An Algorithm for Cavity Reconstruction in Electrical Impedance Tomography

We consider the inverse problem of finding cavities within some object from electrostatic measurements on the boundary. By a cavity we understand any object with a different electrical conductivity from the background material of the body. We give an algorithm for solving this inverse problem based on the output nonlinear least-square formulation and the regularized Newton-type iteration. In particular, we present a number of numerical results to highlight the potential and the limitations of this method.     

与封堵溃口有关的重物落水后运动过程模型

洪涝灾害经常会造成溃坝溃堤,进而引发泥石流灾害,造成国家和人民生命财产的严重损失,物体填堵方法是有效解决溃坝溃堤问题的一种手段,主要针对物体填堵时在何处投放物体最有效的问题进行了解决.在合理假设的前提下,通过对试验模型中各单件相关数据进行分析并参考相关资料,得出影响重物在水中运动的主要因素,包括流体结构、投放高度、投放方式、物体形状等.然后按照物体是否完全浸入水中把运动过程分成两个阶段,再分别从垂直和水平两个运动方向考虑,利用已知的试验数据和相关知识,建立了能够适应不同情况的、描述重物水中运动过程的数学模型.以大实心方砖为例进行分析,利用Matlab对所建的模型进行求解,对比拟合试验数据得到的和所建模型得到的运动方程,从而可以计算出离散时间点的相对误差,其值大约为8%-13%,符合容许条件,证明所建模型还是比较合理的.     

Exact solutions of functionally graded piezoelectric material sandwich cylinders by a modified Pagano method

The three-dimensional (3D) coupled analysis of simply-supported, functionally graded piezoelectric material (FGPM) circular hollow sandwich cylinders under electro-mechanical loads is presented. The material properties of each FGPM layer are regarded as heterogeneous through the thickness coordinate, and obey an exponent-law dependent on this. The Pagano method is modified to be feasible for the study of FGPM sandwich cylinders. The modifications are as follows: a displacement-based formulation is replaced by a mixed formulation; a set of the complex-valued solutions of the system equations is transferred to the corresponding set of real-valued solutions; a successive approximation method is adopted to approximately transform each FGPM layer into a multilayered piezoelectric one with an equal and small thickness for each layer in comparison with the mid-surface radius, and with the homogeneous material properties determined in an average thickness sense; and a transfer matrix method is developed, so that the general solutions of the system equations can be obtained layer-by-layer, which is significantly less time-consuming than the usual approach. A parametric study is undertaken of the influence of the aspect ratio, open- and closed-circuit surface conditions, and material-property gradient index on the assorted field variables induced in the FGPM sandwich cylinders.     

Planning and coordination of production and distribution facilities for multiple commodities

We study an integrated logistics model for locating production and distribution facilities in a multi-echelon environment. Designing such logistics systems requires two essential decisions, one strategic (e.g., where to locate plants and warehouses) and the other operational (distribution strategy from plants to customer outlets through warehouses). The distribution strategy is influenced by the product mix at each plant, the shipments of raw material from vendors to manufacturing plants and the distribution of finished products from the plants to the different customer zones through a set of warehouses. First we provide a mixed integer programming formulation to the integrated model. Then, we present an efficient heuristic solution procedure that utilizes the solution generated from a Lagrangian relaxation of the problem. We use this heuristic procedure to evaluate the performance of the model with respect to solution quality and algorithm performance. Results of extensive tests on the solution procedure indicate that the solution method is both efficient and effective. Finally a `real-world' example is solved to explore the implications of the model.     

A Finite Element Formulation for the Nonlinear Analysis of Piezoelectric Three-Dimensional Beam Structures

A finite element formulation for a three-dimensional piezoelectric beam which includes geometrical and material nonlinearities is presented. To account for the piezoelectric effect, the coupling between the mechanical stress and the electrical displacement is considered. Based on the Timoshenko theory, an eccentric beam formulation is introduced which provides an efficient model to analyze piezoelectric structures. The geometrically nonlinear assumption allows the calculation of large deformations including buckling analysis. A quadratic approximation of the electric potential through the cross section of the beam ensures the fulfilment of the charge conservation law exactly. This assumption leads to a finite element formulation with six mechanical and five electrical degrees of freedom per node. To take into account the typical ferroelectric hysteresis phenomena, a nonlinear material model is essential. For this purpose, the phenomenological Preisach model is implemented into the beam formulation which provides an efficient determination of the remanent part of the polarization. The applicability of the introduced beam formulation is discussed with respect to available data from literature. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Symbolic objects: order structure and pyramidal clustering

We recall a formalism based on the notion of symbolic object (Diday [15], Brito and Diday [8]), which allows to generalize the classical tabular model of Data Analysis. We study assertion objects, a particular class of symbolic objects which is endowed with a partial order and a quasi-order. Operations are then defined on symbolic objects. We study the property of completeness, already considered in Brito and Diday [8], which expresses the duality extension intension. We formalize this notion in the framework of the theory of Galois connections and study the order structure of complete assertion objects. We introduce the notion ofc-connection, as being a pair of mappings (f,g) between two partially ordered sets which should fulfil given conditions. A complete assertion object is then defined as a fixed point of the composedf o g; this mapping is called a completeness operator for it completes a given assertion object. The set of complete assertion objects forms a lattice and we state how suprema and infima are obtained. The lattice structure being too complex to allow a clustering study of a data set, we have proposed a pyramidal clustering approach [8]. The symbolic pyramidal clustering method builds a pyramid bottom-up, each cluster being described by a complete assertion object whose extension is the cluster itself. We thus obtain an inheritance structure on the data set. The inheritance structure then leads to the generation of rules.     

Multiple traces boundary integral formulation for Helmholtz transmission problems

We present a novel boundary integral formulation of the Helmholtz transmission problem for bounded composite scatterers (that is, piecewise constant material parameters in ??subdomains??) that directly lends itself to operator preconditioning via Calderón projectors. The method relies on local traces on subdomains and weak enforcement of transmission conditions. The variational formulation is set in Cartesian products of standard Dirichlet and special Neumann trace spaces for which restriction and extension by zero are well defined. In particular, the Neumann trace spaces over each subdomain boundary are built as piecewise $\widetilde{H}^{-1/2}$ -distributions over each associated interface. Through the use of interior Calderón projectors, the problem is cast in variational Galerkin form with an operator matrix whose diagonal is composed of block boundary integral operators associated with the subdomains. We show existence and uniqueness of solutions based on an extension of Lions?? projection lemma for non-closed subspaces. We also investigate asymptotic quasi-optimality of conforming boundary element Galerkin discretization. Numerical experiments in 2-D confirm the efficacy of the method and a performance matching that of another widely used boundary element discretization. They also demonstrate its amenability to different types of preconditioning.     

ALE-based 3D FE simulation of electromagnetic forming

Electromagnetic forming is a contact-free high-speed forming process. The deformation of the work piece is driven by the Lorentz force which results from the interaction of a pulsed magnetic field with eddy currents induced in the work piece by the field itself. The purpose of this work is to present a fully-coupled three-dimensional simulation of this process. For the mechanical structure, a thermoelastic, viscoplastic, electromagnetic material model is relevant, which is incorporated in a large-deformation dynamic formulation. The electromagnetic fields are governed by Maxwell's equations under quasistatic conditions. To consider their reduced regularity at material interfaces Nédélec elements are applied. Coupling takes the form of the Lorentz force, the electromotive intensity and the current geometry of the work piece. A staggered solution scheme based on a Lagrangian mesh for the work piece and an ALE formulation for the electromagnetic field is employed. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Analysis of stress and strain in tension cylindrical sample

One of the basic engineering problem occurring during the numerical analysis is to define the function of yield stress of material in the real conditions of a technological process. These properties are necessary to calculate the deformation and the state of stress and strain in the surface layer of an object. An inappropriate selection of the mechanical properties of the material is the reason of the occurrence of errors in numerical calculations of a continuous object, considered as a boundary and initial problem. Scientific investigations are being conducted with the aim to develop a database concerning yield stresses for different metals, depends on complex conditions of thermo-dynamical loads, e.g. temperature, the equivalent of the strain and the strain rate. The article presents a method of the determination of this dependence while using an experimental and numerical analysis. During the model investigations on the INSTRON testing machine, the force of elongation of the sample is measured and then calculations are made of the displacement of nodes of finite elements, plotted on outside surface of sample. The process is considered as a multi nonlinear problem. For this reason, an incremental method of motion and deformation of solid in an updated Lagrange formulation is used. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A mathematical programming approach to optimise insurance premium pricing within a data mining framework

In this paper we provide evidence of the benefits of an approach which combines data mining and mathematical programming to determining the premium to charge automobile insurance policy holders in order to arrive at an optimal portfolio. An non-linear integer programming formulation is proposed to determine optimal premiums based on the insurer's need to find a balance between profitability and market share. The non-linear integer programming approach to solving this problem is used within a data mining framework which consists of three components: classifying policy holders into homogenous risk groups and predicting the claim cost of each group using k-means clustering; determining the price sensitivity (propensity to pay) of each group using neural networks; and combining the results of the first two components to determine the optimal premium to charge. We have earlier presented the results of the first two components. In this paper we present the results of the third component. Using our approach, we have been able to increase revenue without affecting termination rates and market share.     

A unified formulation of PVD-based finite cylindrical layer methods for functionally graded material sandwich cylinders

A unified formulation of finite cylindrical layer methods (FCLMs) based on the principle of virtual displacements (PVDs) is developed for the quasi-three-dimensional (3D) bending and free vibration analyses of simply-supported, functionally graded material (FGM) sandwich circular hollow cylinders, in which the material properties of the FGM layer are assumed to obey the power-law distributions of the volume fractions of the constituents through the thickness coordinate. In this formulation, the cylinder is divided into a number of cylindrical finite layers, where the trigonometric functions and Lagrange polynomials are used to interpolate the in- and out-of-surface variations of the displacement components of each individual layer, respectively. Because an h-refinement is adopted in this article to yield the convergent solutions, the relative orders used for expansion of the displacement components remain variable, and can be freely chosen as linear, quadratic and cubic ones. The accuracy and convergence rate of a variety of PVD-based FCLMs developed in this article are assessed by comparing their solutions with the available 3D ones.     

An extended tube model for thermo-viscoelasticity of rubberlike materials: Parameter identification and examples

The extended tube-model was presented by KALISKE & HEINRICH (RCT 72, 602-632) in 1999 as a novel approach for isothermal hyperelasticity of rubberlike materials. This contribution is dedicated to its further development to finite non-linear thermo-viscoelasticity. A non-linear evolution law and a thermo-mechanical coupled free energy formulation are the kernel of the phenomenological approach where the elastic material response is inspired by statistical-mechanical theory. The representation of viscoelasticity is based on a multiplicative decomposition of the deformation gradient. The Helmholtz free energy of the material is formulated in terms of isothermal free energy functions multiplicatively coupled with non-linear temperature evolution functions. The non-linear evolution law for the viscous material branch is solved by applying a predictor-corrector algorithm with an exponential mapping scheme. In today's literature, several sophisticated thermo-mechanical material models are available. However, they are built upon a considerable number of material parameters governing the mechanical and thermal material response which need to be identified for practical application. Therefore, particular emphasis is given to an appropriate parameter identification technique for the thermal field. For the latter, a uniaxial extension test is carried out where the recorded data of the temperature field of the rubber specimen under cyclic loading is used for parameter identification. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Investigation of stress-velocity LSFEMs for the incompressible Navier-Stokes equations

In this contribution three mixed least-squares finite element methods (LSFEMs) for the incompressible Navier-Stokes equations are investigated with respect to accuracy and efficiency. The well-known stress-velocity-pressure formulation is the basis for two further div-grad least-squares formulations in terms of stresses and velocities (SV). Advantage of the SV formulations is a system with a smaller matrix size due to a reduction of the degrees of freedom. The least-squares finite element formulations, which are investigated in this contribution, base on the incompressible stationary Navier-Stokes equations. The first formulation under consideration is the stress-velocity-pressure formulation according to [1]. Secondly, an extended stress-velocity formulation with an additional residual is derived based on the findings in [1] and [5]. The third formulation is a pressure reduced stress-velocity formulation based on a condensation scheme. Therefore, the pressure is interpolated discontinuously, and eliminated on the discrete level without the need for any matrix inverting. The modified lid-driven cavity boundary value problem, is investigated for the Reynolds number Re = 1000 for all three formulations. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Caracterización de la delaminación en materiales compuestos mediante la teoría de mezclas serie/paralelo

This paper presents a new procedure to deal with the delamination problem found in laminated composites, based in a continuum mechanics formulation. The procedure proposed obtains the composite constitutive performance with the Serial/Parallel mixing theory, developed by F. Rastellini. This theory characterizes composite materials by coupling the constitutive behaviour of the composite components, imposing an iso–strain relation among the components in the fibre (or parallel) direction and an iso-stress relation in the remaining directions (serial directions). The proposed procedure uses a damage formulation to characterize the constitutive behaviour of matrix component in order to obtain the stress-strain performance of this material.With these two formulations, the delamination phenomenon is characterized naturally by the numerical simulation, being unnecessary the definition of special elements or computationally expensive techniques like the definition of contact elements or mesh separation. Matrix failure, as a result of the stress state found in it, leads to a reduction of the stiffness and strength capacity of the composite in its serial directions, among them, the shear component. This stiffness reduction provides a composite performance equivalent to what is found in a delaminated material.To prove the ability of the formulation proposed to solve delamination problems, the End Notch Failure test is numerically simulated and the results obtained are compared with experimental ones. The agreement found in the results with both simulations, numerical and experimental, validate the proposed methodology to solve the delamination problem.     

Positive definite balancing Neumann–Neumann preconditioners for nearly incompressible elasticity

In this paper, a positive definite Balancing Neumann–Neumann (BNN) solver for the linear elasticity system is constructed and analyzed. The solver implicitly eliminates the interior degrees of freedom in each subdomain and solves iteratively the resulting Schur complement, involving only interface displacements, using a BNN preconditioner based on the solution of a coarse elasticity problem and local elasticity problems with natural and essential boundary conditions. While the Schur complement becomes increasingly ill-conditioned as the materials becomes almost incompressible, the BNN preconditioned operator remains well conditioned. The main theoretical result of the paper shows that the proposed BNN method is scalable and quasi-optimal in the constant coefficient case. This bound holds for material parameters arbitrarily close to the incompressible limit. While this result is due to an underlying mixed formulation of the problem, both the interface problem and the preconditioner are positive definite. Numerical results in two and three dimensions confirm these good convergence properties and the robustness of the methods with respect to the almost incompressibility of the material.     

Static plane-strain deformation of transversely isotropic magneto-electro-elastic and layered cylinders to general surface loads

Anisotropic and layered cylinders are important composite structures; however, their system of governing equations is usually solved numerically due to the complicated geometry and material anisotropy involved. In this paper, we analytically solve the plane-strain equations for general static deformation of a cylindrically anisotropic, layered magneto-electro-elastic (MEE) cylinder. We assume that the layers are perfectly bonded at the interfaces. We solve the equations through separation of variables and eigenfunction expansion. Results for each mode shape (2π periodic) are solved independently. Because the eigenspace of the mode shapes is the set of all continuous functions on the interval, any continuous loading can be applied and the corresponding solution can be found analytically through superposition of the mode-shape results. To check our formulation, we consider a cylinder with two isotropic-elastic layers under simple radial loading and reproduce the known, exact results. Then, we compare our formulation to an FEA solution for a layered piezo-electric (PE) cylinder. Finally, we apply a radial stress to three comparable MEE cylinders (one uniform MEE cylinder and two layered cylinders made of alternating piezo-electric (PE) and piezo-magnetic (PM) materials). Deformation and stress amplitudes are plotted for the first six mode shapes of each cylinder as benchmarks for further reference.     

A mixed variational formulation for a class of contact problems in viscoelasticity

We consider a deformable body in frictionless unilateral contact with a moving rigid obstacle. The material is described by a viscoelastic law with short memory, and the contact is modeled by a Signorini condition with a time-dependent gap. The existence and uniqueness results for a weak formulation based on a Lagrange multipliers approach are provided. Furthermore, we discuss an efficient algorithm approximating the weak solution for the more general case of a two-body contact problem including friction. In order to illustrate the theory we present two numerical examples in 3D.     

An adaptive approach for modeling a fiber-matrix composite with the FE2 method

In materials with a complicated microstructre [1], the macroscopic material behaviour is unknown. In this work a Fiber-Matrix composite is considered with elasto-plastic fibers. A homogenization of the microscale leads to the macroscopic material properties. In the present work, this is realized in the frame of a FE² formulation. It combines two nested finite element simulations. On the macroscale, the boundary value problem is modelled by finite elements, at each integration point a second finite element simulation on the microscale is employed to calculate the stress response and the material tangent modulus. One huge disadvantage of the approach is the high computational effort. Certainly, an accompanying homogenization is not necessary if the material behaves linear elastic. This motivates the present approach to deal with an adaptive scheme. An indicator, which makes use of the different boundary conditions (BC) of the BVP on microscale, is suggested. The homogenization with the Dirichlet BC overestimates the material tangent modulus whereas the Neumann BC underestimates the modulus [2]. The idea for an adaptive modeling is to use both of the BCs during the loading process of the macrostructure. Starting initially with the Neumann BC leads to an overestimation of the displacement response and thus the strain state of the boundary value problem on the macroscale. An accompanying homogenization is performed after the strain reaches a limit strain. Dirichlet BCs are employed for the accompanying homogenization. Some numerical examples demonstrate the capability of the presented method. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Design of balanced MBA student teams

In some schools and universities, students must sometimes be divided into several teams in such a way that each team provides a good representation of the classroom population. In this paper, two different ways of measuring the balance among teams are proposed: min-sum and min-max objective functions. For the first function and the L₁-norm used in the space of attributes, an exact solution method based on a set partitioning formulation and on the enumeration of all possible team patterns is presented. For the second objective function, a set partitioning formulation is also considered, but as an approximation. In order to solve large problem instances, we have also developed metaheuristics based on variable neighbourhood search. Models and methods are tested on data from an MBA programme.