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In the present paper algorithms for constructing a finite element mesh of compound domains and minimizing the ribbon width of the system of resolving equations by the finite element method (FEM) are considered. A technology for constructing a finite element mesh by connecting elementary subdomains, a semi-automatic method for partitioning a two-dimensional multiply connected domain with a curvilinear boundary, and ordering the node numbers of a finite element mesh is described. In this case, the algorithms allow, by ordering the numbering of nodes, to determine such a sequence in which the ribbon width of non-zero coefficients of the system of resolving equations by the FEM will be locally minimal. [ABSTRACT FROM AUTHOR]

In this paper micro-electro-mechanical systems (MEMS) deformable mirror (DM) for its use in adaptive optics in Indus-2 is studied. DMs are used to correct optical aberrations by precisely adjusting the deflection of mirror surface. A piezo based micro-actuator array of 19 keystone shape elements in diameter of 10 mm on silicon of 20 µm thickness is considered for the study. The finite element method (FEM) simulations were carried out using COMSOL Multiphysics 5.4 to estimate the displacement profile. In order to evaluate the applicability of this MEMS based DM in adaptive optics system, piezo response function matrix was determined by applying dc voltage of 1volt to each actuator one by one while keeping the others at zero voltage. The optimum voltage of each actuator to produce a target profile was determined using TLBO algorithm in MATLAB. In this way the obtained voltages are used to generated the low order Zernike mode shapes. [ABSTRACT FROM AUTHOR]

The analysis of the interpolation error is particularly important for the error analysis of the finite element methods. In the previous paper, we proved that the finite element solution converges to an exact solution if the maximum circumradius of the triangular elements converges to zero. We call such situation "circumradius condition" and claimed that the circumradius condition is more essential than the well-known maximum angle condition. It is considered that the better finite element solution can be obtained by using the mesh division consists of "good" triangles. However, the generation of such mesh division is time consuming task within the simulation process of the finite element method. On the other hand, the effecient algorithm is known for computing Delaunay triangulation. However, the mesh division produced by Delaunay triangulation sometimes contains collapsed triangles. In this paper, we will introduce "circumradius condition" and show that the effecient error estimate can be obtained by the circumradius condition with Delaunay triangulation. [ABSTRACT FROM AUTHOR]

The ability to produce accurate scattering data for imaging is important in the field of NDT for both the development of new algorithms and iterative methods which improve the scatterer reconstruction by trial and error. Error analysis for FE simulations is typically performed for plane wave propagation in a homogeneous space. In this paper it is demonstrated that the mesh refinement must be significantly improved to achieve the same accuracy for scattering problems. A study of meshing techniques suggests that a uniform mesh is necessary to obtain a suitable dynamic range. [ABSTRACT FROM AUTHOR]

This paper presents an approach for a weld connection modeling in the finite element method using the method of Lagrange multipliers. The key issue is to fulfil contact conditions of the weld connection with the possibility to use it for connection of non-conforming meshes. That is why a general node-to-segment (NTS) algorithm which enables to define the connection between nonconforming meshes is used. [ABSTRACT FROM AUTHOR]

The paper proposes the algorithm for the determination of the coefficients of the Williams series expansion in notched semidisks with different angles of the notch. The algorithm is based on the experimental procedure of the photoelasticity method and the finite element analysis. The large series of experiments for semidiscs was performed. Digital photoelasticity method is used to analyze experimentally the complete Williams series expansion of the stress and displacement fields in the vicinity of the crack tip in isotropic linear elastic plates under Mixed Mode loading. The distribution of the isochromatic fridge patterns is employed for obtaining the stress field near the crack tip by the use of the complete Williams asymptotic expansion for various classes of the experimental specimens (plates with two collinear cracks under tensile loading and under mixed mode loading conditions). The higher order terms of the Williams series expansion are taken into account and the coefficients of the higher order terms are experimentally obtained. The stress field equation of Williams up to fifty terms in each in mode I and mode II has been considered. The comparison of the experimental results and the calculations performed with finite element analysis has shown the importance and significant advantages of photoelastic observations for the multi-parameter description of the stress field in the neighborhood of the crack tip. [ABSTRACT FROM AUTHOR]

It’s crucial for process engineers to determine optimal value and combination of process parameters in the design of sheet metal forming. The multi-objective genetic algorithm (MOGA) based on Pareto approach and numerical simulation codes were integrated in this paper to fulfill the optimal formability in the sheet metal forming. Three objective functions of local formability on fracture, wrinkling and insufficient stretching were presented based on the strains state at the end of the forming process on the Forming Limit Diagram. By using Pareto-based MOGA, the optimal global formability which represents the trade-off between different local formability was decided. For the efficiency and accuracy of optimization procedure, both inverse and incremental finite element analysis were used to evaluate the value of objective functions. This method was applied to a complex engineering optimization problem: an engine hood outer panel, the optimal blank holder force and draw bead restraining forces were determined to satisfy the given objective functions for the forming of the auto body panels. The approach proposed in this paper has been shown to be a powerful tool than manual numerical simulation procedure. © 2005 American Institute of Physics [ABSTRACT FROM AUTHOR]

Improved stability of the node-to-node (NTN) algorithm gained by modification of the algorithm with regard to the explicit method is presented in this paper in order to enable fast and precise analysis of models containing NTN contacts in structural dynamics using Finite Element Method. The key issue is to fulfil contact conditions and prevent solution instability. The instability can be observed if the time step exceeds the critical time step, which is directly derived from the element stiffness and tends towards zero as connected nodes get closer to each other [1]. This is the main problem of NTN contacts in the explicit method. [ABSTRACT FROM AUTHOR]

The paper presents results of applying various approaches to simulation of contact surfaces fracture under high velocity interaction of solid bodies. Three basic methods have been distinguished having the difference in the algorithms of mass distribution after elements fracture at contact boundaries. Authors own finite element computer software program EFES has been used for the calculations. The calculation was carried out in a complete three-dimensional formulation. The obtained results using all three algorithms have been compared to the experimental results. [ABSTRACT FROM AUTHOR]

In order to estimate the mechanical properties of the overall structure of the body accurately and quickly in conceptual design phase of the body, the beam and shell mixing elements was used to build simplified finite element model of the body. Through the BP neural network algorithm, the parameters of the mechanical property of joints element which had more affection on calculation accuracy were calculated and the joint finite element model based on the parameters was also constructed. The case shown that the method can improve the accuracy of the vehicle simulation results, while not too many design details were needed, which was fit to the demand in the vehicle body conceptual design phase. [ABSTRACT FROM AUTHOR]

In the past few years graphical processing units (GPUs) have shown tremendous improvements in computational throughput over standard CPU architecture. However, this comes at the cost of restructuring the algorithms to meet the strengths and drawbacks of this GPU architecture. A major drawback is the state of limited memory, and hence storage of FE stiffness matrices on the GPU is important. In contrast to storage on CPU the GPU storage format has significant influence on the overall performance. This paper presents an investigation of a storage strategy in the implementation of a two-dimensional finite element-boundary integral (FE-BI) model for Eddy current NDE applications, on GPU architecture. Specifically, the high dimensional matrices are manipulated by examining the matrix structure and optimally splitting into structurally independent component matrices for efficient storage and retrieval of each component. Results obtained using the proposed approach are compared to those of conventional CPU implementation for validating the method. [ABSTRACT FROM AUTHOR]

The paper focuses on the miniaturization of the bulging test for material characterization of micro tubes. For the design of the experimental device, numerical simulations are conducted first. Even if no scale effect is taken into account in material modeling, numerical results give some information before designing the set-up and performing experimental works: level of pressure inside the tube, volume of fluid necessary to create such a level of pressure and bulge height to measure. The main results are a design of the experimental device and choices for its instrumentation. [ABSTRACT FROM AUTHOR]

Computer aided process planning (CAPP) is the bridge between CAD and CAM. Setup planning is the major key to transform design concept into manufacturing domain, which is mainly experience based activity in modern manufacturing industry. Setup planning is a complicated non-linear task constrained by many factors such as tool approach direction, geometric feature relationship, fixturing constrain, tolerance requirement and manufacturing practice. The objective of setup planning is to determine the number of setup needed, the orientation of the workpiece and the machining surfaces in each setup. This paper focuses on the development of a formalized procedure for automatic generation of setup plan. Tolerance relations are used as critical constraints for setup planning. The tasks that are performed are: (a) identifying groups of features that can be machined in a single setup, (b) determining a suitable work piece orientation, i.e. the suitable datum planes for each setup, (c) determining all the feasible setup plans to machine the given set of features of prismatic parts, and (d) evaluating the feasible setup plans on the basis of technological conditions. Trial runs with industrial parts indicate that the system is applicable for industrial use. [ABSTRACT FROM AUTHOR]

ABSTRACT This paper reports work in progress towards achieving improved simulation tools for ultrasonic Nondestructive Evaluation (NDE) in the power generation industry. Hybrid models are shown to arise as a natural consequence of a modular approach to tackling complex processes, which is attractive in the face of the increasing sophistication of practical ultrasonic inspection. It is argued that although such models are not new to the community, there is an urgent need for developing them to be independent of their constituent methods and that an interface mechanism capable of handling field quantities in the near-field is essential to achieve optimal performance. A domain-linking algorithm capable of stable performance in the near-field is then presented and preliminary Finite Element simulation studies for validating the procedure and demonstrating its capabilities show positive results . [ABSTRACT FROM AUTHOR]

This paper introduces a model-based approach to reconstruct the three-dimensional defect profiles using eddy-current heat exchanger tube inspection signals. The method uses a Woodbury’s substructure finite element forward model to simulate the underlying physics, a state space defect representation, and a tree search algorithm to solve the inverse problem. The advantage of the substructure method is that it divides the whole solution domain into two substructures and only the region of interest (ROI) with dramatic material changes will be updated in each iterative step. Since the number of elements inside the ROI is very small compared with the number of elements in the entire mesh, the computational effort needed in both LU factorization and coefficient matrix assembly is reduced. Therefore, the execution time is reduced significantly making the inversion very efficient. The initial inversion results are presented to confirm the validity of the approach. [ABSTRACT FROM AUTHOR]

In this paper we will present an effective numerical method for the Black-Scholes equation with transaction costs for the limiting price u(s, t;a). The technique combines the Rothe method with a two-grid (coarse-fine) algorithm for computation of numerical solutions to initial boundary-values problems to this equation. Numerical experiments for comparison the accuracy ant the computational cost of the method with other known numerical schemes are discussed. [ABSTRACT FROM AUTHOR]

The paper shows the a-priori error estimates for the Fedorenko finite superelement method in application to physical problems with small-scale singularities. [ABSTRACT FROM AUTHOR]

The present paper is concerned with the frictionless bilateral or unilateral contact problem between two elastic bodies. An algorithm is introduced to solve the resulting finite element system by a non-overlapping domain decomposition method. This technique enable us to transform the solution of the global problem to the solutions of the elasticity equations for each body separately and the solution of the Schur complement problem on the contact surface. The main goal of this work is the construction of the interface preconditioner for the Schur complement problem. The solution is obtained by using a successive approximation method. Finally, some numerical results of the proposed method are given. [ABSTRACT FROM AUTHOR]

Modelling of macroscopic behaviour of materials, consisting of several layers or components, whose microscopic (at least stochastic) analysis is available, as well as (more general) simulation of non-local phenomena, complicated coupled processes, etc., requires both deeper understanding of physical principles and development of mathematical theories and software algorithms. Starting from the (relatively simple) example of phase transformation in substitutional alloys, this paper sketches the general formulation of a nonlinear system of partial differential equations of evolution for the heat and mass transfer (useful in mechanical and civil engineering, etc.), corresponding to conservation principles of thermodynamics, both at the micro- and at the macroscopic level, and suggests an algorithm for scale-bridging, based on the robust finite element techniques. Some existence and convergence questions, namely those based on the construction of sequences of Rothe and on the mathematical theory of two-scale convergence, are discussed together with references to useful generalizations, required by new technologies. [ABSTRACT FROM AUTHOR]

Constitutive models for the crystal plasticity have the common objective which relates the behavior of microscopic single crystals in the crystallographic texture to the macroscopic continuum response. This paper presents the texture analysis of polycrystalline materials using the rate-dependent single crystal plasticity to develop a multi-scale description of the mechanism at the grain and aggregate levels. The texture analysis requires a numerical algorithm for integrating the constitutive equations. The implicit deformation gradient approach is employed to update the stresses and texture orientations as an integration algorithm. It considers elastic or plastic deformation gradient as the primary unknown variables and constructs the residual of the elastic and plastic velocity gradients as the governing equations. This algorithm is shown to be an efficient and robust algorithm in rather large time steps. The texture analysis of the asymmetric rolling process is also presented to show investigation of the effect of texture evolution based on the finite element analysis as a numerical example. The analysis result for texture evolution is investigated by comparing the pole figure before and after the asymmetric rolling process. © 2007 American Institute of Physics [ABSTRACT FROM AUTHOR]

Coupling Finite Element (FEM) simulations to mathematical optimisation techniques provides a high potential to improve industrial metal forming processes. In order to optimise these processes, all kind of optimisation problems need to be mathematically modelled and subsequently solved using an appropriate optimisation algorithm. Although the modelling part greatly determines the final outcome of optimisation, the main focus in most publications until now was on the solving part of mathematical optimisation, i.e. algorithm development. Modelling is generally performed in an arbitrary way. In this paper, we propose an optimisation strategy for metal forming processes using FEM. It consists of three stages: a structured methodology for modelling optimisation problems, screening for design variable reduction, and a generally applicable optimisation algorithm. The strategy is applied to solve manufacturing problems for an industrial deep drawing process. © 2007 American Institute of Physics [ABSTRACT FROM AUTHOR]

The solution of linear systems of equations is the most time-consuming part in large-scale implicit FE computations of wave propagation problems. Traditionally, direct solvers have been used but recent developments of iterative solvers and precondition techniques may impose a change. In particular, preconditioning by multigrid seems to be favorable for finite element (FE) applications since it has a natural interpretation and substantially improves the rate of convergence of the conventional iterative solvers. The multigrid preconditioner uses a sequence of grids on which the fine-grid residual forces are prolongated to coarser grids and computed corrections are interpolated back to the fine grid such that the fine-grid solution successively is improved. By this technique, large 3D problems, invincible for solvers based on direct methods, can be solved in acceptable time and at low memory requirements. The proposed adaptive multigrid FE-method combines adaptivity and multigrid solution strategy in a sophisticated manner. The sequence of computational grids is successively refined (adapted) and generated according to the guidance of a posteriori error estimates until the solution fulfils a predefined accuracy specification. In contrast to standard adaptive procedures where rejected grids are deleted, the adaptive multigrid algorithm uses previous solution and generated grids to speed up the solution process. A refinement strategy based on element splitting and introduction of hanging nodes requires special care since the constraint equations of the hanging nodes are incorporated in the system by usage of Lagrange multipliers. The approach leads to indefinite systems and hence a special preconditioner that enforces the constraint equations to be fulfilled while iterating has been developed. The paper presents results using the adaptive multigrid procedure on an elasto-plastic wave propagation problem. © 2006 American Institute of Physics [ABSTRACT FROM AUTHOR]

This paper presents several approaches for preform shape optimization in 3D forging. The process simulation is carried out using the FORGE3® finite element software, and the optimization problem regards the shape of initial axisymmetrical preforms. Several objective functions are considered, like the forging energy, the forging force or a surface defect criterion. Both deterministic and stochastic optimization algorithms are tested for 3D applications. The deterministic approach uses the sensitivity analysis that provides the gradient of the objective function. It is obtained by the adjoint-state method and semi-analytical differentiation. The study of stochastic approaches aims at comparing genetic algorithms and evolution strategies. Numerical results show the feasibility of such approaches, i.e. the achieving of satisfactory solutions within a limited number of 3D simulations, less than fifty. For a more industrial problem, the forging of a gear, encouraging optimization results are obtained. © 2004 American Institute of Physics [ABSTRACT FROM AUTHOR]

The goal of this paper is to solve the post buckling phenomena of a large deformed elastic beam by a canonical dual mixed finite element method (CD-FEM). The total potential energy of this beam is a nonconvex functional which can be used to model both pre-and post-buckling problems. Different types of dual stress interpolations are used in order to verify the triality theory. Applications are illustrated with different boundary conditions and external loads by using semi-definite programming (SDP) algorithm. The results show that the global minimum of the total potential energy is stable buckled configuration, the local maximum solution leads to the unbuckled state, and both of these two solutions are numerically stable. While the local minimum is unstable buckled configuration and very sensitive to both stress interpolations and the external loads. [ABSTRACT FROM AUTHOR]

Finite element method (FEM) is an efficient computational algorithm and has been widely applied to strip rolling process. For on-line application, two key issues, i.e. calculating speed and calculating precious, have to be achieved to the industrial requirements. In this paper, we present an algorithm named improved gradient and Newton method that combines Cholesky factorization method and Newton method to solve the strip rolling problem. In the proposed algorithm, Cholesky factorization method is used to search descend direction (gradient), while Newton method mainly focuses on searching step factor. Due to the excellent ability of Cholesky factorization method in solving the decomposed equations of FEM, the calculating speed is absolutely improved. Accordingly, the ability of Newton method in finding exact step factor improves the calculating precious. The global convergence of proposed algorithm can be proved according to the convergence proof of Newton method. Computational experiments demonstrate that the proposed algorithm is efficient and steady in strip rolling. [ABSTRACT FROM AUTHOR]

Drop test simulation via finite element methods can help simulate the effects of high impact and shock. It has become an indispensable tool during the virtual product design processes to reduce the cost of experimental test and to help improve the durability of products. The choice of a reliable contact method is critical for drop test simulation. Of all the contact algorithms, the penalty method has the advantage of taking the contact constraint into account without increasing the degrees of freedom while being easy to implement into existing software. The implicit analysis is generally known to be more accurate than the explicit analysis, but has convergence issues. This paper presents a penalty finite element method based on dynamic implicit scheme to implement impact planes for drop test simulation. An idea of impact element groups, which allows multiple impact planes with different normal directions, is presented. Two impact plane types are implemented: 'Full general' and 'Slide/no bounce'. The general drop process is divided into three durations with different time step sizes to efficiently and accurately capture the fast change within the microtime of the impact. Typical and interesting drop test models are simulated and discussed for the presented method. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the simulation of linear elastic behaviour of plates using a 3D approach which numerical cost only scales like a 2D one. In the case of plates, the kinematic hypothesis introduced in plate theories to go from 3D to 2D is usually unsatisfactory where one cannot rely on St Venant's principle (usually close to the plate edges). We propose to apply the PGD (Proper Generalized Decomposition) method [1] to the simulation of the linear elastic behavior of plates. This method allows us to separately search for the in-plane and the out-of plane contributions to the 3D solution, yielding significant savings in computational cost. The method is validated on a simple case and its full potential is then presented for the simulation of the behavior of laminated composite plates. [ABSTRACT FROM AUTHOR]

This paper presents the formulation of an axi-symmetric element based on an efficient method called 'Inverse Approach' (I.A.) for the numerical modeling of cold forging process. In contrast to the classical incremental methods, the Inverse Approach exploits the known shape of the final part and executes the calculation from the final part to the initial billet. The assumptions of the proportional loading and the simplified tool actions make the I.A. calculation very fast. The metal's incompressibility is ensured by the penalty method. The comparison with ABAQUS® and FORGE® shows the efficiency and limitations of the I.A. This simplified method will be a good tool for the preliminary preform design. [ABSTRACT FROM AUTHOR]

The paper deals with the development of the technique for J-integral computation using the vector fields obtained by digital image correlation method. The proposed computing algorithm includes several steps following each other: (i) construction of displacement vector field; (ii) calculation of deformations and stresses; (iii) calculation of the J-integral value. A comparative study of the results obtained by the proposed technique and by finite element simulation was carried out. The errors of the data modeled in the ANSYS from the computed J-integral values were estimated at various tensile loads. [ABSTRACT FROM AUTHOR]

Coupling optimisation algorithms to Finite Element Methods (FEM) is a very promising way to achieve optimal metal forming processes. However, many optimisation algorithms exist and it is not clear which of these algorithms to use. This paper investigates the sensitivity of a Sequential Approximate Optimisation algorithm (SAO) proposed in [1–4] to an increasing number of design variables and compares it with two other algorithms: an Evolutionary Strategy (ES) and an Evolutionary version of the SAO (ESAO). In addition, it observes the influence of different Designs Of Experiments used with the SAO. It is concluded that the SAO is very capable and efficient and its combination with an ES is not beneficial. Moreover, the use of SAO with Fractional Factorial Design is the most efficient method, rather than Full Factorial Design as proposed in [1–4]. © 2007 American Institute of Physics [ABSTRACT FROM AUTHOR]

This paper presents an approach of combined direct compensation and surface approximation implemented in a forging optimization system in order to achieve net-shape forging for aeroengine blade components. This approach is based on modification of individual nodal positions on the die surface and approximation of the modified die surface using a B-spline surface for improved surface quality. The results show that, with this method, forging optimization computations not only produce fast converged solution in forging simulation but also provide significant reduction of the total forging error. © 2007 American Institute of Physics [ABSTRACT FROM AUTHOR]

The simplified (one step) method also called “inverse approach”(IA) for the numerical analysis of the stamping process has been continuously developed by the authors since the end of the eighties (1, 2, 3, 4). In the present paper we recall the main finite element formulation aspects of a robust IA analysis code, called FAST_STAMP, for an efficient estimation of the large elastoplastic strains (in particular the thickness strains) encountered in deep drawing operations. Our results will be presented and compared with others, obtained either from experiments or from incremental codes such as ABAQUS or STAMPACK. The presentation includes “math based” optimization algorithms and strategies for process parameter design. The cost functions and constraints are mainly express to reduce or control the thickness changes, the localized necking, the wrinkling tendency, the springback effects after forming. The design variables are describing the shape of the blank and the tools, the restraining forces due to drawbeads, material properties such as anisotropy coefficient and hardening exponent. Results will be presented to show the actual capabilities of the coupled analysis and optimization strategy with application to the design of stamping parameters. © 2007 American Institute of Physics [ABSTRACT FROM AUTHOR]

Treatment of contact between a sheet and tools is one of the most difficult problems to deal with in finite-element simulations of sheet forming processes. In order to obtain more accurate tool models without increasing the number of elements, this paper describes a new formulation for contact problems using interpolation proposed by Nagata for tool surfaces. A contact search algorithm between sheet nodes and the interpolated tool surfaces was developed and was introduced into the static-explicit elastoplastic finite-element method code STAMP3D. Simulations of a square cup deep drawing process with a very coarsely discretized punch model were carried out. The simulated results showed that the proposed algorithm gave the proper drawn shape, demonstrating the validity of the proposed algorithm. © 2005 American Institute of Physics [ABSTRACT FROM AUTHOR]

The design of addendum surfaces in sheet forming process is very important for the product quality, but it is very time-consuming and needs tedious trial-error corrections. In this paper, we propose a methodology to automatically generate the addendum surfaces and then to optimize them using a forming modelling solver. The surfaces’ parameters are taken as design variables and modified in course of optimization. The finite element mesh is created on the initial addendum surfaces and mapped onto the modified surfaces without remeshing operation. The Feasible Sequential Quadratic Programming (FSQP) is adopted as our algorithm of optimization. Two objective functions are used: the first one is the thickness function to minimize the thickness variation on the workpiece ; the second one is the appearance function aiming to avoid the scratching defects on the external surfaces of panels. The FSQP is combined with our “Inverse Approach” or “One Step Approach” which is a very fast forming solver. This leads to a very efficient optimization procedure. The present methodology is applied to a square box. The addendum surfaces are characterised by four geometrical variables. The influence of optimization criteria is studied and discussed. © 2004 American Institute of Physics [ABSTRACT FROM AUTHOR]

This paper describes an efficient method that integrates finite element analysis (FEA), mesh morphing and response surface based optimization in order to implement an automated and flexible software tool to optimize stamping tool and process design. For FEA, a robust and extremely fast inverse solver is chosen. For morphing, a state of the art mesh morpher that interactively generates shape variables for optimization studies is used. The optimization algorithm utilized in this study enables a global search for a multitude of parameters and is highly flexible with regards to the choice of objective functions. A quality function that minimizes formability defects resulting from stretching and compression is implemented. © 2004 American Institute of Physics [ABSTRACT FROM AUTHOR]

Over the past two decades, various finite element formulations and solution techniques for metal forming analysis have been developed. Most finite element codes for bulk metal forming used in the industry today are based on static implicit solution schemes wherein a non-linear system of equations is solved iteratively for each time increment. For simple 2D problems, static implicit analysis models are generally known to be more accurate and efficient than dynamic explicit analysis models. However, for complex 3D forming problems, the static implicit procedures encounter a number of inherent difficulties especially in incremental forming processes such as ring rolling in which several surface nodes repeatedly make contact with and separate from the dies. Static implicit finite element formulations require a very long computational time for the analysis of ring rolling. Several solution techniques have been developed to reduce the computational time of static implicit finite element analysis, namely the dual mesh technique, Arbitrary Lagrangian Eulerian (ALE) technique, etc. The dynamic explicit method on the other hand appears to be very effective in analyzing complex incremental forming problems. In this paper, a comparison of the analysis results obtained using dynamic explicit finite element method and static implicit method using a dual mesh approach is presented. © 2004 American Institute of Physics [ABSTRACT FROM AUTHOR]

The paper is concerned with the comparison of optimization methods (OM) and control algorithms (CA) and their applications in tube hydroforming. Two sensitivity methods, the finite differentiation method and the direct differentiation method are also compared for the computation of the gradient of the objective functions in the case of optimization method. The results demonstrate that both methods could be applied for hydroforming optimization and control, but it is clearly demonstrated that control algorithms lead to better results in terms of accuracy and computational time than optimization methods. © 2004 American Institute of Physics [ABSTRACT FROM AUTHOR]

The rising hydroforming technology is taking an increasing interest in the industrial environment, particularly due to the weight reduction and uniform thickness distribution that can be achieved by this technology when compared to standard stamping process. Simple sheet and tube hydroforming have been the first studied and applied, now double sheets is a new variety of hydroforming which could offers a substantial improvement in cycle time production since two parts are formed simultaneously. In this paper we deal with the numerical simulation aspect and experimental validation on elliptical bulge tests. An implicit finite element formulation in velocity/pressure is used to solve the 3D volumic problem. Two algorithms to deal with the hydrostatic pressure are discussed. The first one is called “load control” method, consisting in solving the hydroforming equilibrium problem with an increasingly imposed pressure. Nevertheless, when a maximum of pressure is reached, the algorithm can fails. The second family of methods called “arc-length methods” have the advantage to go through the previous instability point, we have in particular developed a modified displacement control method. The Modified Maximum Force Criterion was modified by introducing the strain rate sensitivity effect and then used to predict necking. Comparison with the experiments was then made. © 2004 American Institute of Physics [ABSTRACT FROM AUTHOR]

The simulation of high-velocity impact and penetration is inhibited by complex material behavior and large deformations. Lagrangian formulations best model complex materials because history-dependent variables and material boundaries are not advected. However, Lagrangian finite elements are limited by large deformations. Recently, meshfree particle methods have been used to avoid such limitations, and have demonstrated greater accuracy than traditional erosion methods (wherein deformed elements are removed). Though the variable connectivity of particles enables them to model large deformations, it requires more computational effort than (fixed-connectivity) elements. Therefore, an algorithm was designed to convert deformed elements to particles, thus providing the ability to model large deformations where needed, while maintaining the efficiency of elements elsewhere. This combination is essential in three dimensions, where problem size demands efficiency. In this paper, the conversion algorithm is demonstrated for several three-dimensional simulations of high-velocity impact and penetration. © 2004 American Institute of Physics [ABSTRACT FROM AUTHOR]

In order to describe the meso-damage of the refractories more accurately, and to study of the relationship between the mesostructured of the refractories and the macro-mechanics, this paper takes the magnesia-carbon refractories as the research object and uses the molecular dynamics method to instead the traditional sequential algorithm to establish the meso-particles filling model including small and large particles. Finally, the finite element software-ABAQUS is used to conducts numerical simulation on the meso-damage evolution process of refractory materials. From the results, the process of initiation and propagation of microscopic interface cracks can be observed intuitively, and the macroscopic stress-strain curve of the refractory material is obtained. The results show that the combination of molecular dynamics modeling and the use of Python in the interface to insert the cohesive element numerical simulation, obtaining of more accurate interface parameters through parameter inversion, can be more accurate to observe the interface of the meso-damage evolution process and effective to consider the effect of the mesostructured of the refractory material on its macroscopic mechanical properties. [ABSTRACT FROM AUTHOR]

Error estimations of H1 mixed finite element method for the Benjamin-Bona-Mahony equation are considered. The problem is reformulated into a system of first order partial differential equations, which allows an approximation of the unknown function and its derivative. Local parabolic error estimates are introduced to approximate the true errors from the computed solutions; the so-called a posteriori error estimates. Numerical experiments show that the a posteriori error estimates converge to the true errors of the problem. [ABSTRACT FROM AUTHOR]

In the present study we demonstrate the construction of a robust multilevel preconditioner for biquadratic FE elliptic problems. In the general setting of an arbitrary elliptic operator it is well known that the standard hierarchical basis two-level splittings for higher order FEM elliptic systems deteriorate with increasing the anisotropy ratio. An alternative approach resulting in a robust hierarchical two-level splitting of the finite element space of continuos piecewise biquadratic functions involves the semi-coarsening mesh procedure. This evokes us to analyze the behavior of the constant in the strengthened CBS inequality, which is a quality measure for hierarchical two-level splittings of the FEM stiffness matrices, for the particular case of balanced semi-coarsening mesh refinement. We present new theoretical estimates which further we support by numerically computed CBS constants over a rich set of parameters (coarsening factor and anisotropy ratio). An optimal order multilevel algorithm is constructed on the basis of the proven uniform estimates and the theory of the Algebraic MultiLevel Iteration (AMLI) methods. Its total computational cost is proportional to the size of the discrete problem with a proportionality constant independent of the anisotropy ratio [ABSTRACT FROM AUTHOR]

We consider stationary linear and nonlinear problems on non-connected layers with distinct material properties. A version of the finite element method (FEM) is used for discretization of the continuous problems. We formulate sufficient conditions under which we prove the discrete maximum principle and convergence of the numerical higher-order finite elements solution. Efficient algorithm for solution of the FEM algebraic equations is proposed. Numerical experiments are also discussed. [ABSTRACT FROM AUTHOR]

This paper introduces spatial decomposition algorithms to the volume integral method, which will enable the integral equation method to efficiently solve electromagnetic scattering problems where the scatterer extends across several layers or multiple scatterers exist in multiple layers. Model comparisons with the finite element methods are used validate the approach. Studies of typical aging aircraft eddy current inspection problems are conducted using the new formulation. © 2006 American Institute of Physics [ABSTRACT FROM AUTHOR]

A method to extract mechanical properties of polycrystalline thin-films is proposed herein for Micro-Electro-Mechanical Systems (MEMS) components. The micro structural evolution of thin film deposition is considered to alleviate the size effects in experiments by employing a lattice based stochastic model. A stable numerical algorithm is described. The kinetics parameters, which are the key parameters for the microstructure evolution based on the nucleation and growth mechanism, are extracted from the given micrograph of a polycrystalline material by an inverse method. The proposed method is verified by comparing the quantitative measures; the number of grains and the grain size distribution, for the actual and simulated microstructures. Two dimensional mesh generation algorithm for the lattice based microstructure is developed and used to calculate the equivalent Young’s modulus of several polycrystalline materials with anisotropic single crystals. © 2004 American Institute of Physics [ABSTRACT FROM AUTHOR]

Mathematical modeling of a flow in fractured porous media is important problem in subsurface simulations. Therefore, the development of mathematical models and efficient computational algorithms for numerical modeling of such processes is an actual problem. The mathematical model should take into account the entire complex of complicated, multiscale processes occurring in fractured porous media. In this work, we construct a coupled mixed dimensional model for simulation of the flow process in the fractured porous media with dual continuum background model. Mathematically the problem is described by a coupled system of equations consisting a d-dimensional equation for flow in porous matrix and a (d − 1)-dimensional equation for fracture networks with a specific exchange term for coupling them. In order to reduce size of the system and efficient solution of the presented problem, we construct coarse grid approximation using Mixed Generalized Multiscale Finite Element method. We present results of the numerical simulations for two-dimensional model problem. [ABSTRACT FROM AUTHOR]

The numerical modelling of a plate structure was performed with the finite element method and a one-mode approach based on Koiter's method. The first order approximation of Koiter's method enables one to solve the eigenvalue problem. The second order approximation describes post-buckling equilibrium paths. In the finite element analysis, the Lanczos method was used to solve the linear problem of buckling. Simulations of the non-linear problem were performed with the Newton-Raphson method. Detailed calculations were carried out for a short Z-column made of general laminates. Configurations of laminated layers were non-symmetric. Due to possibilities of its application, the general laminate is very interesting. The length of the samples was chosen to obtain the lowest value of local buckling load. The amplitude of initial imperfections was 10% of the wall thickness. Thin-walled structures were simply supported on both ends. The numerical results were verified in experimental tests. A strain-gauge technique was applied. A static compression test was performed on a universal testing machine and a special grip, which consisted of two rigid steel plates and clamping sleeves, was used. Specimens were obtained with an autoclave technique. Tests were performed at a constant velocity of the cross-bar equal to 2 mm/min. The compressive load was less than 150% of the bifurcation load. Additionally, soft and thin pads were used to reduce inaccuracy of the sample ends. [ABSTRACT FROM AUTHOR]

The advent of Giant Magneto-Resistive (GMR) technology permits development of novel highly sensitive array probes for Eddy Current (EC) inspection of multi-layer riveted structures. Multi-frequency GMR measurements with different EC pene-tration depths show promise for detection of bottom layer notches at fastener sites. However, the distortion of the induced magnetic field due to flaws is dominated by the strong fastener signal, which makes defect detection and classification a challenging prob-lem. This issue is more pronounced for ferromagnetic fasteners that concentrate most of the magnetic flux. In the present work, a novel multi-frequency mixing algorithm is proposed to suppress rivet signal response and enhance defect detection capability of the GMR array probe. The algorithm is baselinefree and does not require any assumptions about the sample geometry being inspected. Fastener signal suppression is based upon the random sample consensus (RANSAC) method, which iteratively estimates parameters of a mathematical model from a set of observed data with outliers. Bottom layer defects at fastener site are simulated as EDM notches of different length. Performance of the proposed multi-frequency mixing approach is evaluated on finite element data and experimental GMR measurements obtained with unidirectional planar current excitation. Initial results are promising demonstrating the feasibility of the approach. [ABSTRACT FROM AUTHOR]

A Bayesian approach for characterizing the damage in beams utilizing guided waves is presented. The proposed methodology treats the damage location, length, depth and the Young's modulus of the material as unknown model parameters. A two-stage optimization approach is applied for damage characterization using simulated annealing algorithm to first guarantee that the solution is close to the global optimum, followed by a standard simplex search method that maximizes the probability density function of a damage scenario conditional on the measurement data. One advantage of the proposed method is that instead of only pinpointing the damage location and extent, the uncertainty associated with the damage characterization results is also quantified. A series of comprehensive numerical case studies utilizing the spectral finite element method to model the wave propagation and scattering at the step damage are used to examine the accuracy and robustness of the proposed methodology. The studies include investigations of the influence of practical situations such as the effects of measurement noise, uncertainty of Young's modulus due to the temperature change, and interference of boundary reflections and scattered waves on the damage characterization results. [ABSTRACT FROM AUTHOR]

A two-grid algorithm for FEM solution of nonlinear reaction diffusion equations was constructed. The algorithm involves solving one small, nonlinear problem on the coarse-grid system, one-linear problem on the fine-grid system. Three meshes (Shishkin’s, Bakhvalov’s and Vulanovic’s) are examined. All of the approximations are uniformly convergent with respect to the small parameter. We prove that when the mesh step parameters are chosen appropriately, the error in the two-grid algorithm is comparable to the error in solving the fully nonlinear problem on the fine mesh. We also provide an analysis of numerical experiments. [ABSTRACT FROM AUTHOR]