bluuebunny/crossref_metadata_2025_split huggingface dataset:
An ALE hydrodynamic lubrication finite element method with application to strip rolling
Authors: Hu Yu‐Kan , Liu Wing Kam 
Published: August 2005

AbstractA method that incorporates the hydrodynamic lubrication analysis into the arbitrary Lagrangian Eulerian (ALE) finite element analysis is developed for steady‐state strip rolling simulation. By employing the ALE formulation, only part of the workpiece, which is subjected to large plastic deformation within the roll‐bite region, is modelled, so that the computational cost is substantially reduced. In the hydrodynamic lubrication formulation, the effect of surface roughness on the lubricant flow is taken into consideration by the use of an average flow model. The friction stress is expressed in terms of forming variables such as surface roughness, lubricant and workpiece properties, film thickness, forming speed and process geometry. Furthermore, the elastic deformation of rolls is also analysed by the boundary element method to avoid the finite element discretization inside the rolls. Two numerical examples, aluminium and steel strip rolling processes, are presented to demonstrate the merits of the proposed method.
Elastic stability of skew laminated composite plates subjected to biaxial follower forces
Authors: Liao C.‐L. , Lee Z.‐Y. 
Published: August 2005

AbstractThe present study investigates the elastic stability of skew laminated composite plates subjected to biaxial inplane follower forces by the finite element method. The plate is assumed to follow first‐order shear deformation plate theory (FSDPT). The kinetic and strain energies of skew laminated composite plate and the work done by the biaxial inplane follower forces are derived by using tensor theory. Then, by Hamilton's principle, the dynamic mathematical model to describe the free vibration of this problem is formed. The finite element method and the isoparametric element are utilized to discretize the continuous system and to obtain the characteristic equations of the present problem. Finally, natural vibration frequencies, buckling loads (also the instability types) and their corresponding mode shapes are found by solving the characteristic equations. Numerical results are presented to demonstrate the effects of those parameters, such as various inplane force combinations, skew angle and lamination scheme, on the elastic stability of skew laminated composite plates subjected to biaxial inplane follower forces.
Three‐dimensional analysis of thermally loaded cracks
Authors: Raveendra S. T. , Banerjee P. K. , Dargush G. F. 
Published: August 2005

AbstractThe stress intensity factors for cracks in three‐dimensional, thermally stressed structures are computed by using the boundary element method. While many boundary and volume‐integral‐based formulations are available for the treatment of thermoelastic problems in solids, the present analysis is based on a recently developed boundary‐only formulation. The accuracy of the solutions in the present work is improved by using special elements at the crack front that accurately model the variation of displacement, temperature fields and singularity of traction, flux fields.
Construction of stiffness matrices to maintain the convergence rate of distorted finite elements
Authors: Ingber M. S. , Schreyer H. L. 
Published: August 2005

AbstractHigh‐order elements are an option for providing an enhanced rate of convergence. However, it is not widely known that if a high‐order element based on a mapping from a master‐element space is distorted by displacing one of the side nodes slightly from the traditional midside position then the rate of convergence drops one order. The proof for a three‐node element in one dimension has been given previously. Here, a numerical demonstration is presented to show how quickly the rate is lost as the second node is moved from the midpoint. For a six‐node triangular element, a similar convergence study is performed in two dimensions in which one of the side nodes is moved off centre along a straight line joining the vertices of the triangle. Again, a loss in the order of convergence is shown although the loss is only apparent for sufficiently small element size. To prevent this drop in the rate of convergence as a side node is displaced, a procedure is given for developing the element stiffness matrix without formulating element basis functions. For the six‐node triangle, a complete quadratic representation is retained, but at the expense of element compatibility between nodes. The numerical investigation shows that convergence appears to be retained but that the error associated with the incompatibility is greater than the error obtained with the use of distorted isoparametric elements. The results of this study are particularly appropriate for domains with curved boundaries and for non‐linear problems in which node positions are updated according to the deformation history.
State‐space representation and optimal control of non‐linear material deformation using the finite element method
Authors: Grandhi Ramana V. , Kumar Anand , Chaudhary Anil , Malas James C. 
Published: August 2005

AbstractA state‐space model for representing the non‐linear material deformation and an optimal control scheme for obtaining desired process conditions in the deforming material are presented in this paper. The formulation is general for various metal‐forming processes including forging and extrusion operations. The state variables selected in the formulation are the die/billet contact nodal velocities and the nodal velocities of the critical finite elements of the billet. The control input is the ram velocity, which is determined by using the linear quadratic regulator (LQR) theory to maintain desired strain rates within the selected finite elements. The influence of an optimally designed ram velocity on the deforming material is studied using performance measures. This paper includes the development of the state‐space model from non‐linear finite element formulation, optimal control strategy and numerical example cases with discussions.
Lagrangian finite‐element analysis of time‐dependent viscous free‐surface flow using an automatic remeshing technique: Application to metal casting flow
Authors: Muttin F. , Coupez T. , Bellet M. , Chenot J. L. 
Published: August 2005

AbstractThe Navier‐Stokes incompressible model is used to describe two‐dimensional metal casting flow. Such flows involve moving free boundaries. A new numerical algorithm has been developed using the Lagrangian finite‐element method. It allows treatment of flows with moderate Reynolds numbers. The main feature is to avoid the calculation of the convective term, together with an automatic remeshing technique, to cure the mesh distortions. The problem of the free oscillation of a liquid is treated to verify the formulation. An application of this method to the computation of an industrial metal casting flow situation is presented.
A new approach to 2‐D eigenvalue shape design
Authors: Melnikov Y. U. A. , Titarenko S. A. 
Published: August 2005

AbstractA new approach to solve problems in the optimal shape design of eigenvalues is presented. The idea behind the approach is based on a combination of the known material derivative method4,7 and a specially adapted Green's functions formulation.14 In the current study, numerical testing has been limited to two‐dimensional shape optimization. The two test cases involve the first eigenvalues of boundary value problems which model (i) free vibrations of a fixed membrane and (ii) natural frequencies of clamped thin plates. The basic algorithm can easily be adapted to serve other types of boundary value problems dealing with the highest eigenvalues that occur in applied mechanics. Computational aspects of the proposed approach, such as accuracy of the obtained sensitivities, cost of computation and so on are discussed in References 16 (in preparation).
A new approach to magnetic field analysis by the dual reciprocity boundary element method
Authors: Yamada T. , Wrobel L. C. 
Published: August 2005

AbstractThis paper presents an application of the dual reciprocity boundary element method to non‐linear magnetic field analysis. Advanced techniques employed in the procedure include discontinuous elements, quasi‐singular and hyper‐singular integration schemes and the Galerkin formulation. Numerical results are included to show the performance of the proposed approach.
High‐order integration of smooth dynamical systems: Theory and numerical experiments
Authors: Austin Mark 
Published: August 2005

AbstractThis paper describes a new class of algorithms for integrating linear second‐order equations and those containing smooth non‐linearities. The algorithms are based on a combination of ideas from standard Newmark integration methods and extrapolation techniques. For the algorithm to work, the underlying Newmark method must be stable, second‐order accurate, and produce asymptotic error expansions for response quantities containing only even‐ordered terms. It is proved that setting the Newmark parameter γ equal to 1/2 gives a desirable asymptotic expansion, irrespective of the setting for β. Numerical experiments are conducted for one linear and two non‐linear applications.
Fundamental frequency analysis of laminated rectangular plates by differential quadrature method
Authors: Farsa Jalaleddin , Kukreti Anant R. , Bert Charles W. 
Published: August 2005

AbstractIn this paper a differential quadrature method is presented for computation of the fundamental frequency of a thin laminated rectangular plate. The partial differential equations of motion for free vibration are solved for the boundary conditions by approximating them by substituting weighted polynomials functions for the differential operator. By doing this, the coupled partial differential equations of motion are reduced to sets of homogeneous algebraic equations. These sets of homogeneous algebraic equations are combined to give a set of general eigenvalue equations for the problem. Three types of laminated plate problems, which include symmetric, antisymmetric cross‐ply, and symmetric, balanced angle‐ply laminates, are analysed by the method and the results obtained are compared with solutions reported in the literature for other numerical methods. The effects of the level of discretization on the accuracy and rate of convergence of the results are also discussed. The method presented gives accurate results and is found to use not much computer time.
Shape optimization using adaptive shape refinement
Authors: Kohli H. S. , Carey G. F. 
Published: August 2005

AbstractA large part of the computational effort in shape optimization problems is expended in the numerical computation of the gradients for sensitivity information. This effort increases dramatically with an increase in the number of variables used to represent the shape. An adaptation of the gradient projection algorithm for shape optimization problems is described here along with a method to reduce the intermediate size of the optimization problem by allowing adaptive refinement of the shape. The method is demonstrated with a simple representative test case.
Application of singular quadratic distorted isoparametric elements in linear fracture mechanics
Authors: Lim I. L. , Johnston I. W. , Choi S. K. 
Published: August 2005

AbstractThe understanding of the performance of the quarter‐point and transition elements is of considerable importance as these singular elements are widely used in linear elastic fracture mechanics (LEFM) analyses. However, a number of issues remain unresolved although numerous investigations into their performance have been conducted. In particular is the question of optimum quarter‐point element and transition element size. This study examines several aspects in relation to the size effect by performing a large number of numerical analyses on several standard problems. Interpretation of the numerical results was aided by the use of two concepts, the ‘zones of dominance’ and ‘zones of representation’. This study proposes a means of explaining the errors in stress intensity factor computation through the interaction between both types of zones. Consequently, a number of new and significant observations were made regarding the singular elements' performance. This study concludes with some recommendations for the application of these elements.
A direct application of higher‐order parametric programming techniques to structural optimization
Authors: Ohsaki M. , Arora J. S. 
Published: August 2005

AbstractComputational methods based on a sequence of parametric programming problems are presented for solving constrained optimization problems (COP) without any parameter. An auxiliary parametric programming problem (APPP) is formulated in order to solve COP. The procedure is started with an arbitrary initial solution which is the trivial solution of APPP corresponding to the initial value of the parameter. Then the optimal solution for the final value of the parameter, which is the optimal solution of COP, is estimated by Taylor's expansion with respect to the parameter where higher‐order terms are incorporated. It is shown that the incorporation of the higher‐order terms indeed leads to a faster convergence of the solution. As an extension of the method, a general algorithm is presented for optimum design problems with state variable constraints which are implicit functions of the design variables. Logarithmic penalty functions are incorporated and the weight coefficients for the penalty terms are updated continuously. The derivatives of the state variables with respect to the parameter and their sensitivity coefficients are expressed explicitly in terms of those of the design variables. Finally, a method of simultaneous analysis and optimization is developed for trusses with geometrical non‐linearity.
Design optimization of non‐linear structures with rate‐dependent and rate‐independent constitutive models
Authors: Jao S. Y. , Arora J. S. 
Published: August 2005

AbstractA design optimization process for non‐linear structures with history‐dependent materials modelled using the endochronic constitutive theory is described. This constitutive model does not use the concept of a yield surface and describes plastic, viscoplastic and viscoelastic behaviour with one set of equations. Therefore, development of the yield surface is not traced in numerical calculations, simplifying the implementation of response and sensitivity analyses. The total Lagrangian formulation incorporating both geometric and material non‐linear effects is used. Shape, non‐shape and material design parameters are treated simultaneously using the control volume concept, and static and dynamic problems are treated. A simple structure is optimized for several cases of static and impact loading conditions to demonstrate the procedure. Plastic and viscoplastic material behaviour as well as shape and non‐shape design parameters are treated in the example problems.
Detecting symmetry‐breaking bifurcation points of symmetric structures
Authors: Carstensen C. , Wagner W. 
Published: August 2005

AbstractIn engineering applications often problems with symmetric system and symmetric loading occur. It is well known that these symmetry conditions can be used to reduce the computational effort. Thus, only a symmetric reduced system is treated with sufficient boundary and loading conditions. Especially for non‐linear problems this procedure is very effective. Such a strategy allows the computation of solution paths with the constraint that the solution has to be symmetric. Consequently in a stability analysis, only limit points and bifurcation points with associated symmetrical eigenvectors can be found. Often the stability behaviour is dominated by symmetry‐breaking bifurcation points which cannot be detected considering only the tangent stiffness matrix of the reduced system. Hence, in case of stability considerations a calculation of the complete system is necessary. This paper introduces a special form of stability analysis of the complete system using only certain matrices known from the symmetric reduced system, and some transformations concerning the topology of the total system. The proposed methods base on a substructure technique for symmetry under reflections and rotations, and are formulated for the finite element method. Numerical examples are given to show the efficiency of the proposed procedures and algorithms.
Linked interpolation for Reissner‐Mindlin plate elements: Part I—A simple quadrilateral
Authors: Zienkiewicz Olgierd C. , Xu Zhongnian , Zeng Ling Fu , Samuelsson Alf , Wiberg Nils‐Erik 
Published: August 2005

AbstractIn most plate elements using the Reissner‐Mindlin assumptions, the interpolations used for the lateral displacements (w) and the rotation (θ) involve the independent representation of each variable by its nodal values, usually with identical interpolations. To ensure a higher order of expansion for displacement w its representation is linked in the present paper with both sets of nodal variables.Conditions necessary for the use of such expansions are established here and the paper shows the development of a linear quadrilateral element (Q4BL) whose performance and robustness are good (although it possesses one singularity if only three degrees of freedom are prescribed).In Part II we apply the identical formulation to develop a triangular element (T3BL) which performs equally well and is fully robust.
A general methodology for structural shape optimization problems using automatic adaptive remeshing
Authors: Bugeda G. , Oliver J. 
Published: August 2005

AbstractThe proposed methodology is based on the use of the adaptive mesh refinement (AMR ) techniques in the context of 2D shape optimization problems analysed by the finite element method. A suitable and very general technique for the parametrization of the optimization problem, using B‐splines to define the boundary, is first presented. Then mesh generation, using the advancing frontal method, the error estimator and the mesh refinement criterion are studied in the context of shape optimization problems In particular, the analytical sensitivity analysis of the different items ruling the problem (B‐splines. finite element mesh, structural behaviour and error estimator) is studied in detail. The sensitivities of the finite element mesh and error estimator permit their projection from one design to the next one leading to an a priori knowledge of the finite element error distribution on the new design without the necessity of any additional structural analysis. With this information the mesh refinement criterion permits one to build up a finite element mesh on the new design with a specified and controlled level of error. The robustness and reliability of the proposed methodology is checked by means of several examples.
Adaptive multivlevel methods in three space dimensions
Authors: Bornemann Folkmar , Erdmann Bodo , Kornhuber Ralf 
Published: August 2005

AbstractWe consider the approximate solution of self‐adjoint elliptic problems in three space dimensions by piecewise linear finite elements with respect to a highly non‐uniform tetrahedral mesh which is generated adaptively. The arising linear systems are solved iteratively by the conjugate gradient method provided with a multilevel preconditioner. Here, the accuracy of the iterative solution is coupled with the discretization error. As the performance of hierarchical bases preconditioners deteriorates in three space dimensions, the BPX preconditioner is used, taking special care of an efficient implementation. Reliable a posteriori estimates for the discretization error are derived from a local comparison with the approximation resulting from piecewise quadratic elements. To illustrate the theoretical results, we consider a familiar model problem involving reentrant corners and a real‐life problem arising from hyperthermia, a recent clinical method for cancer therapy.
Dynamic optimization of structures with non‐linearities
Authors: Liu Xiaojian 
Published: August 2005

AbstractDynamic optimal design of structural systems with local non‐linearities is proposed and the corresponding mathematical programming is established in this paper. A predictor‐corrector method is presented for state and sensitivity analysis of the systems which is based on partitioning and interface prediction of linear and non‐linear regions. The non‐linear programming problem is linearized and solved by a coarse search SLP approach. A model of an automatic weapon is optimized and some interesting results are given to illustrate the effectiveness of the present method.
An alternative pseudoperipheral node finder for resequencing schemes
Authors: Souza Luiz T. , Murray David W. 
Published: August 2005

AbstractMany resequencing algorithms for reducing the bandwidth, profile and wavefront of sparse symmetric matrices have been published. In finite element applications, the sparsity of a matrix is related to the nodal ordering of the finite element mesh. Some of the most successful algorithms, which are based on graph theory, require a pair of starting pseudoperipheral nodes. These nodes, located at nearly maximal distance apart, are determined using heuristic schemes. This paper presents an alternative pseadoperipheral node finder, which is based on the algorithm developed by Gibbs, Poole and Stockmeyer. This modified scheme is suitable for nodal reordering of finite meshes and provides more consistency in the effective selection of the starting nodes in problems where the selection becomes arbitrary due to the number of candidates for these starting nodes. This case arises, in particular, for square meshes. The modified scheme was implemented in Gibbs‐Poole‐Stockmeyer, Gibbs‐King and Sloan algorithms. Test problems of these modified algorithms include: (1) Everstine's 30 benchmark problems; (2) sets of square, rectangular and annular (cylindrical) finite element meshes with quadrilateral and triangular elements; and (3) additional examples originating from mesh refinement schemes. The results demonstrate that the modifications to the original algorithms contribute to the improvement of the reliability of all the resequencing algorithms tested herein for the nodal reordering of finite element meshes.
Finite element analysis of laminated composites with contact constraint by extended interior penalty methods
Authors: Kim Seung Jo , Kim Jin Hee 
Published: August 2005

AbstractIn this paper the extended interior penalty methods are applied to solve the bolted joint problems of the laminated composite plates. The conventional interior penalty methods have the weak point such that the searches for optimized solution in the neighbourhood of the constraint surfaces are difficult since the values of penalty term in the infeasible domain are infinity. To improve the weak point, the extended interior penalty formulation is proposed. In this work mathematical analysis on the characteristics of the solutions is attempted and the convergence of the penalized solutions is estimated. As a numerical example, first, the case of single bolted joint is solved for a variety of lamination angles of the composite plates. The computed results are compared with the previous works and are proved to agree well. Next the problem of the two bolt holes in series and in parallel are treated in a similar manner. It is concluded that the formulations for the class of the problems by the extended interior penalty methods are mathematically sound and numerically efficient.