Imposition of time-dependent boundary conditions in FEM formulations for elastodynamics: critical assessment of penalty-type methods

This paper is concerned with the variationally consistent incorporation of time dependent boundary conditions. The proposed methodology avoids ad hoc procedures and is applicable to both linear as well as nonlinear problems. An integral formulation of the dynamic problem serves as a basis for the imposition of the corresponding constraints, which are enforced via the consistent form of the penalty method, e.g. a form that complies with the norm and inner product of the functional space where the weak formulation is posed. Also, it is shown that well known and broadly implemented modelling techniques such as “large mass” and “large spring” methods, arise as limiting cases of the penalty formulation. Further extension of the proposed methodology is provided in the case where a generalized weak formulation of the dynamic problem with an independent velocity field is assumed. Finally, a few examples serve to illustrate the above concepts.     

Exploiting intrinsic fluctuations to identify model parameters

Parameterisation of kinetic models plays a central role in computational systems biology. Besides the lack of experimental data of high enough quality, some of the biggest challenges here are identification issues. Model parameters can be structurally non‐identifiable because of functional relationships. Noise in measured data is usually considered to be a nuisance for parameter estimation. However, it turns out that intrinsic fluctuations in particle numbers can make parameters identifiable that were previously non‐identifiable. The authors present a method to identify model parameters that are structurally non‐identifiable in a deterministic framework. The method takes time course recordings of biochemical systems in steady state or transient state as input. Often a functional relationship between parameters presents itself by a one‐dimensional manifold in parameter space containing parameter sets of optimal goodness. Although the system''s behaviour cannot be distinguished on this manifold in a deterministic framework it might be distinguishable in a stochastic modelling framework. Their method exploits this by using an objective function that includes a measure for fluctuations in particle numbers. They show on three example models, immigration‐death, gene expression and Epo‐EpoReceptor interaction, that this resolves the non‐identifiability even in the case of measurement noise with known amplitude. The method is applied to partially observed recordings of biochemical systems with measurement noise. It is simple to implement and it is usually very fast to compute. This optimisation can be realised in a classical or Bayesian fashion.Inspec keywords: biochemistry, physiological models, stochastic processes, measurement errors, fluctuations, parameter estimationOther keywords: model parameter identification, deterministic framework, biochemical system, steady state, transient state, stochastic modelling framework, objective function, immigration‐death model, gene expression, Epo–EpoReceptor interaction, stochastic fluctuations, measurement noise     

Automatic mesh generation for computing symmetric local stresses by 2d-viscoplastic BEM with modified transfinite method

This paper presents a scheme of automatic mesh generation for computing the local stresses by 2D-viscoplastic boundary element method (BEM) with modified transfinite mapping method. The advanced techniques for mesh spacing and region of transfinite mapping method in BEM are studied. The applications demonstrate that the method in BEM gives high computational efficiency and precise modelling of boundaries. This reduces the time and effort required of the analyst to set up a nonlinear model, the amount of input data required is reduced greatly. The numerical examples are given in a later section.     

Modelling and estimating the reliability of stochastic dynamical systems with Markovian switching

In this paper, a general framework for the modelling of physical phenomena with stochastic dynamical systems switched by jump Markov processes is given. A methodology of the associated estimation procedures is provided. A particular attention is paid to the estimation of the underlying jump process, which is not observable.As an application, a stochastic model is proposed for the fatigue crack growth problem. The estimation of the model parameters is made on a real crack growth data set. We are thus able to simulate some crack growth paths which are used for reliability analysis through Monte Carlo techniques.     

Sequential application of heterogeneous models for the safetyanalysis of a control system: a case study

This paper shows how heterogeneous stochastic modelling techniques of increasing modelling power can be applied to assess the safety of a digital control system. First, a Fault-Tree (FT) has been built to model the system, assuming two-state components and independent failures. Then, the FT is automatically converted into a Bayesian Network, allowing to include more modelling details and localized dependencies. Finally, in order to accommodate repair activities and perform an availability analysis, the FT is converted into a Stochastic Petri Net (SPN). Moving from a combinatorial model (the FT) to a state space based model (the SPN) increases the modelling flexibility, but incurs into the state space explosion problem. In order to alleviate the state space explosion problem, this paper resorts to the use of a particular type of high level (coloured) Petri nets called SWN. A digital control system is considered as a case study, and safety measures have been evaluated, referring to the emergent standard IEC 61508.     

Stochastic optimization using a sparse grid collocation scheme

In computational sciences, optimization problems are frequently encountered in solving inverse problems for computing system parameters based on data measurements at specific sensor locations, or to perform design of system parameters. This task becomes increasingly complicated in the presence of uncertainties in boundary conditions or material properties. The task of computing the optimal probability density function (PDF) of parameters based on measurements of physical fields of interest in the form of a PDF, is posed as a stochastic optimization problem. This stochastic optimization problem is solved by dividing it into two problems—an auxiliary optimization problem to construct stochastic space representations from the PDF of measurement data, and a stochastic optimization problem to compute the PDF of problem parameters. The auxiliary optimization problem is solved using a downhill simplex method, whilst a gradient based approach is employed for solving the stochastic optimization problem. The gradients required for stochastic optimization are defined, using appropriate stochastic sensitivity problems. A computationally efficient sparse grid collocation scheme is utilized to compute the solution of these stochastic sensitivity problems. The implementation discussed, requires minimum intrusion into existing deterministic solvers, and it is thus applicable to a variety of problems. Numerical examples involving stochastic inverse heat conduction problems, contamination source identification problems and large deformation robust design problems are discussed.     

Elastic wave propagation in a 3‐D unbounded random heterogeneous medium coupled with a bounded medium. Application to seismic soil–structure interaction (SSSI)

We present a sub‐structuring method for the coupling between a large elastic structure, and a stratified soil half‐space exhibiting random heterogeneities over a bounded domain and impinged by incident waves. Both media are also weakly dissipative. The concept of interfaces classically used in sub‐structuring methods is extended to ‘volume interfaces’ in the proposed approach. The random dimension of the stochastic fields modelling the heterogeneities in the soil is reduced by introducing a Karhunen–Loéve expansion of these stochastic fields. The coupled overall problem is solved by Monte‐Carlo simulation techniques. A realistic example of a large industrial structure interacting with an uncertain stratified soil medium under earthquake is finally presented. This case study and others validate the presented methodology and its ability to handle complex mechanical systems. Copyright © 2002 John Wiley & Sons, Ltd.     

Numerical modelling of acoustic–elastodynamic coupled problems by stabilized boundary element techniques

In this work, an efficient, flexible, accurate and stable algorithm to numerically model interacting acoustic–elastodynamic sub-domains is described. Stabilized time-domain boundary element techniques are considered to discretize each sub-domain of the model and proper numerical expressions on acoustic–elastodynamic interfaces are presented. Moreover, stabilized iterative coupling procedures are adopted and different time and space sub-domain discretizations are allowed, improving the robustness and versatility of the methodology. At the end of the paper, numerical results are presented, illustrating the potentialities of the proposed formulation.     

Tabu-search simulation optimization approach for flow-shop scheduling with multiple processors — a case study

The flow shop with multiple processors (FSMP) environment is relatively common and has a variety of applications. The majority of academic authors solve the scheduling problem of FSMP using deterministic data that ignore the stochastic nature of a real-world problem. Discrete-event simulation can model a non-linear and stochastic problem and allows examination of the likely behaviour of a proposed manufacturing system under selected conditions. However, it does not provide a method for optimization. The present paper proposes to solve the FSMP scheduling problem by using a tabu-search simulation optimization approach. It features both the stochastically modelling capability of the discrete-event simulation and the efficient local-search algorithm of tabu search. A case study from a multilayer ceramic capacitor manufacturing illustrates the proposed solution methodology. Empirical results show promise for the practical application of the proposed methodologies. Future research opportunities are then addressed.     

A galerkin symmetric boundary-element method in elasticity: Formulation and implementation

Static discontinuities (i.e. distributions of forces along a line or a surface, implying a jump of tractions across it) and kinematic (displacement) discontinuities are considered simultaneously as sources acting on the unbounded elastic space Ω∞ along the boundary Γ of a homogeneous elastic body Ω embedded in Ω∞. The auxiliary elastic state thus generated in the body is associated with the actual elastic state by a Betti reciprocity equation. Using suitable discretizations of actual and fictitious boundary variables, a symmetric Galerkin formulation of the direct boundary element method is generated. The following topics are addressed: reciprocity relations among kernels with particular attention to the role of singularities; conditions to be satisfied by the boundary field modelling in order to achieve the symmetry of the coefficient matrix; variational properties of the solution. With reference to two-dimensional problems, a technique based on a complex-variable formalism is proposed to perform the double integrations involved in this approach. An implementation of this technique for elastic analysis is described assuming straight elements, with continuous linear displacements and piecewise-constant tractions; all the double integrations are carried out analytically. Comparisons, from the computational standpoint, with the traditional non-symmetric method based on collocation and single integration, demonstrate the effectiveness of the present approach.     

A new active error compensatory method of machinery accuracy†

A new active error compensatory method for on-line cutting control has been developed for reduction of the form errors in machining. This approach is a combination of in-process gauging and model active compensatory control. In this approach, there are two features of substantial importance: stochastic modelling and optimum forecasting. Through stochastic modelling, the cutting tool error motions can be represented by a simple model without the necessity of obtaining the complex cause-and-effect relationships between various errors and error sources, and more importantly, it is possible to account for both repeatable and non-repeatable parts of errors. Optimum forecasting is an important prerequisite for a rational control strategy, considering the inevitable time delay associate with sensing, computation and actuation. The proposed control method was implemented for the control of cylindricity in boring operations. Through the controller simulation based on experimental measurements, the improvement in cylindricity accuracy confirms the effectiveness of this proposed strategy     

环境激励下基于奇异谱互熵的结构损伤诊断方法

环境激励下的结构响应是一个随机过程,结构发生破损时其响应将随之变化,因而可将描述随机过程特性的参数作为评判结构状况的指标。熵是测量随机过程不确定性的一个比较方便的方法,能够用于高斯及非高斯分布的情况。在相空间重构与奇异值分解的基础上建立了奇异谱互熵的概念,提出了一种环境激励下用奇异谱互熵诊断结构损伤的方法。以ASCE学会提出的基准结构为对象进行研究,利用NExT技术获得响应,采用伪邻近法确定相空间的嵌入维数,讨论了不同工况及噪声对诊断结果的影响,分析结果验证了该方法的有效性和鲁棒性。     

One-way Fluid Structure Interaction modelling methodology for boiler tube fatigue failure

A modelling methodology developed for dealing with fatigue failures on large boiler tube assemblies, as used by power generation industries, is described. Boiler tube fatigue failures are resultant to a coupled combination of fluid flow and heat transfer mechanisms, inducing thermal expansion leading to fatigue failure. A combination of modelling tools is effectively combined for one-way Fluid Structure Interaction, solving for and extracting stress results efficiently. A one dimensional fluid solver is used to approximate and model the thermal flow components. The study case considered implemented the developed methodology on a quarter boiler hopper section made up of 3022 tube and membrane structure with a collective length of 4787 m. Operating conditions are iteratively adjusted in the one dimensional pipe flow model until a correlation is formed with instrumented data. This validated model enables further use for various postulated plant conditions and operational sequences through transient start-up conditions. The boiler tube temperatures obtained from the one dimensional model are transferred and used as boundary conditions in a full three dimensional finite element analysis where deformations are solved for and stress results obtained due to thermal expansion within the boiler tube walls and the adjacent support structure. The model is used for redesign of sections of the boiler to reduce stress in those areas and subsequently reduce fatigue failures.     

Scattering from two eccentric spheroids: Theory and numerical investigation

In this paper, the direct acoustic scattering problem of a point source field by a penetrable spheroidal scatterer hosting an impenetrable spheroidal body of arbitrary position, size and orientation, is considered. The application background corresponds to the near field measurement of the acoustic field, scattered by a soft-tissue organ including a hard inhomogeneity. The methodology incorporates two independent techniques which are modified appropriately to fit together and are combined for the first time: first, the Vekua method, which is based on the well known Vekua transformation, providing with fully analytic solutions of Helmholtz equation and second, the method of auxiliary sources in order to represent the net wave contribution of the inhomogeneity. The satisfaction of transmission and boundary conditions is accomplished via the collocation method while the wave character of the fields and the outwards propagating property of the exterior wave are implicitly guaranteed in exact form through the analytic nature of the method. Special effort has been devoted to the self-evaluation of the method by constructing and calculating an indicative error function representing the failure of satisfaction of the boundary conditions on a rich grid over the interfaces, much larger than the set of collocation points, where the error is by construction negligible. This numerical approach leads to very reliable results. The determination of the near scattered field as well as of the far-field pattern are the final outcomes of the present work, providing a thorough solution of the direct scattering problem and giving insight to the corresponding inverse problem.     

Simultaneous reconstruction of the time-dependent Robin coefficient and heat flux in heat conduction problems

This paper aims to solve an inverse heat conduction problem in two-dimensional space under transient regime, which consists of the estimation of multiple time-dependent heat sources placed at the boundaries. Robin boundary condition (third type boundary condition) is considered at the working domain boundary. The simultaneous identification problem is formulated as a constrained minimization problem using the output least squares method with Tikhonov regularization. The properties of the continuous and discrete optimization problem are studied. Differentiability results and the adjoint problems are established. The numerical estimation is investigated using a modified conjugate gradient method. Furthermore, to verify the performance of the proposed algorithm, obtained results are compared with results obtained from the well-known finite-element software COMSOL Multiphysics under the same conditions. The numerical results show that the proposed algorithm is accurate, robust and capable of simultaneously representing the time effects on reconstructing the time-dependent Robin coefficient and heat flux.     

A variational formulation based contact algorithm for rigid boundaries in two-dimensional SPH applications

Smooth particle Hydrodynamics (SPH) is one of the most effective meshless techniques used in computational mechanics. SPH approximations are simple and allow greater flexibility in various engineering applications. However, modelling of particle-boundary interactions in SPH computations has always been considered an aspect that requires further research. A number of techniques have been developed to model particle-boundary interactions in SPH and allied methods. In this paper, an innovative approach is introduced to handle the contact between Lagrangian SPH particles and rigid solid boundaries. The formulation of boundary contact forces are derived based on a variational formulation, thus directly ensuring the conservativeness of the governing equations. In addition, the new elegant boundary contact force terms maintain the simplicity of the SPH governing equations.     

A two‐dimensional BEM/FEM coupling applied to viscoelastic analysis of composite domains

A coupling between the boundary‐element and finite‐element methods is studied for the viscoelastic analysis of reinforced media. The viscous behaviour of the composed body is taken into account by an alternative BEM methodology developed for the Boltzmann model. This methodology is based on differential constitutive relations for viscoelasticity. The reinforcements are modelled by finite elements and are considered elastic. The coupling is based on the sub‐region technique due to its generality and easy implementation. The resulting time‐marching process is able to represent both the instantaneous and the time‐dependent behaviour of a body subjected to general boundary conditions. The method is validated by an experimental result and its accuracy tested by comparing numerical results with analytical solutions. The generality of the method is proved by an infinite domain application. Copyright © 2003 John Wiley & Sons, Ltd.     

Progressive damage and failure of mechanically fastened joints in CFRP laminates – Part II: Failure prediction of an industrial junction

In part II of this study, a methodology is presented to compute the failure of large-scale bolted joints in composite structures. This methodology is based both on a multilevel calculation strategy and on virtual testing. At the global level, coarse FE modelling of the structure is used to assess the load distribution between the fasteners. The most loaded fasteners are identified and the loads issued from the global calculation are used as boundary conditions for the local failure analysis, based on fast semi-empirical models. Nevertheless, in this work, instead of using experimental data, prevision of failure is achieved by fully numerical means. The parameters of the semi-empirical models are evaluated by virtual testing, using the refined FE model proposed in part I of this paper.     

Numerical modelling of fracture of particulate composites using SPH method

Simplicity of mesh generation and robustness against mesh entanglement during large deformations are key attractive features of particle based methods. These features can be exploited in number of engineering problems where traditional techniques suffer due to aforementioned limitations. Numerical modelling of particulate composites is one of such ideal engineering applications where particle based methods can be effectively used due to their simplicity and robustness. Complicated geometrical configurations of particulate composites obtained from techniques such as scanning electron microscopy (SEM) can be easily converted to particle based mesh without loosing much information. This enables more accurate analysis of the chosen composite materials. Therefore, a smooth particle hydrodynamics (SPH) based numerical technique is developed here to investigate the mechanical properties and evolution of debonding process in particulate composites. To perform the numerical study, a Lagrangian corrected SPH (CSPH) method is presented together with an appropriate numerical model for treating material interface discontinuity within the particulate composites. The material interface discontinuity is enforced using an innovative method which combines penalty formulation with a bilinear interface cohesive model for SPH method. The proposed SPH methodology is used in a number of numerical examples involving composite materials and related interface problems. The effect of penalty value on the interface model and of the smoothing length of the SPH method are also analysed during these simulations. The results illustrate the effectiveness, robustness and potential of the developed methodology. It is concluded that the proposed numerical techniques can be easily and effectively applied to simulate multi-phase composites with various interface conditions and, can provide useful information regarding the inherent mechanism of damage evolution and fracture of particulate or fibre reinforced composites.