells of rotation subjected to an annular flow of compressible fluid (gas) having both the axial and tangential velocity components. The behavior of the rotating and flowing fluid is described in the framework of the potential theory. The elastic shell is considered based on the model of the classical shell theory. Numerical simulation is done using a semi-analytical variant of the finite element method. The results of numerical experiments made to analyze the stability of shells with different boundary conditions, geometrical dimensions and widths of the annular gap are discussed. The influence of the fluid rotation on the critical flow velocities and the influence of the axial flow on the critical angular velocities of fluid rotation are estimated with reference to the variants, in which one of the velocity components is not taken into account. The effect of elasticity of the outer shell on the boundary of hydroelastic stability is analyzed. [Copyright &y& Elsevier]

Abstract: This paper presents a displacement reconstruction scheme using acceleration measured at a high sampling rate and displacement measured at a considerably low sampling rate. The governing equation and the boundary conditions for the reconstruction are derived using the variational statement of an inverse problem to minimize the errors between measured and reconstructed responses. The transfer function of the governing equation is identically 1 over whole frequency domain, and the proposed scheme would not result in any reconstruction error. A finite impulse response filter (FIR filter) is formulated through the finite element discretization of the governing equation. The Hermitian shape function is adopted to interpolate the displacement in a finite element. The transfer functions of the FIR filter are derived, and their characteristics are thoroughly discussed. It is recommended that the displacement sampling rate should be higher than the Nyquist rate of the target frequency, which is the lowest physically meaningful frequency in measured acceleration. In case the displacement sampling rate is lower than the recommended rate, the use of a higher target accuracy, which is the predefined accuracy at the target frequency, is required. The reconstruction of velocity with the proposed scheme is also presented. The validity of the proposed scheme is demonstrated with a numerical simulation study and a field test on a simply-supported railway bridge. [Copyright &y& Elsevier]

Abstract: This paper presents higher order methods for the numerical modeling of two-phase flow with simultaneous transport and adsorption of viscosifying species within the individual phases in permeable porous media. The numerical scheme presented addresses the three major challenges in simulating this process. Firstly, the component transport is strongly coupled with the viscous and capillary forces that act on the movement of the carrier phase. The discretization of the capillary parts is especially difficult since its effect on flow yields non-linear parabolic conservation equations. These are amenable to non-linear finite elements (FEs), while the capillary contribution on the component transport is first-order hyperbolic, where classical FEs are unsuitable. We solve this efficiently by a Strang splitting that uses finite volumes (FVs) with explicit time-stepping for the viscous parts and a combined finite element–finite volume (FEFV) scheme with implicit time-stepping for the capillary parts. Secondly, the components undergo hydrodynamic dispersion and discerning between numerical and physical dispersion is essential. We develop higher-order formulations for the phase and component fluxes that keep numerical dispersion low and combine them with implicit FEs such that the non-linearities of the dispersion tensor are fully incorporated. Thirdly, subsurface permeable media show strong spatial heterogeneity, with coefficients varying over many orders of magnitude and geometric complexity that make the use of unstructured grids essential. In this work, we employ node-centered FVs that combine their ability to resolve flow with the flexibility of FEs. Numerical examples of increasing complexity are presented that demonstrate the convergence and robustness of our approach and prove its versatility for highly heterogeneous, and geometrically complex fractured porous media. [Copyright &y& Elsevier]

Abstract: The paper deals with the numerical simulation of the acoustic field in two-dimensional cavities in which absorbing materials are present. Though Finite Element Method (FEM) could be employed for this purpose, the discretization level required for achieving reasonable accuracy renders the method impractical in the mid-frequency range. To alleviate this limitation, the Partition of Unity Finite Element Method (PUFEM) using plane wave functions has been shown to be very effective for solving short wave Helmholtz problems. In the present work, the method is extended to the computation of the pressure wave field within the absorbing media which is modeled as a bulk-reacting material characterized by a complex-valued and frequency dependent mean density and dynamic compressibility. Lagrange multipliers are used to enforce the transmission conditions at the air–material interface. Performances of the PUFEM are compared with a standard FEM in several examples of practical interests. It is shown that the technique is a good candidate for solving noise control problems at high frequency. [Copyright &y& Elsevier]

Abstract: In this paper fluid–structure interaction simulations regarding a gust generator experiment are presented, which has been conducted in 2010 in the Transonic Wind Tunnel in Göttingen (DNW-TWG), Germany. The main objective of the experiment was the investigation of the dynamic response problem of an elastic wing model concerning an encountering generic gust induced by a gust generator. Fluid–structure simulations, using a finite element structural model and a computational fluid dynamics model based on time-accurate, Reynolds-averaged Navier–Stokes equations, are compared to the experiment to validate the numerical methodology. Comparisons include steady and unsteady deflections of the elastic wing and pressure distributions. Finally, the results of simulated transfer functions of the gust generator to the elastic wing are presented in comparison to the test data. [Copyright &y& Elsevier]

Abstract: A fast prototyping method for the active vibration control system of 3D mechanical structures is presented in the paper. To control such system piezo-stack actuators were used. The subsequent steps of the prototyping procedure are explained for the bar structure as an example. The Finite Element Modeling (FEM) approach was used to find the quasi-optimal location of piezo-stacks in the structure. Next, the structure with inbuilt piezo-actuators was designed and tested in the laboratory. The more accurate mathematical model of the structure dynamics was obtained as a result of the identification procedure. The mathematical model was reduced and decoupled to change the Two Input Two Output (TITO) system into two Single Input Single Output (SISO) systems. Such approach allowed us to design simple control laws with the aid of the computer simulation procedure. In the last chapter the tests on the laboratory stand of the active vibration control system with local Proportional-Derivative (PD) controllers are described. Experimental results have proved that these PD controllers work good increasing the damping level. Additional damping causes an excellent vibration reduction of the whole mechanical structure. [Copyright &y& Elsevier]

Abstract: Flow-induced vibration (FIV) by vortex shedding behind a submerged cylinder can lead to damage of nuclear components. With respect to such a serious scenario, various experiments and numerical simulations have been conducted to predict the vibration phenomena. Especially in simulation, the immersed finite element method (IFEM) is a promising approach to solve fluid-structure interaction problems because it needs less computational resources. In this paper, two-dimensional motions of cylinders are simulated by using IFEM to obtain their vibration characteristics. Three benchmark tests such as flow past a fixed circular cylinder, in-line oscillation of a circular cylinder and flow-induced vibration with uni-directional motion are performed to verify the proposed numerical method. Furthermore, bi-directional motions of two horizontally and vertically arranged cylinders as well as that of a single cylinder in fluid flow are analyzed, and then key findings are fully discussed. [Copyright &y& Elsevier]

Abstract: The vibration problems associated with geared systems have been the focus of research in recent years. As the torque is mainly transmitted by the geared system, a slant crack is more likely to appear on the gear shaft. Due to the slant crack and its breathing mechanism, the dynamic behavior of cracked geared system would differ distinctly with that of uncracked system. Relatively less work is reported on slant crack in the geared rotor system during the past research. Thus, the dynamic analysis of a geared rotor-bearing system with a breathing slant crack is performed in the paper. The finite element model of a geared rotor with slant crack is presented. Based on fracture mechanics, the flexibility matrix for the slant crack is derived that accounts for the additional stress intensity factors. Three methods for whirling analysis, parametric instability analysis and steady-state response analysis are introduced. Then, by taking a widely used one-stage geared rotor-bearing system as an example, the whirling frequencies of the equivalent time-invariant system, two types of instability regions and steady-state response under the excitations of unbalance forces and tooth transmission errors, are computed numerically. The effects of crack depth, position and type (transverse or slant) on the system dynamic behaviors are considered in the discussion. The comparative study with slant cracked geared rotor is carried out to explore distinctive features in their modal, parametric instability and frequency response behaviors. [Copyright &y& Elsevier]

Abstract: In this paper we propose and analyze a finite element method to the solution of a quasi-static contact problem between a nonlinear beam and a rigid obstacle. Error estimates and energy decay are obtained and some numerical simulations described. [Copyright &y& Elsevier]

Abstract: Numerical simulation of metamaterials has attracted more and more attention since 2000, after the first metamaterial with negative refraction index was successfully constructed. In this paper we construct a fully-discrete leap-frog type finite element scheme to solve the three-dimensional time-dependent Maxwell’s equations when metamaterials are involved. First, we obtain some superclose results between the interpolations of the analytical solutions and finite element solutions obtained using arbitrary orders of Raviart–Thomas–Nédélec mixed spaces on regular cubic meshes. Then we prove the superconvergence result in the discrete l 2 norm achieved for the lowest-order Raviart–Thomas–Nédélec space. To our best knowledge, such superconvergence results have never been obtained elsewhere. Finally, we implement the leap-frog scheme and present numerical results justifying our theoretical analysis. [Copyright &y& Elsevier]

Abstract: A finite-element algorithm is proposed to investigate the dynamic behavior of elastic shells of revolution containing a quiescent or a flowing inviscid fluid in the framework of linear theory. The fluid behavior is described using the perturbed velocity potential. The shell behavior is treated in the framework of the classical shell theory and variational principle of virtual displacements incorporating a linearized Bernoulli equation for calculation of hydrodynamic pressure acting on the shell. The problem reduces to evaluation and analysis of the eigenvalues in the connected system of equations obtained by coupling the equations for velocity perturbations with the equations for shell displacements. For cylindrical shells, the results of numerical simulations are compared with recently published experimental, analytical and numerical data. The paper also reports the results of studying the dynamic behavior of shells under various boundary conditions for the perturbed velocity potential. The investigation made for conical shells has shown that under certain conditions an increase in the cone angle can change a divergent type of instability to a flutter type. [Copyright &y& Elsevier]

Abstract: In this paper, sound transmission through an aircraft sidewall representative double panel structure is investigated theoretically and parametric and validation studies are conducted. The studied configuration is composed of a trim panel (receiver side panel) attached to a ribbed skin panel (source side panel) with periodically spaced resilient mounts. The structure is considered infinite in order to use space harmonic expansion. The partition is also assumed planar for simplicity. The model allows for a 3D incident field and the panels can be metallic and/or composite. A four-pole formulation is employed for modeling of the mounts and the absorption provided by the fiberglass that fills the cavity between the leaves is addressed with an equivalent fluid model. The investigation of mount stiffness, damping and spacing show that properly designed mounts can increase the TL significantly (up to 20dB of difference between rigid and resilient mounts). However, they can create undesirable resonances resulting from their interaction with the panels. The influence of cavity absorption is also studied and results illustrate the fact that it is not worth investing in a highly absorbent fiber if the structure-borne transmission path is not adequately insulated, and likewise that it is not worth investing in highly resilient mounts without sufficient cavity absorption. Moreover, the investigation of panel damping confirms that when structure-borne transmission is present, raising skin damping can increase the TL even below coincidence, but that on average, greater improvements are achieved by raising trim damping. Finally, comparison between the periodic model and finite element simulations for structure-borne transmission shows that the average level of transmitted energy is well reproduced with the periodic approach. However, the modes are only captured approximately due to the assumption of an infinite structure. [Copyright &y& Elsevier]

Abstract: In this paper we present a new parallel multi-frontal direct solver, dedicated for the hp Finite Element Method (hp-FEM). The self-adaptive hp-FEM generates in a fully automatic mode, a sequence of hp-meshes delivering exponential convergence of the error with respect to the number of degrees of freedom (d.o.f.) as well as the CPU time, by performing a sequence of hp refinements starting from an arbitrary initial mesh. The solver constructs an initial elimination tree for an arbitrary initial mesh, and expands the elimination tree each time the mesh is refined. This allows us to keep track of the order of elimination for the solver. The solver also minimizes the memory usage, by de-allocating partial LU factorizations computed during the elimination stage of the solver, and recomputes them for the backward substitution stage, by utilizing only about 10% of the computational time necessary for the original computations. The solver has been tested on 3D Direct Current (DC) borehole resistivity measurement simulations problems. We measure the execution time and memory usage of the solver over a large regular mesh with 1.5 million degrees of freedom as well as on the highly non-regular mesh, generated by the self-adaptive -FEM, with finite elements of various sizes and polynomial orders of approximation varying from to . From the presented experiments it follows that the parallel solver scales well up to the maximum number of utilized processors. The limit for the solver scalability is the maximum sequential part of the algorithm: the computations of the partial LU factorizations over the longest path, coming from the root of the elimination tree down to the deepest leaf. [Copyright &y& Elsevier]

Abstract: This paper deals with local damages identification for strongly and weakly coupled beam systems with close and repeated natural frequencies based on the measured dynamic responses of the systems under external moving forces. The dynamic responses of the coupled beam systems are calculated from Newmark integration method and they are used for structural damage detection. The mode localization phenomenon due to local damage(s) in the weakly coupled beam system is studied. In the inverse analysis, a dynamic response sensitivity-based finite element model updating method is employed for the detection of local damage(s) in the coupled beam systems. Numerical simulation shows that the proposed method is effective in identifying the damages in the coupled beam systems with good accuracy from several measurements. It is found the proposed method is insensitive to artificial measurement noise and has the potential for practical applications. [Copyright &y& Elsevier]

Most of finite element model updating techniques do not employ damping matrices and hence, cannot be used for accurate prediction of complex frequency response functions (FRFs). In this paper, damped finite element model updating procedure is proposed and tested with the objective that the damped finite element updated model is able to predict the measured FRFs accurately. The proposed damped updating procedure is a two-step procedure. In the first step, mass and stiffness matrices are updated using FRF data and in the second step, damping matrix is identified using updated mass and stiffness matrices that are obtained in the previous step. The effectiveness of the proposed procedure is demonstrated by numerical examples as well as by actual experimental data. Firstly, a study is performed using a numerical simulation based on fixed¿fixed beam structure with non-proportional viscous damping model. The numerical study is followed by case involving actual measured data for the case of F-shaped test structure. The results have shown that the proposed procedure can be used for accurate prediction of the complex FRFs. [Copyright &y& Elsevier]

This paper investigates the dynamic response of a rotating multi-span shaft with general boundary conditions subjected to an axially moving load. The system equations of motion are derived based on the global assumed mode method and a modified transformation matrix is proposed to deal with the multi-span geometric constraints. The numerical results are solved by the Runge–Kutta method. To ensure the validity of the method, the convergence test for dynamic response and the comparison of natural frequencies obtained by both the present method and finite element method are demonstrated. Numerical simulations are performed to study the effects of the moving speed of the load, the number of spans, and the rotational speed of the shaft on the deflections under the moving load. In addition, the effects on the occurring position of maximum deflection are presented. The numerical results show that the maximum deflection in the direction of the load may occur at any span and near the midpoint of one span. However, the maximum deflection induced by the gyroscopic effect in the direction perpendicular to the load always occurs at the first span. Moreover, the occurring position of maximum deflection is independent of the rotational speed. [Copyright &y& Elsevier]

Abstract: This paper takes a fresh look at the geometric conservation law (GCL) from the perspective of the finite element method (FEM) for incompressible flows. The GCL arises naturally in the context of Arbitrary Lagrangian Eulerian (ALE) formulations for solving problems on deforming domains. GCL compliance is traditionally interpreted as a consistency criterion for applying an unsteady flow solution algorithm to simulate exactly a uniform flow on a deforming domain. We introduce an additional requirement: the time integrator must maintain its fixed mesh accuracy when applied to deforming meshes. A review of the literature shows that while many authors use an ALE FEM, few of them discuss the GCL issues. We show how a fixed mesh unsteady FEM using high order time integrator (up to fifth order in time) can be transposed to solve problems on deforming meshes and preserve its fixed mesh high order temporal accuracy. An appropriate construction of the divergence of the mesh velocity guarantees GCL compliance while a separate construction of the mesh velocity itself allows the time-integrator to deliver its fixed mesh high order temporal accuracy on deforming domains. Analytical error analysis of problems with closed form solutions provides insight on the behavior of the time integrators. It also explains why high order temporal accuracy is achieved with a conservative formulation of the incompressible Navier–Stokes equations, while only first order time accuracy is observed with the non-conservative formulation and all time-integrators investigated here. We present thorough time-step and grid refinement studies for simple problems with closed form solutions and for a manufactured solution with a non-trivial flow on a deforming mesh. In all cases studied, the proposed reconstructions of the mesh velocity and its divergence for the conservative formulation lead to optimal time accuracy on deforming grids. [Copyright &y& Elsevier]

Abstract: In this study, two different dynamic models, a finite elements-based deformable-body model and a simplified discrete model, and a surface wear model are combined to study the interaction between gear surface wear and gear dynamic response. The proposed dynamic gear wear model includes the influence of worn surface profiles on dynamic tooth forces and transmission error as well as the influence of dynamic tooth forces on wear profiles. This paper first introduces the nonlinear dynamic models that include gear backlash and time-varying gear mesh stiffness, and a wear model separately. It presents a comparison to experiments for validation of the dynamic models. The dynamic models are combined with the wear model to study the interaction of surface wear and dynamic behavior in both linear and nonlinear response regimes. At the end, several sets of simulation results are used to demonstrate the two-way relationship between nonlinear gear dynamics and surface wear. [Copyright &y& Elsevier]

This paper presents an optimization-based inverse procedure for the determination of external loads applied to a given mechanical structure, by using information concerning the dynamic behavior of the system and its corresponding finite element model. The influence of the stress-stiffening effect on the dynamic characteristics of structural systems is used to establish a relation between the dynamic responses and the applied external forces. An optimization problem is formulated in which the objective function represents the difference between the measured modal characteristics of the loaded structure and their finite element counterparts. The loading parameters (magnitude, position and direction) assumed as being unknown, are considered as design variables. The identification procedure is illustrated by means of numerical simulations and experimental tests, in which a heuristic technique known as LifeCycle model was used. [Copyright &y& Elsevier]