bluuebunny/crossref_metadata_2025_split huggingface dataset:
Studies of domain‐based formulations for computing exterior problems of acoustics
Authors: Harari Isaac , Hughes Thomas J. R. 
Published: August 2005

AbstractThe propagation and decay of acoustic waves in exterior domains in an essential ingredient in the study of fluid–structure interaction. A strategy must be devised to compute solutions over domains which are unbounded. Exact impedance conditions at an artificial external boundary are specified by the DtN method, yielding an equivalent problem that is suitable for domain‐based computation. The DtN boundary condition is non‐reflective, giving rise to exact (and thereby unique) solutions. The truncated DtN operator, which is employed in practice, fails to inhibit the reflection of higher modes, so that non‐unique solutions may occur at their harmonics. Simple expressions determine a sufficient number of terms in the truncated operator for unique solutions at any given wave number. There are three characteristic length scales in the computational problem: the radius of the artificial boundary, the geometry of the body (represented by the internal boundary) and the mesh size. Numerical studies examine the dependence of the conditioning of finite element coefficient matrices on the number of terms in the truncated DtN operator vs. the wave number non‐dimensionalized by each of the length scales. Analytic results regarding the number of terms sufficient for unique solutions are confirmed. As long as this criterion is respected, no upper limit on the allowable wave number is detected. A local approximation of the boundary conditions restores uniqueness for all wave numbers.
The interaction of a submerged axisymmetric shell and three‐dimensional internal systems
Authors: Ettouney Mohammed M. , Daddazio Raymond P. , Abboud Najib N. 
Published: August 2005

AbstractThe problem of axisymmetric shells submerged in an infinite fluid subjected to an arbitrary loading is usually solved by reducing the system to a set of two‐dimensional problems. This is accomplished by using Fourier series, thereby uncoupling the circumferential harmonics of the axisymmetric system. Thus, a computationally expensive three‐dimensional solution is replaced by a computationally efficient set of two‐dimensional solutions without any loss of accuracy. However, with the addition of arbitrary three‐dimensional subsystems internal to the submerged axisymmetric shell, the circumferential harmonics become coupled. In this case, the computational advantage attributable to the circumferential Fourier decomposition compared to a fully three‐dimensional solution is greatly reduced.This paper introduces a novel method to solve such three‐dimensional systems while keeping the circumferential harmonics of the axisymmetric shell uncoupled. This is accomplished by relating the admittance matrix of the three‐dimensional substructure, expressed in terms of its connection degrees of freedom, and the response of the empty system to solve for the interaction forces between the axisymmetric shell and the internal system. Using these interaction forces, the response of the full system can be obtained, Thus, the efficiency of the two‐dimensional solution is maintained while solving an arbitrary three‐dimensional problem. Sample problems illustrating the performance of this approach will be solved.
The Cartesian collapsed‐dimension method for use in numerical 2‐D radiation calculations in absorbing–emitting media
Authors: Blank David A. 
Published: August 2005

AbstractA new numerical approach has been devised for performing accurate absorbing–emitting non‐scattering radiation calculations for Cartesian co‐ordinate based problems with one ordinate symmetry using only the solution plane formed by the other two ordinates. To accomplish this, the method makes use of ‘effective intensity rays’ which only exist and have meaning in the solution plane of the problem but which are made, through a special procedure, to contain the information of the third dimension. This novel procedure thus eliminates the problem of solid angles and greatly reduces both the complexity and computational expense involved in the solution of such problems. Yet it can do this without producing loss in accuracy. The approach is ultimately intended for use in combustion problems involving high temperatures and optically thin media. For verification purposes the method is applied to the problem of heat exchange in infinitely long rectangular enclosures and is found to give excellent results over a optical thickness range that includes the optically very thin case.
Hyperbolic paraboloid shell analysis via mixed finite element formulation
Authors: Omurtag M. H. , Aköz A. Y. 
Published: August 2005

AbstractAn isoparametric rectangular mixed finite element is developed for the analysis of hypars. The theory of shallow thin hyperbolic paraboloid shells is based on Kirchhoff–Love's hypothesis and a new functional is obtained using the Gâteaux differential. This functional is written in operator form and is shown to be a potential. Proper dynamic and geometric boundary conditions are obtained. Applying variational methods to this functional, the HYP9 finite element matrix is obtained in an explicit form. Since only first‐order derivatives occur in the functional, linear shape functions are used and a C0 conforming shell element is presented. Variation of the thickness is also included into the formulation without spoiling the simplicity. The formulation is applicable to any boundary and loading condition. The HYP9 element has four nodes with nine Degrees Of Freedom (DOF) per node—three displacements, three inplane forces and two bending, one torsional moment (4 × 9). The performance of this simple, and elegant shell element, is verified by applying it to some test problems existing in the literature. Since the element matrix is obtained explicitly, there is an important save of computer time.
Safeguarded use of the implicit restarted lanczos technique for solving non‐linear structural eigensystems
Authors: Abdel‐Aziz Mohammedi R. 
Published: August 2005

AbstractThis paper presents a new algorithm for evaluating the eigenvalues and their corresponding eigenvectors for large‐scale non‐linear eigensystems in structural dynamics. The algorithm is based on solving a sequence of algebraic eigenproblems and updating the parameter λ. The implicitly restarted Lanczos method had been determined to be well suited for solving the linear eigenproblems that arise in this context. A zero‐finder approach that uses rational interpolation to approximate the generalized eigenvalues has been developed to update λ.The methodology of the new algorithm developed here is designed to evaluate a subset of the parametrized non‐linear eigencurves at specific values of λ. Numerical experiments show that the new eigensolution technique is superior to existing approaches for large‐scale problems and competitive for small‐size problems. The main emphasis of this contribution is the derivation and analysis of this scheme for non‐linear structural eigensystems.
Model reduction and process control of thermomechanical behaviour of non‐linear material deformation
Authors: Grandhi Ramana V. , Thiagarajan Ramesh 
Published: August 2005

AbstractThis paper describes a design procedure for metal forming processes by using the controllable subspace of the full system. The velocity profile of the moving die is designed using the reduced order system. The metal forming processes are simulated using non‐linear finite element methods based on the rigid viscoplastic flow formulation. The balanced model reduction technique is applied to reduce the full state space model to a reduced order model that retains the controllable subspace of the thermomechanical system. The linear quadratic regulator theory with output tracking is used as an off‐line design tool to design the die velocity schedule. The process design is carried out to maintain the strain rate of the critical portion of the billet at a desired value. The procedure for designing the process parameters is demonstrated using two case studies.
A new family of explicit time integration methods for linear and non‐linear structural dynamics
Authors: Chung Jintai , Lee Jang Moo 
Published: August 2005

AbstractA new family of explicit single‐step time integration methods with controllable high‐frequency dissipation is presented for linear and non‐linear structural dynamic analyses. The proposed methods are second‐order accurate and completely explicit with a diagonal mass matrix, even when the damping matrix is not diagonal in the linear structural dynamics or the internal force vector is a function of velocities in the non‐linear structural dynamics. Stability and accuracy of the new explicit methods are analysed for the linear undamped/damped cases. Furthermore, the new methods are compared with other explicit methods.
Bandwidth reduction by simulated annealing
Authors: Dubuc Eduardo J. 
Published: August 2005

AbstractThe method of Simulated Annealing (SA) is investigated in the concrete problem of bandwidth reductio. We develop a very efficient way to compute the transitions, and this allows long annealing sessions (Monte Carlo runs) in reasonable time, enabling meaningful experimenting. It is demonstrated (empirically) that the neighbourhood relation in the space of states of the system greatly influences the convergence of the annealing. A pure SA algorithm is developed and used to obtain new lower bounds for the bandwidth in the 30 Everstine problems used as a benchmark for testing bandwidth reduction algorithms. An hybrid algorithm is also developed to be used in practice. It consists of an annealing session (without previous melting) run in cascade after the Cuthill‐McKee algorithm. The running times are of the same order as those of the deterministic algorithms now in use, and improvements of (typically) 20 per cent are obtained on the 30 Everstine problems.
Second‐order sensitivity analysis in vibration and buckling problems
Authors: Godoy Luis A. , Taroco Edgardo O. , Feuoo Raul A. 
Published: August 2005

AbstractA perturbation approach for the first‐ and second‐order sensitivity analysis of eigenvalue problems, as they arise in buckling and vibration of structural systems, is presented. A particular feature introduced in the formulation is the dependence of all matrices that model the problem not only on the design parameter, but also on a pre‐critical state. Thus, the sensitivity of the response of the fundamental path in buckling problems, or a pre‐stressed state, in vibration problems, are introduced in the analysis. Two techniques are considered in this work: the direct and the adjoint methods. First‐ and second‐order sensitivity equations for eigenvalues and eigenvectors are obtained, and it is shown that second‐order sensitivity of an eigenvalue can be accomplished by using only one adjoint problem.
Finite element hydrodynamic friction model for metal forming
Authors: Liu Wing Kam , Hu Yu‐Kan 
Published: August 2005

AbstractThe complex contact conditions on the three‐dimensional (3‐D) tooling‐workpiece interface, such as non‐penetrations, slip–stick phenomena and friction forces due to the relative motion of contacting surfaces, are of vital importance in metal forming operations. Usually, a lubricant is provided as an interface medium between the tool and the workpiece to avoid strain localization, wear and surface damage. Hence, a simple friction law such as Coulomb friction, involving only a constant friction coefficient, cannot model the contact phenomena accurately. In this research, a realistic friction model, which accounts for the tribological behaviour, and most importantly, the effect of surface roughness on the lubricated contact, is developed. This model has been implemented in a 3‐D arbitrary Lagrangian Fulerian finite element code for metal forming analysis. The applicability of the proposed model is demonstrated by the simulation of fluid‐lubricated thrust bearing and sheet metal stretch forming.
Successive conjugate gradient methods for structural analysis with multiple load cases
Authors: Suarjana Made , Law Kincho H. 
Published: August 2005

AbstractThis paper discusses the use of conjugate gradient method for structural engineering analysis with multiple load cases. Specifically, we introduce a modified conjugate gradient method for the solution of a system of linear equations with multiple right‐hand sides. We show how this method can be used to improve the performance of block conjugate gradient method. Numerical results are presented to illustrate the effectiveness of the numerical schemes developed in this study.
Numerical solution of Bernoulli‐type free boundary value problems by variable domain method
Authors: Mejak George 
Published: August 2005

AbstractThe variable domain method for a free surface problem is considered as a weighted residual method. This considerably simplifies discretization of the problem and at the same time allows implementation of any standard discretization technique. Discretization of the problem results in a non‐linear system of equations for discrete values of a field variable and co‐ordinates of the nodes on the free boundary. Variables corresponding to a field variable are eliminated and the resulting non‐linear system is of considerable smaller size. Some new update strategies of the Jacobian together with discussion of the cost‐effectiveness and covergence rate are introduced and compared to Broyden's method. Numerical results which confirm validity of the presented discussion are given for three potential free surface problems, (i) two‐dimensional free jet impingement against an infinite wall, (ii) axisymmetric free jet impingement subjected to gravity and surface tension forces, and (iii) computation of critical flow over a weir. In case (i) comparison with known analytical results is given, while in case (iii) a good agreement with previously published results is established.
From the individual element test to finite element templates: Evolution of the patch test
Authors: Felippa Carlos A. , Haugen Bjørn , Militello Carmelo 
Published: August 2005

AbstractThis paper starts a sequence of three articles that follow an unconventional approach in finite element research. The ultimate objective is to construct high‐performance elements and element‐level error estimators for those elements. The approach takes off from our previous work in high‐performance elements and culminates with the development of finite element templates. The present paper concentrates on the patch test and evolved versions of the test that have played a key role in this research. Following a brief review of the historical roots, we present the Individual Element Test (IET) of Bergan and Hanssen in an expanded context that encompasses several important classes of new elements. The relationship of the IET to the multielement forms A, B and C of the patch test and to the single‐element test are investigated. An important consequence of the IET application is that the element stiffness equations decompose naturally into basic and higher‐order parts. The application of this decomposition to the “sanitization” of the non‐convergent BCIZ element is described and verified with numerical experiments. Two sequel papers in preparation are subtitled ‘the algebraic approach’ and ‘element‐level error estimation’. These apply the fundamental decomposition to the derivation of templates for specific mechanical elements and to the construction of element‐level error estimators, respectively.
Refined nine‐parameter triangular thin plate bending element by using refined direct stiffness method
Authors: Cheung Y. K. , Wanji Chen 
Published: August 2005

AbstractBased on a new generalized variational principle, a refined direct stiffness method (RDSM) which can be directly used to improve non‐conforming elements is proposed. The formulation is similar to that of the direct stiffness method (DSM), but the constraint condition of interelement continuity is satisfied in an average sense and as a result convergence and high accuracy are insured. The well‐known BCIZ nine‐parameter triangular thin plate bending element is refined by the RDSM to yield a new nine‐parameter thin plate bending element RT9. Numerical examples are presented to show that the present model passes the patch test and possesses high accuracy.
Optimal design of material properties and material distribution for multiple loading conditions
Authors: Bendsøe Martin P. , Díaz Alejandro R. , Lipton Robert , Taylor John E. 
Published: August 2005

AbstractAn extension of recent work1 on the simultaneous optimization of material and structure to address the design of structures under multiple loading conditions is presented. Material properties are represented in the most general form possible, namely, as elements of the unrestricted set of positive‐semi‐definite constitutive tensors of a linearly elastic continuum. Existence of solutions can be shown when the objective is a weighted average of compliances and a resource constraint measured as the 2‐norm or the trace of the constitutive tensors is included. The optimized material properties can be derived analytically. The optimization of the layout of the material leads to a sizing problem of structural optimization involving a non‐linear, non‐smooth elasticity analysis. The computational solution of this problem is discussed and illustrated with examples.
A finite element method for stability problems in finite elasticity
Authors: Reese S. , Wriggers P. 
Published: August 2005

AbstractIn this paper a finite element method is developed to treat stability problems in finite elasticity. For this purpose the constitutive equations are formulated in principal stretches which allows a general representation of the derivatives of the strain energy function with respect to the principal stretches. These results can then be used to derive an efficient numerical scheme for the computation of singular points.
New finite element model for analysis of Kirchhoff plate
Authors: Zhao Zhenfeng , Chen Wanji 
Published: August 2005

AbstractA new kind of approach to formulate an isotropic thin plate bending element is presented. The strain energy of the element is decomposed into two parts: an integral concerning the first strain invariant and a line integral around the elemental boundary. The former can be discretized by quasi‐conforming technique1 and the latter can be directly calculated using the interpolation of the deflection and its normal slope along the element boundary. By this method, an assumed first strain invariant quadrilateral element (AFSIQ) is derived. The procedure of formulating the element and the numerical examples show that the new kind of element not only simplifies the formulation considerably but also has excellent accuracy.
Improved finite difference method for equilibrium problems based on differentiation of the partial differential equations and the boundary conditions
Authors: Arad M. , Segev R. , Ben‐Dor G. 
Published: August 2005

AbstractA numerical algorithm for producing high‐order solutions for equilibrium problems is presented. The approximated solutions are improved by differentiating both the governing partial differential equations and their boundary conditions.The advantages of the proposed method over standard finite difference methods are: the possibility of using arbitrary meshes; the possibility of using simultaneously approximations with different (distinct) orders of accuracy at different locations in the problem domain; an improvement in approximating the boundary conditions; the elimination of the need for ‘fictitious’ or ‘external’ nodal points in treating the boundary conditions.Furthermore, the proposed method is capable of reaching approximate solutions which are more accurate than other finite difference methods, when the same number of nodal points participate in the local scheme.A computer program was written for solving two‐dimensional problems in elasticity. The solutions of a few examples clearly illustrate these advantages.
Heat conduction effects on strain localization in plane‐strain tension
Authors: Tuǧcu P. 
Published: August 2005

AbstractThe deformation behaviour of a rectangular block under tension is investigated for a rate‐ and temperature‐dependent solid using the finite element method. Isotropic behaviour is assumed and the effect of deformation‐induced heat generation is studied in conjunction with heat conduction. Localization into diffuse necking is examined by applying the instability criterion defined for the particular rate‐dependent behaviour. The influence of different thermal boundary conditions on the deformation mode considered, is demonstrated by means of parametric studies.
Reduced minimization in Lagrangian Mindlin plate element with arbitrary orientation under uniform isoparametric mapping
Authors: Yong‐Woo Kim , Oak‐Key Min 
Published: August 2005

AbstractFor the displacement‐based Lagrangian Mindlin plate elements oriented arbitrarily under uniform isoparametric mapping without internal distortion, a theoretical interpretation on the conventional shear‐reduced integration is presented by introducing the concept of reduced minimization. It reveals that the conventional shear‐reduced integration such as URI and SRI prevents the unmatched coefficients of shear strains from becoming spurious constraints. Thus, the shear‐reduced integration eliminates spurious constraints and prevents locking.
Coarse division transform based preconditioner for boundary element problems
Authors: Bulgakov V. E. , Białecki R. A. , Kuhn G. 
Published: August 2005

AbstractThis paper is devoted to the development of efficient preconditioners for an iterative solution of equation sets arising in the Boundary Element Method (BEM). A standard collocation system of equations is transformed to a new basis associated with an auxiliary coarse division model for boundary unknowns and solved in this basis. New systems have rapidly decreasing coefficients and by neglecting a large number of them it is possible to construct readily invertible, sparse preconditioners for iterative procedures. The specific features of the transformed matrix can be attributed to the analytical properties of integral equations. Although the transformation is based on an auxiliary coarse division model, it does not require any additional operations with boundary elements. All manipulations necessary to construct the mapping are performed on the level of algebraic equations. Numerical experiments included in the paper confirm a high rate of convergence of the developed iterative scheme.
On the incompressible constraint of the 4‐node quadrilateral element
Authors: Hueck Ulrich , Schreyer Howard L. , Wriggers Peter 
Published: August 2005

AbstractThe standard plane 4‐node element is written as the summation of a constant gradient matrix, usually obtained from underintegration, and a stabilization matrix. The split is based on a Taylor series expansion of element basis functions. In the incompressible limit, the ‘locking’‐effect of the quadrilateral is traced back to the stabilization matrix which reflects the incomplete higher‐order term in the Taylor series.The incompressibility condition is formulated in a weak sense so that the element displacement field is divergence‐free when integrated over the element volume. The resulting algebraic constraint is shown to coincide with a particular eigenvector of the constant gradient matrix which is obtained from the first‐order terms of the Taylor series. The corresponding eigenvalue enforces incompressibility implicitly by means of a penalty‐constraint. Analytical expressions for that constant‐dilatation eigenpair are derived for arbitrary element geometries. It is shown how the incompressible constraint carries over to the element stiffness matrix if the element stabilization is performed in a particular manner.For several classical and recent elements, the eigensystems are analysed numerically. It is shown that most of the formulations reflect the incompressible constraint identically. In the incompressible limit, the numerical accuracies of the elements are compared.