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Springback, the elastically-driven change of shape of a part after forming, has been simulated with 2-D and 3-D finite element modeling. Simulations using solid and shell elements have been compared with draw-bend measurements presented in a companion paper. Plane-stress and plane-strain simulations revealed the dramatic role of numerical tolerances and procedures on the results. For example, up to 51 integration points through the sheet thickness were required for accuracy within 1%, compared with 5–9 typically acceptable for forming simulations. Improvements were also needed in the number of elements in contact with the tools, and in the numerical tolerance for satisfying equilibrium at each step. Significant plastic straining took place in some cases upon unloading; however the choice of elastic–plastic unloading scheme had little effect on the results. While 2-D simulations showed good agreement with experiments under some test conditions, springback discrepancies of hundreds of percent were noted for one alloy with sheet tension near the yield stress. 3-D simulations provided much better agreement, the major source of error being identified as the presence of persistent anticlastic curvature. Most of the remaining deviation in results can be attributed to inaccuracies of the material model. In particular, the presence of a Bauschinger effect changes the results markedly, and taking it into account provided good agreement. Shell elements were adequate to predict springback accurately for R/t greater than 5 or 6, while solid elements were required for higher curvatures. As R/t approaches 2, springback simulated with solid elements tends to disappear, in agreement with measurements presented in the companion paper and in the literature. [Copyright &y& Elsevier]

Finite element ring rolling simulation by conventional Lagrangian codes carries an excessive computational cost. The main reason for this is the large number of incremental stages typically required to complete a full simulation. The nature of ring rolling however means that the amount of deformation taking place in a given increment is relatively small compared with typical metal forming processes. This paper describes measures that make the analysis of ring rolling a practicable proposition. The resulting model is based on a threefold approach, comprising the finite element flow formulation, an arbitrary Lagrangian Eulerian update strategy, and a novel iterative solution scheme called the successive preconditioned conjugate gradient method. The approach exploits the slowly evolving nature of the problem with the effect of reducing the time penalty for each deformation increment. In addition, a number of issues specific to ring rolling have been addressed including the problem of how the mandrel interface is dealt with for arbitrarily shaped rollers. The importance of addressing this particular issue is also illustrated. The method is validated by comparison with earlier experimental work and previously developed models for both pure radial, and radial–axial ring rolling. [Copyright &y& Elsevier]

The paper gives a bibliographical review of finite element methods (FEMs) applied for the analysis of pressure vessel structures/components and piping from the theoretical as well as practical points of view. This bibliography is an addendum to the Finite elements in the analysis of pressure vessels and piping—a bibliography (1976–1996) published [Int J Press Vess Piping 69 (1996) 279] and Finite elements in the analysis of pressure vessels and piping, an addendum (1996–1998) published [Int J Press Vess Piping 76 (1999) 461]. The new bibliography at the end of the paper contains approximately 670 references to papers and conference proceedings on the subject that were published in 1998–2001. These are classified in the following categories: linear and nonlinear, static and dynamic, stress and deflection analyses; stability problems; thermal problems; fracture mechanics problems; contact problems; fluid–structure interaction problems; manufacturing of pipes and tubes; welded pipes and pressure vessel components; development of special finite elements for pressure vessels and pipes; finite element software; and other topics. [Copyright &y& Elsevier]

The purpose of this paper is to propose a method for the evaluation of plate elements in the finite element engineering software comparatively to the Kirchhoff and Reissner plate theories. The method is based on the study of transverse deflection near a crack tip. A numerical work has been conducted for the shell elements in Abaqus software with different crack lengths and various thicknesses. The deflection can be written as a function of the exponent of the distance between the crack tip and one point along the crack. This exponent is accepted to describe the behaviour of finite elements. [Copyright &y& Elsevier]

This paper presents a new transition element for modelling solid-to-beam and plate-to-beam connections. The approach is based upon the hybrid stress method and the resulting transition element is hypostatic, i.e. the number of independent stress parameters is less than the number of independent displacements. As a consequence, there are further displacement modes called spurious kinematic modes which are eliminated by means of a suitable “penalty” method. The numerical performance of the proposed element is assessed by a number of relevant tests. [Copyright &y& Elsevier]

The temperature field of 50CrV4 automobile gear bar steel in continuous rolling is simulated by FEM. The temperature variations of the bar during continuous rolling are obtained. The cross-sectional temperature field for some passes has been solved simultaneously. It is clear that the surface temperature of a bar calculated by FEM accords well with the temperature found in practice. The simulated results in this paper describe the temperature pattern of rolling in great detail. Especially, this paper offers reference data for the TMCP treatment of bar steel. [Copyright &y& Elsevier]

The influence of the shape and the initial position of the preform in precision forging of a compressor blade has been studied by 3D rigid–viscoplastic finite element method (FEM) in this paper. The results show the following: (1) a short and thick preform results in necking at the arc transition zone between the tenon and the blade body, and at the zone near the tip of the blade during deformation; (2) a long and slender preform produces bending in the middle of the blade body during deformation; (3) if a long and slender preform is bent in advance, an advisable product without flash can be obtained; (4) a reasonable initial position of the preform deviates to the thinner side of the blade die cavity; (5) this research is beneficial for the practice of the precision forging process of a compressor blade and it has a general significance for other types of blade. [Copyright &y& Elsevier]

A common method used for the determination of material flow stress is the application of a compression test. At a low strain rate and deformation, the precise flow stress can be obtained in this method, but at a large level of deformation, the friction in the interface between the die and the specimen leads to inevitable bulging of the sample and thereby to inhomogeneous strain and stress. As a result, the flow-stress precision is affected because of the above-mentioned bulging. To reduce the error caused by inhomogeneous deformation, a new method combining compression tests with FEM simulation (C-FEM) is described in this paper. This method takes AISI 1006 and AISI 5140 as examples, and inputs their flow stress determined by compression tests into FEM programs. Then the flow stress is applied in the analysis of upsetting tests. On the basis of load–stroke curves determined by FEM simulation and compression tests, a target-function for evaluating flow-stress precision is set up. The flow stress direct from compression tests can be corrected by optimizing the target-function repeatedly, and as a result the precision of the material flow stress is improved. [Copyright &y& Elsevier]

Springback is the main defect in U-shaped part forming, which can badly affect the shape of a part. Applying reasonable variable blankholder force in the forming process is one of the useful methods to solve this problem, but determination of the curve of blankholder force vs. punch displacement is still difficult. A method is advanced in this paper to control the forming process of a U-shaped part, by which a reasonable blankholder force curve can be easily gained. Comparing with constant blankholder force, higher forming quality can be obtained in both avoiding cracking and improving dimension accuracy. The benchmarks of the 2D draw bending problem in NUMISHEET’93 has been utilized to validate the method by FEM, and good results of springback elimination have been obtained. [Copyright &y& Elsevier]

A considerable amount of research has been carried out in order to improve the quality and feasibility of stents in recent years. However, published works on simulation of stent expansion using computer software are relatively rare. In this paper, a nonlinear finite-element method was employed to analyse the expansion of a stent using internal pressure. The pressure was applied as a surface load on the inner surface, expanding the stent radially past its elastic limit to a maximum diameter. The total reduction in length as the stent expands radially was also calculated. The analyses were performed using finite-element packages LS-DYNA for solution of the problem and ANSYS (version 5.5) as a pre- and post-processor. Two different load application speeds were investigated in the simulations and the results were compared. This paper concentrates on the effect of the speed of pressure applied on a stent during the expansion process. The issues discussed in this study include the extent of expansion, foreshortening of the stent and the stress levels at different increments of pressure due to the different speeds of application of the pressure. [Copyright &y& Elsevier]

Part 1 of this two-part paper presents the laboratory experiments on straight flanging, in which the influence of process variables, such as die shoulder radius, punch-die clearance, punch nose radius, pad force and material properties were discussed. This second part summarizes the FEM predictions for flanging and compares these results with some experimental data. Furthermore, flanging with coining to reduce springback has been investigated and evaluated by FEM for better dimensional control in flanging and hemming processes. [Copyright &y& Elsevier]

The technological and economical pressure in production engineering requires an optimisation of existing production processes. The finite element method (FEM) is an appropriate tool to gain the necessary knowledge of these processes. This paper will present some examples of the application of FEM in different branches of manufacturing technology: cutting with a geometrically defined and an undefined cutting edge; electro-erosion technology; metal forming processes; tribology. After the presentation of the problem, the simulation set-up for each example will be discussed and the results will be presented. Thus, this paper will provide an overview of the current possibilities for the application of FEM in manufacturing technology. [Copyright &y& Elsevier]

In this paper, we present an adaptive finite element method for steady-state rolling contact in finite deformations along with a residual based a posteriori error estimator for rolling contact problem with Coulomb friction. A general formulation of rolling contact geometry is derived from the point of view of differential geometry. Solvability conditions for the rolling contact problems are discussed. We use Newton''s method to solve variational equations derived from a penalty regularization of the finite element approximation of the rolling contact problem. We provide a numerical example to illustrate the method. [Copyright &y& Elsevier]

This paper presents a higher order stabilized finite element formulation for hyperelastic large deformation problems involving incompressible or nearly incompressible materials. A Lagrangian finite element formulation is presented where mesh dependent terms are added element-wise to enhance the stability of the mixed finite element formulation. A reconstruction method based on local projections is used to compute the higher order derivatives that arise in the stabilization terms, specifically derivatives of the stress tensor. Linearization of the weak form is derived to enable a Newton–Raphson solution procedure of the resulting non-linear equations. Numerical experiments using the stabilization method with equal order shape functions for the displacement and pressure fields in hyperelastic problems show that the stabilized method is effective for some non-linear finite deformation problems. Finally, conclusions are inferred and extensions of this work are discussed. [Copyright &y& Elsevier]

The mechanical response of heterogeneous structures, such as weldments, is largely governed by the response of the local constituents. In the present paper, the global and local mechanical response of friction stir welded AA2024 is examined experimentally and numerically. Full field strain measurements are obtained on transversely loaded tensile specimens via the digital image correlation technique. Assuming an iso-stress configuration, local constitutive data were determined for the various weld regions and used as input for a 2-D finite element model. The simulation results were compared with the experimental results to assess the viability of the modeling approach and the validity of the iso-stress assumption [Copyright &y& Elsevier]

The paper proposes two quadrilateral finite elements for the analysis of plane elastic problems. The elements are designed to obtain a mechanical response characterized by improved in-plane bending behaviour, a response which is difficult to obtain by the usual compatible elements. The adopted assumed stress approach enables either an easy formulation of the elements or a careful tuning of the desired mechanical response. The proposed elements behave well in classical numerical tests and are suitable for use with rough meshes. [Copyright &y& Elsevier]

This paper presents a unified framework for creep modeling of anisotropic materials, which is specified in more detail to the cases of isotropy, cubic symmetry and transverse isotropy. To this end an additive decomposition of the elastic and inelastic strain tensors into dilational and isochoric Kelvin modes is assumed. Each of these modes is obtained from fourth-order projection operators, resulting from solution of the eigenvalue problem for the anisotropic fourth-order elasticity tensor. The amount of strain rate for each mode is modeled with a Norton-type ansatz in terms of an equivalent stress. The formulation for the equivalent stress in terms of quadratic forms with aid of the projection operators is compared with polynomial expressions from the literature. The experimental phenomenon of primary creep is taken into account by a back stress tensor of Armstrong–Frederick type, which is also decomposed into Kelvin modes. As a consequence of the mode decomposition the classical radial-return method of isotropic elasto-plasticity is generalized to the different cases of anisotropy. Furthermore the implications on parameter identification are addressed. Two numerical examples are concerned with a superalloy CMSX-4. [Copyright &y& Elsevier]

Theories on intrinsic or material length scales find applications in the modeling of size-dependent phenomena. In elasticity, length scales enter the constitutive equations through the elastic strain energy function, which, in this case, depends not only on the strain tensor but also on gradients of the rotation and strain tensors. In the present paper, the strain-gradient elasticity theories developed by Mindlin and co-workers in the 1960s are treated in detail. In such theories, when the problem is formulated in terms of displacements, the governing partial differential equation is of fourth order. If traditional finite elements are used for the numerical solution of such problems, then C1 displacement continuity is required. An alternative “mixed” finite element formulation is developed, in which both the displacement and the displacement gradients are used as independent unknowns and their relationship is enforced in an“integral-sense”. A variational formulation is developed which can be used for both linear and non-linear strain-gradient elasticity theories. The resulting finite elements require only C0 continuity and are simple to formulate. The proposed technique is applied to a number of problems and comparisons with available exact solutions are made. [Copyright &y& Elsevier]

Nodal ordering for the formation of suitable sparsity patterns for stiffness matrices of finite element meshes are often performed using graph theory and algebraic graph theory. In this paper a hybrid method is presented employing the main features of each theory. In this method, vectors containing certain properties of graphs are taken as Ritz vectors, and using methods for constructing a complementary Laplacian, a reduced eigenproblem is formed. The solution of this problem results in coefficients of the Ritz vectors, indicating the significance of each considered vector.The present method uses the global properties of graphs in ordering, and the local properties are incorporated using algebraic graph theory. The main feature of this method is its capability of transforming a general eigenproblem into an efficient approach incorporating graph theory. Examples are included to illustrate the efficiency of the presented method. [Copyright &y& Elsevier]

In this paper, the dynamic stability of a completely free cylindrical shell under a follower force is analyzed. Both edges of the shell are assumed to have rings to increase the rigidity of the structure. Hamilton''s principle is used to derive the equations of motion, and the finite element method is applied to investigate the dynamic stability of the shell. Numerical analysis is performed for each circumferential wave number by using the orthogonality of the vibration modes of the shell. The kinetic or static analysis is carried out according to whether the circumferential wave number is equal to one or not. Numerical results show that the stiffening ring stabilizes the circumferential higher modes. On the other hand, it is found that the ring may destabilize the beam-like mode. [Copyright &y& Elsevier]

The objective of this paper is to demonstrate how the asymptotic behavior of a shell structure, as the thickness (t) approaches zero, can be evaluated numerically. We consider three representative shell structural problems; the original Scordelis–Lo roof shell problem, a herein proposed modified Scordelis–Lo roof shell problem and the partly clamped hyperbolic paraboloid shell problem. The asymptotic behavior gives important insight into the shell load bearing capacity. The behavior should also be known when a shell problem is used to test a shell finite element procedure. We briefly review the fundamental theory of the asymptotic behavior of shells, develop our numerical schemes and perform the numerical experiments with the MITC4 shell finite element. [Copyright &y& Elsevier]

For the mathematically sound, cost effective, flexible and automatic computation of structural mechanical problems with error tolerances, adaptive finite element meshes (h-adaptivity) and elements with different Ansatz order (p-adaptivity) and dimension (d-adaptivity) are desirable. Furthermore, because of the numerical effort, the use of parallel computers is adequate. Object-oriented data structures and algorithms are presented which support these adaptive formulations. In this paper, we describe a refinement algorithm which adapts hexahedral meshes in a node regular way, i.e. without hanging nodes. Moreover, classes implementing the mathematical operators and structures arising in the finite element formulation are introduced within the object oriented concept. They offer the means to implement FE formulations in a way, very similar to the mathematical notation. For these purposes, an object-oriented language is strongly required in order to get a general and simple program structure, even for highly complex tasks with h-, p- and d-adaptivity and distributed data. [Copyright &y& Elsevier]

This paper presents the exact stiffness matrix of 3D-beam element with a class of continuously varying cross-sectional properties, which is derived using direct stiffness method and transfer functions of the beam. A nodal load vector for continuously distributed beam loading is also described using transfer functions. All the transfer functions, which occur in the stiffness matrix and nodal load vector, are evaluated numerically. Results of numerical experiments show that this new element satisfies all the relevant equations. [Copyright &y& Elsevier]

This paper presents a careful finite element investigation into interfacial stresses in reinforced concrete (RC) beams strengthened with a bonded soffit plate, with the aims of assessing the accuracy of existing approximate closed-form analytical solutions based on simplifying assumptions and highlighting aspects which are omitted by them. Finite element modelling issues are first discussed, with particular attention on stress singularities in such beams and appropriate finite element meshes for the accurate determination of interfacial stresses. Finite element stresses are then carefully examined and compared with the predictions from a closed-form solution recently derived by the authors. The finite element results show that stresses vary strongly across the adhesive layer, with the stresses along the adhesive-to-concrete (AC) interface being very different from those along the plate-to-adhesive (PA) interface. In particular, near the end of the plate, the interfacial normal stress is tensile along the AC interface but compressive along the PA interface, offering a plausible explanation for the fact that PA interfacial failure in tests has rarely been if at all reported. The closed-form solution, being based on the assumption of uniform stresses in the thickness direction in the adhesive layer, is incapable of predicting such complex stresses, but nevertheless provides a reasonably close prediction of stresses along the middle-thickness section of the adhesive layer, particularly when the adhesive layer is not very thin. This and other similar closed-form solutions are therefore believed to still form a useful basis on which design rules against debonding failures can be built, with appropriate tuning using experimental data. Finally, the effect of spew fillets on interfacial stresses is examined. [Copyright &y& Elsevier]

An approximate model has been developed to improve our understanding of flow control at the exit of an extrusion die. This paper deals with the design of traditional die flow correctors used in flat-faced aluminum extrusion dies. The numerical model uses the finite-element method combined with techniques of mathematical programming. Analytical sensitivities have been developed from the discretized finite-element equations in order to compute the necessary derivatives during optimization. The model includes thermal effects, and the extruded material is assumed to be strain-rate and temperature dependent. [Copyright &y& Elsevier]

In this paper, the steady-state reference rupture stresses are presented for a wide geometry range of internally pressurised pipes, under a closed-end condition, in order to investigate the applicability of the approach in life prediction. Creep damage mechanics finite element (FE) calculations were performed to obtain accurate failure lives and to determine the skeletal point rupture stresses, using material constants for two low alloy ferritic steels. Analytical solutions were used to derive steady-state reference rupture stresses, from which the effects of pipe dimensions and the tri-axial stress state parameter can be assessed. The accuracy of the life predictions was assessed, for a number of different stress levels and the design rule based on the mean diameter hoop stress. The results confirm the validity of the steady-state reference rupture stress in life prediction for a wide range of pipe geometries and tri-axial stress state parameter. [Copyright &y& Elsevier]

The paper presents a study of the strength of thin-walled I-sections in combined compression and major axis bending. The beam-columns are subjected to equal and opposite end moments causing bending in single curvature. Failure occurs by in-plane bending, local buckling and yielding at short lengths, and by flexural–torsional buckling, local buckling and yielding at intermediate and long lengths. The focus is on how the interaction curve is affected by local buckling. A geometric and material nonlinear finite element analysis is used to produce interaction curves for four cross-sections covering the range from slender to compact. The finite element model has been developed by the authors in a separate paper and shown to agree well with tests. For each cross-section, interaction curves are produced for four overall slenderness values including short and long beam-columns. The interaction curves are compared with design strengths obtained using the Australian Steel Structures Standard AS4100, the American Institute of Steel Construction Load and Resistance Factor Design Specification, and Eurocode 3: Part 1.1. The design strengths are shown to be generally conservative, particularly for slender cross-sections. Improved design interaction curves are proposed. [Copyright &y& Elsevier]

This paper presents a magnetic circuit model to the estimation of machine parameters of an interior permanent magnet synchronous machine. It extends the earlier work of Hwang and Cho that focused mainly on the magnetic aspects of motor design. The proposed model used to calculate EMF, d- and q-axis reactances. These calculations are compared to those from finite element analysis and measurement with good agreement. [Copyright &y& Elsevier]

Spinning is frequently used for manufacturing axi-symmetric shapes where press tooling might not be justified on grounds of size and production volumes. Spinning also has the possibility of producing parts that cannot be deep drawn. In this paper, conventional spinning is studied that is a rotational forming process that does not set out to change the sheet thickness. Both the blank and the finished product have roughly the same thickness.Previous authors have proposed various analyses of the spinning process. This paper reports the finite element modelling of metal spinning. Domain decomposition is a commercially available technique, which enables the partition of a finite element problem into sub-problems that can be solved by using parallel processing techniques in a greatly reduced time. The software used is MARC as provided by MSC Software. The hardware platforms used were Dell/Intel single and dual processor machines.Earlier papers reported the difficulties that a finite element modelling of spinning presented. An outline is given of how these problems are tackled. Outstanding problems are reviewed with some potential solutions discussed. The results from the finite element models are compared with experimental results obtained using a numerically controlled spinning process. The NC spinning was done using a light gauge sheet aluminium (Al 99.0-Werkstoff 30205, material condition HH, 0.2% yield 110 MPa). [Copyright &y& Elsevier]

The present paper investigates the formulation of 3D co-rotational beam elements for the buckling and post-buckling analysis of frame structures. Following Pacoste and Eriksson [Comput. Methods Appl. Mech. Engrg. 144 (1997) 163], the term co-rotational relates here to the provision of a local reference frame that continuously rotates and translates with the element. Within this context, several issues are emphasised. The first one refers to the parameterisation of finite 3D rotations. The alternative put forth in the paper is based on the spatial form of the incremental rotational vector. The second issue concerns warping effects which are introduced by adding a seventh degree of freedom at each node. Different types of local formulations are considered and it is shown that at least some degree of non-linearity must be introduced in the local strain definition in order to obtain correct results for certain classes of problems. Within the present approach the centroid and shear center of the cross-section are not necessarily coincident. Finally, in the context of instability problems, a method for the direct computation of critical points is also briefly discussed. This is based on a minimal augmentation procedure as developed by Eriksson [Comput. Methods Appl. Mech. Engrg. 156 (1998) 45; Comput. Methods Appl. Mech. Engrg. 179 (1999) 265; Int. J. Struct. Stability Dynamic 1 (1) (2001)]. Ten examples, including large displacement and stability problems, are used in order to assess the performances of the elements. [Copyright &y& Elsevier]

Preform design in forging processes is an important aspect for improving the forging quality and decreasing the production cost. Forward and backward simulations of the forging process based on rigid visco-plastic finite element methods (FEMs) can directly provide a preform shape from the final forged shape at a given stage. The objective of this effort is to reduce the material lost as flash by the design of an improved busting operation for a track link forging. This paper uses the FEM-based inverse die contact tracking method to design the preform shapes for a representative plane-strain cross section of the track link blocker forging. This procedure establishes a record of the boundary condition time sequence via forward simulation, using a candidate preform, into the final forged shape. This recorded time sequence is then modified according to the material flow characteristics and the state of die fill to satisfy the requirement of material utilization and forging quality. The modified boundary condition sequence is then applied to control die/node separation during the backward deformation simulation. The backward simulation for the section analyzed provided the blocker preform shape from which the buster dies can be designed. The preform for the section is then evaluated by forward FEM simulation and compared with the results from the original busting operation. Performance measures for the comparison includes die fill, flash size, strain variance, frictional power and die load. Use of round billet stock was also investigated for producing the required preform shape. [Copyright &y& Elsevier]

The support shaft is a key part in the automobile industry. Its annual production quantity is usually very large. The current manufacturing process is conducted with much machining work including drilling the hollow, which results in a great waste of material. This paper gives a new manufacturing method by the implementation of extrusion processes. It can not only save much material but can also improve properties of the support shaft. The new manufacturing processes include a two-stage extrusion process. A reasonable preform shape was determined through finite element based simulation. The whole forming process is simulated and verified by the finite element method using the DEFORM™ system. The die designs of the two extrusion processes are also given. The two-stage extrusion process and related die designs were recommended to one forging company that presently manufactures the support shaft with the traditional method. [Copyright &y& Elsevier]

A laser beam can be used as a flexible sheet metal forming tool. Its mechanism is the forming caused by thermal stresses resulting from the irradiation of laser beam scanning. Because of the complexity of this process, numerical simulation becomes necessary for its analysis. In this paper, the deformation field during the laser bending of sheet metal is studied using the 3D thermoelastoplastic finite element method. Considering the coexistence of the temperature and stress arising and dropping during the laser forming, a handling technique for the transitional zone between the elastic zone and plastic zone is adopted. In order to increase the accuracy of calculation, the reduced integration method is applied in the calculation. The results show that: (i) the laser bending process may be divided into two stages: in the first stage, a small counter-bending away from the laser source appears, and in the second stage, a bending angle facing the laser source is just formed finally; (ii) the counter-bending angle away from the laser source in a narrow sheet is greater than that in a wide sheet, i.e. the wider the sheet, the smaller the counter-bending angle; (iii) in the zone being passed through by the laser beam and its neighbouring zone, the stresses change severely with time and place. The form of the displacement field and its change obtained from the FEM simulation calculation is identical with the observed results from experiments, and the calculated bending-angle also agrees well with the experimental data. [Copyright &y& Elsevier]

In this paper, the finite element method and the dual-stream functions upper bound method are selected to analyze the tube rolling process with a planetary rolling mill. Three-dimensional elastic–plastic finite element simulations with special emphasis on the determination of the roller profile and realistic contact conditions between the rollers, workpiece and mandrel are used to reveal the deformation characteristics of seamless tube during the rolling process. In addition, the kinematically admissible velocity field of the deforming tube is described in terms of two stream functions so that the velocity components of the deforming tube can be obtained through the upper bound analysis. In both analysis methods, the equation of meshing is used to determine the contact condition between the rollers and the workpiece. The results from both methods with different variables are observed and compared. [Copyright &y& Elsevier]

This paper presents a high-speed orthogonal cutting model and also establishes a finite element method to analyze the mechanics of steady state in the high-speed orthogonal precision cutting process of oxygen-free high conductivity copper. The paper proposes a variant pseudo-friction coefficient concept to modify the large-deformation finite element formulation and to develop a stress analysis model of the chip–tool interface to solve the problems of the shear stress, normal stress and variant pseudo-friction coefficient on the chip–tool interface. In spite of the high-speed micro-cutting, the effect of high strain rate and high temperature will produce the sticking phenomenon on the rake face of the tool. Not only will the sticking phenomenon shorten tool life, but also will have an effect on the machining accuracy in precision diamond cutting. Therefore, the results in this study can be considered as acceptable consideration during the procedure of high-speed precision cutting. [Copyright &y& Elsevier]

This paper summarizes the results of a numerical study conducted to analyze the effect of selected process parameters on material flow and thread profile in external thread rolling of large diameter blanks. Based on the previous work where a plane strain model was found to provide a reasonable approximation of the thread rolling process, the effect of varying thread form, friction factor, flow stress, and blank diameter on effective strain and thread height was analyzed using the finite element code DEFORM. The results of the study show that for the range of conditions considered, that blank diameter had little effect on the as-rolled thread while flow stress (K and n), friction factor, and thread form all had significant impact on effective strain at the thread root and crest and the achievable thread height. While the rate of work hardening was found to have an effect on the crest profile, the results indicate that it is not the primary factor responsible for seam formation in rolled threads. [Copyright &y& Elsevier]

In this paper, dynamic response of Timoshenko beams under moving mass is analyzed using a numerical method called discrete element technique (DET). In DET, continuous flexible beam elements are replaced by a system of rigid bars and flexible joints. We present a DET model of Timoshenko beams under moving mass. The results of our DET model are compared with the solutions obtained by PAFEC (programs for automatic finite element calculations) for Euler–Bernoulli beams and finite difference method for Timoshenko beams. The effects of beam thickness and moving mass velocity on dynamic response of beams under moving mass are numerically studied. [Copyright &y& Elsevier]

The rise in importance of semi-solid based products has created a need for accurate modelling approaches to coupled solidification and deformation. Current approaches to solidification modelling, using the finite element method (FEM), are principally founded on capacitance methods. Unfortunately they suffer from a major drawback in that energy is not correctly transported through elements, so providing a source of inaccuracy. This paper is concerned with the development and application of a control volume capacitance method (CVCM) to problems where viscoplastic deformation and solidification are combined. The approach adopted is founded on the theory that describes energy transfer through a control volume (CV) moving relative to the deforming mass. This essentially arbitrary Lagrangian–Eulerian (ALE) method facilitates the accurate treatment of discontinuities. The CV approach is tested against known analytical solutions and is shown to be accurate, stable and computationally competitive. [Copyright &y& Elsevier]

This paper is aimed at developing a methodology for studying the transient pressure behavior of horizontal wells with any curvilinear trajectory in an isotropic/anisotropic arbitrarily shaped reservoir. This methodology employs generalized functions to represent the tortuous horizontal well. A particular way of removing the singularities involved in the partial differential equation is based on reducing the original problem to the conventional solution of the homogeneous diffusivity equation under any given initial and boundary conditions. The Green function method and any standard numerical technique are combined in a single computational strategy to obtain the transient pressure response generated by a curved and twisted horizontal well in reservoirs with irregular boundaries. Analytical methods can be also used, whenever possible, to solve the reduced problem. This proposal can be easily broadened to analyze the performance of the pressure transient of any kind of reservoir sources or sinks that can be modeled using generalized functions. Some models are presented. [Copyright &y& Elsevier]

This article considers a generalization of the classical structural flexibility matrix. It expands on previous papers by taking a deeper look at computational considerations at the substructure level. Direct or indirect computation of flexibilities as “influence coefficients” has traditionally required pre-removal of rigid body modes by imposing appropriate support conditions, mimicking experimental arrangements. With the method presented here the flexibility of an individual element or substructure is directly obtained as a particular generalized inverse of the free–free stiffness matrix. This generalized inverse preserves the stiffness spectrum. The definition is element independent and only involves access to the stiffness generated by a standard finite element program and the separate construction of an orthonormal rigid-body mode basis. The free–free flexibility has proven useful in special application areas of finite element structural analysis, notably massively parallel processing, model reduction and damage localization. It can be computed by solving sets of linear equations and does not require processing an eigenproblem or performing a singular value decomposition. If substructures contain thousands of d.o.f., exploitation of the stiffness sparseness is important. For that case this paper presents a computation procedure based on an exact penalty method, and a projected rank-regularized inverse stiffness with diagonal entries inserted by the sparse factorization process. These entries can be physically interpreted as penalty springs. This procedure takes advantage of the stiffness sparseness while forming the full free–free flexibility, or a boundary subset, and is backed by an in-depth null space analysis for robustness. [Copyright &y& Elsevier]

This paper discusses a new method for the solution of the general truss weight-minimisation problem under simultaneous stress and displacement constraints. The method introduces a novel strain-energy-density criterion that refers to the ratio of the virtual strain energy per unit volume in each structural member to its average value on the whole structure. The virtual strain energy comes from the unit-load theorem and it is proportional to the product of the axial member forces due to both the actual loads and a virtual unit load that is applied at the node with the maximum displacement. A simple recursive formula for updating the cross-sectional areas, based on displacement constraints, is presented. A general subsequent algorithm applicable to both single and multiple load cases follows this formula. The results are encouraging since in all test cases the method was found to be robust and generally led to the same weight level as the literature, in both small and large structures. [Copyright &y& Elsevier]

An extended dynamic J integral for functional graded materials (FGM) is presented in this paper. It is then investigated by a coupled finite element and element-free Galerkin method in cases of stationary and propagating cracks. Numerical results show that the extended J varies rationally with time and crack propagation and can be used to describe the dynamic fracture problem in FGM. [Copyright &y& Elsevier]

This paper introduces a structural identification technique built on finite element (FE) model updating. The FE model is parameterized by a structural parameter that continuously describes the damage in the structure, and besides, an evolution equation of this damage parameter is presented. The model updating is accomplished by determining the subset of this damage parameters that minimizes a global error derived from the dynamic residue vectors, which is obtained by introducing the experimental modal properties into the original model eigenproblem. A mode-shape projection technique is used in order to achieve compatibility between the dimension of the experimental and analytical models. The adjusted model maintains basic properties of the analytical model as the sparsity and the symmetry, which plays an important role in model updating-based damage identification. The verification and assessment of the current structural defect identification is performed on a analytically derived bidimensional truss structure and on a cantilever bidimensional Euler–Bernouilli beam through a virtual test simulator. This simulator is used to realistically simulate the corrupting effects of noise, filtering, digital sampling and truncation of the modal spectrum. The eigensystem realization algorithm along with the common-based normalized system identification were utilized to obtain the required natural frequencies and mode shapes. [Copyright &y& Elsevier]

The inverse eigensensitivity method and the response function method of analytical model updating have become relatively more popular among other methods and have been successfully applied to the practice of analytical model improvement. This paper gives a detailed comparison of these two approaches of model updating on the basis of computer simulated experimental data with the objective of studying the convergence of the two methods and the accuracy with which they predict the corrections required in a finite element model. The effect of the amount of experimental data used in the process of model improvement on the quality of an updated model is also studied. The test cases of complete, incomplete and noisy experimental data are considered. The updated models are compared on the basis of some error indices constructed to quantify error in the predicted natural frequencies, mode shapes and response functions. [Copyright &y& Elsevier]

Structural optimisation based on fatigue life of dynamically loaded structures of realistic complexity is rarely attempted due to computational costs. Very efficient stress analysis and fatigue life assessment techniques are needed if this is to become routine. For the first time, this paper compares several approaches to fatigue life prediction using a real automotive engineering case study, taking into account that optimisation based on fatigue life requires accurate relative distribution rather than exact values. The paper concludes that although both the quasi-static and frequency domain approaches are potentially more efficient than transient dynamic analysis, parameter sensitivity of the frequency domain approach may preclude its eventual use. [Copyright &y& Elsevier]

This paper presents a critical assessment of three analytical methods in determining the crack-tip plastic deformation under large scale and gross-section yielding conditions. These theoretical approaches include two stress-based cohesive zone models and a strain-intensity factor approach, all developed on the basis of the principle of superposition. In the two stress-based cohesive zone models, the prospective stresses along the crack path are taken to be the elastic–plastic solution and the nominal elastic solution, respectively. The problem of an edge crack subjected to grossly plastic strain fields with a constant strain gradient is analysed using the finite element method. The plastic zone size and the crack-tip opening displacement determined by the finite element analysis are then compared with the analytical predictions, showing that these theoretical approaches are unable to capture the influence of gross plasticity on the plastic deformation at the crack tip. The present results highlight the deficiencies in existing stress-based superposition approaches. [Copyright &y& Elsevier]

This paper deals with the assessment of vibration control performance using enhanced smart constrained layer damping (ESCLD) treatment with edge elements. A beam finite element model has been developed based on Timoshenko beam theory with partially covered ESCLD. The edge elements are modeled as equivalent springs mounted at the boundaries of the piezoelectric layer. The Golla–Hughes–McTavish (GHM) method has been used to model the viscoelastic layer. The model is validated against published experimental results. Using linear quadratic regulator (LQR) optimal control, the effects of the ESCLD on vibration suppression performance and control effort requirements are investigated. Analysis shows that edge elements significantly improve the active action transmissibility of the SCLD treatment. Due to combined overall active and passive actions, the ESCLD treatment with sufficiently stiff edge elements could outperform both the SCLD treated system and the purely active system. [Copyright &y& Elsevier]

Arbitrary Lagrangian–Eulerian finite element method is being increasingly used for simulation of metal-forming operations, due to its capability to combine the features of both Lagrangian and Eulerian approaches in a single analysis. An important consideration in applying this approach is an algorithm which decides upon the motion of all degrees of freedom of the finite element mesh in every step of the analysis, such that the resulted mesh retains an optimal shape and condition. Such an algorithm has to be effective, general, and computationally efficient.In this paper, an overview of the mesh motion problem is provided in which guidelines are given for designing mesh motion strategies for particular problems, and numerical schemes are proposed for moving the mesh on external boundaries and in the interior of the body consistent with the ALE principles. Some numerical examples are provided which demonstrate that with suitable mesh motion schemes, ALE formulation can be used effectively to solve problems which are otherwise difficult to solve in Lagrangian or Eulerian frameworks. [Copyright &y& Elsevier]