bluuebunny/crossref_metadata_2025_split huggingface dataset:
Control of spurious mechanisms for 20‐node and transition sub‐integrated hexahedral elements
Authors: Sze K. Y. 
Published: August 2005

AbstractIn this paper, control of spurious mechanisms for sub‐integrated 20‐node and transition hexahedral elements is devised by an assumed stress approach. The higher‐order stress modes for stabilizing the sub‐integrated elements are identified by examining the spurious mechanisms. With an admissible simplification of the flexibility matrix, row vectors of the leverage matrix can be used as stabilization vectors. Numerical examples for the stabilized 20‐node element are presented. Accuracy of the derived element is far better than the fully integrated displacement elements. Meanwhile, the former also consumes marginally less CPU time than the latter.
Discrete shape sensitivity equations for aerodynamic problems
Authors: Hou Gene J.‐W. , Taylor Arthur C. , Korivi Vamshi M. 
Published: August 2005

AbstractIntensive research and development in Computational Fluid Dynamics (CFD) has recently produced many powerful CFD codes to simulate complex aerodynamic phenomena. However, in order to enhance the usefulness of these CFD codes for design practice, development of design sensitivity equations compatible to these codes becomes very important. This paper represents a part of such an effort to develop a sensitivity analysts methodology that enables the sensitivity equations to be implemented into existing CFD codes with minimal code modification. The methodology is based upon a pre‐elimination procedure which accounts for consistently linearized boundary conditions. Formulations of both the direct differentiation and the adjoint variable methods will be presented in the paper.
Tangent operators and design sensitivity formulations for transient non‐linear coupled problems with applications to elastoplasticity
Authors: Michaleris Panagiotis , Tortorelli Daniel A. , Vidal Creto A. 
Published: August 2005

AbstractTangent operators and design sensitivities are derived for transient non‐linear coupled problems. The solution process and the formation of tangent operators are presented in a systematic manner and sensitivities for a generalized response functional are formulated via both the direct differentiation and adjoint methods. The derived formulations are suitable for finite element implementations. Analyses of systems, with materials that exhibit history dependent response, may be obtained directly by applying the analyses of transient non‐linear coupled systems. Rate‐independent elastoplasticity is investigated as a case study and a problem with an analytical solution is analysed for demonstration purposes.
Two‐dimensional elastodynamic displacement discontinuity method
Authors: Siebrits E. , Crouch S. L. 
Published: August 2005

AbstractA time‐domain elastodynamic displacement discontinuity method is presented for analysing two‐dimensional problems in solid mechanics. Linear, continuous in time and piecewise linear in space interpolation functions are assumed for the displacement discontinuities. Causal and analytical integrations are used throughout. The resulting numerical algorithms are time marching and implicit. The displacement discontinuity method can be used to model a class of traction boundary value problems, where the unknowns are the transient shear and normal discontinuities in displacement across the surface of a mathematical crack in an infinite, isotropic and homogeneous linear elastic medium.
Multiple quadrature underintegrated finite elements
Authors: Liu Wing Kam , Hu Yu‐Kan , Belytschko Ted 
Published: August 2005

AbstractNew multiple‐quadrature‐point underintegrated finite elements with hourglass control are developed. The elements are selectively underintegrated to avoid volumetric and shear locking and save computational time. An approach for hourglass control is proposed such that the stabilization operators are obtained simply by taking the partial derivatives of the generalized strain rate vector with respect to the natural co‐ordinates so that the elements require no stabilization parameter. To improve accuracy over the traditional one‐point‐quadrature elements, several quadrature points are used to integrate the internal forces, especially for tracing the plastic fronts in the mesh during loading and unloading in elastic–plastic analysis. Two‐ and four‐point‐quadrature elements are proposed for use in the two‐ and three‐dimensional elements, respectively. Other multiple‐quadrature points can also be employed. Several numerical examples such as thin beam, plate and shell problems are presented to demonstrate the applicability of the proposed elements.
Finite volumes and finite elements: Two ‘good friends’
Authors: Idelsohn S. R. , Oñate E. 
Published: August 2005

AbstractIn this paper a comparison between the finite element and the finite volume methods is presented in the context of elliptic, convective–diffusion and fluid flow problems. The paper shows that both procedures share a number of features, like mesh discretization and approximation. Moreover, it is shown that in many cases both techniques are completely equivalent.
A Lagrangian approach to the non‐causal inverse dynamics of flexible multibody systems: The three‐dimensional case
Authors: Ledesma Ragnar , Bayo Eduardo 
Published: August 2005

AbstractThis paper addresses the problem of end‐point trajectory tracking in flexible multibody systems through the use of inverse dynamics. A global Lagrangian approach is employed in formulating the system equations of motion, and an iterative procedure is proposed to achieve end‐point trajectory tracking in three‐dimensional, flexible multibody systems. Each iteration involves firstly, a recursive inverse kinematics procedure wherein elastic displacements are determined in terms of the rigid body co‐ordinates and Lagrange multipliers, secondly, an explicit computation of the inverse dynamic joint actuation, and thirdly, a non‐recursive forward dynamic analysis wherein generalized co‐ordinates and Lagrange multipliers are determined in terms of the joint actuation and desired end‐point co‐ordinates. In contrast with the recursive methods previously proposed, this new method is the most general since it is suitable for both open‐chain and closed‐chain configurations of three‐dimensional multibody systems. The algorithm yields stable,non‐casualactuating joint torques and associated Lagrange multipliers that account for the constraint forces between flexible multibody components.
A temperature‐based formulation for finite element analysis of generalized phase‐change problems
Authors: Celentano Dsego , Oñate Eugenio , Oller Sergio 
Published: August 2005

AbstractA finite element formulation for solving multidimensional phase‐change problems is presented. The formulation considers the temperature as the unique state variable, it is conservative in the weak form sense and it preserves the moving interface condition. In this work, an approximate jacobian matrix that preserves numerical convergence and stability is also derived. Furthermore, a comparative analysis with other different phase‐change finite element techniques is performed. Finally, several numerical examples are analysed in order to show the performance of the proposed methodology.
A numerical method for introducing an arbitrary yield function into rigid–viscoplastic FEM programs
Authors: Zhou D. , Wagoner R. H. 
Published: August 2005

AbstractMany standard yield functions (Hill, von Mises, etc,…) allow the derivation of simple equations relating the effective strain rate to principal strain rates explicitly. Such yield functions are easily implemented in rigid–viscoplastic finite element method programs. Other yield functions (Hosford, e.g.) do not allow for this simple approach. A numerical method was proposed in this paper to solve this problem which meets the requirement of rigid–viscoplastic finite elements and can generate the material stiffness terms (first and second derivatives of the effective strain rate with respect to principal strain rates) at any strain state. The numerical method was found to be numerically efficient, accurate and robust. As an example of the procedure, Hosford's yield function was introduced in a rigid–viscoplastic finite element program and results for the punch stretching simulation were compared with Hill‐type materials. The numerical efficiency of the method was also compared. Simulation of full dome formability test, plane strain and square punch stretching was performed by this numerical method with Hosford's yield function.
A space–time coupled p‐version least‐squares finite element formulation for unsteady fluid dynamics problems
Authors: Bell Brent C. , Surana Karan S. 
Published: August 2005

AbstractThis paper presents a p‐version least‐squares finite element formulation for unsteady fluid dynamics problems where the effects of space and time are coupled. The dimensionless form of the differential equations describing the problem are first cast into a set of first‐order differential equations by introducing auxiliary variables. This permits the use of C° element approximation. The element properties are derived by utilizing p‐version approximation functions in both space and time and then minimizing the error functional given by the space–time integral of the sum of squares of the errors resulting from the set of first‐order differential equations. This results in a true space–time coupled least‐squares minimization procedure.A time marching procedure is developed in which the solution for the current time step provides the initial conditions for the next time step. The space–time coupled p‐version approximation functions provide the ability to control truncation error which, in turn, permits very large time steps. What literally requires hundreds of time steps in uncoupled conventional time marching procedures can be accomplished in a single time step using the present space–time coupled approach. For non‐linear problems the non‐linear algebraic equations resulting from the least‐squares process are solved using Newton's method with a line search. This procedure results in a symmetric Hessian matrix. Equilibrium iterations are carried out for each time step until the error functional and each component of the gradient of the error functional with respect to nodal degrees of freedom are below a certain prespecified tolerance.The generality, success and superiority of the present formulation procedure is demonstrated by presenting specific formulations and examples for the advection–diffusion and Burgers equations. The results are compared with the analytical solutions and those reported in the literature. The formulation presented here is ideally suited for space–time adaptive procedures. The element error functional values provide a mechanism for adaptive h, p or hp refinements. The work presented in this paper provides the basis for the extension of the space–time coupled least‐squares minimization concept to two‐ and three‐dimensional unsteady fluid flow.
Inflation of hyperelastic cylindrical membranes as applied to blow moulding. Part I. Axisymmetric case
Authors: Khayat R. E. , Derdouri A. 
Published: August 2005

AbstractThe free and confined axisymmetric inflation of a cylindrical membrane is considered in this study. The problem is formulated to include single and multiple contacts between the cylinder and the surrounding solid boundary. The material is assumed to obey the Mooney–Rivlin constitutive equation. Unlike various finite element based discretization approaches, the present formulation is based on a set of ordinary differential equations governing the deformation field. The resulting two‐point‐boundary‐value problem is solved using the finite element method. Comparison between theory and experiment leads to good agreement. Stick condition upon contact is assumed. Examples of complex geometries including a blow‐moulded bottle are treated. An example of simultaneous stretch and inflation is also given.
A free‐formulation‐based flat shell element for non‐linear analysis of thin composite structures
Authors: Madenci E. , Barut A. 
Published: August 2005

AbstractA flat shell element based on the free‐formulation finite element concept is developed for analysing geometrically non‐linear thin composite shells. A corotational form of the updated Lagrangian formulation is utilized. Numerical results for typical validation problems are presented in order to demonstrate the accuracy and validity of this element. These results are obtained by solving the incremental equilibrium equations through the cylindrical arc‐length method.
A parallel boundary element formulation for determining effective properties of heterogeneous media
Authors: Ingber Marc S. , Womble David E. , Mondy Lisa A. 
Published: August 2005

AbstractThis paper presents a parallel implementation of the boundary element method for MIMD computer architectures to determine the effective properties of two heterogeneous physical systems. The first physical system is comprised of spheres sedimenting in a viscous fluid at low Reynolds numbers. The effective property is characterized by the hindered settling function which is a measure of the average sedimentation velocity. The second physical system is a short‐fibre reinforced composite. The effective property for this system is the composite modulus. The determination of effective properties of heterogeneous media requires performing statistical analyses of several realizations of physical systems based on defining characteristics of the media. The boundary element method is particularly well suited for studying such systems because of the simplification in the discretization associated with the method. However, as the number of heterogeneities to be modeled is increased so are the computational demands. Parallel computation offers the opportunity to model systems of greater complexity. We discuss a parallel boundary element formulation based on the torus‐wrap mapping. In this approach, blocks of the coefficient matrix associated with the discretized boundary element equations are assigned to processors as opposed to more traditional parallel boundary element implementations where rows or columns are assigned to processors. The torus‐wrap mapping can be shown to minimize communication volume between processors during the LU factorization. Therefore, the present formulation scales well with increases in the number of processors.
Object oriented matrix classes for use in a finite element code using C++
Authors: Zeglinski Gordon W. , Han Ray P. S. , Aitchison Peter 
Published: August 2005

AbstractThis paper presents a new method of writing finite element programs using the programming approach known as object oriented programming (OOP). More specifically, the C++ language is used to illustrate the key OOP concepts. In addition to the OOP finite element examples, a detailed discussion of OOP techniques in the creation of a generalized matrix library is presented. The C++ language is used in this paper because it is more suited to numerical programs than a pure OOP language such as Smalltalk. The efficiency, flexibility and maintainability of the C++ program are shown to be superior to a comparable version written in a non‐OOP language, such as FORTRAN. The matrix library contains a number of matrix objects that are useful for specific types of matrix related problems. Different sparse storage schemes are implemented for each different type of matrix. A large number of functions are provided for each matrix type in order to implement many common matrix operations. In applications, the OOP paradigm allows the functions to be used in a very simple way that is common to all the matrix types. The sample finite element code included in this paper is primarily intended to illustrate the key concepts of OOP style. This paper explains how to set up a finite element hierarchy, material hierarchy and how to integrate this with the matrix hierarchy (library). Thus, a completely object oriented finite element program can be written.
The monomial method and asymptotic properties of algebraic systems
Authors: Burns Scott A. 
Published: August 2005

AbstractThe monomial method is a numerical method for solving systems of algebraic equations. It is related to Newton's method, but is based on an approximation that is monomial, rather than linear, in form. It has been shown previously that the monomial method has a number of properties not shared by Newton's method that are responsible for enhanced performance. This paper demonstrates that many of the performance characteristics of the monomial method can be explained in terms of asymptotic properties of algebraic systems, and the ability of the monomial method to exploit these properties. The monomial method recasts the algebraic system to have monomial asymptotes in all directions, so that the monomial approximation becomes asymptotically exact. This explains the very rapid movement toward a solution in the first iteration from distant starting points that has been observed with the monomial method. Problem types with ‘good asymptotics’ are found to be solved very effectively by the monomial method. Several specific engineering applications with good asymptotics are identified, and suggestions are made regarding other types of engineering applications that are likely to be handled effectively by the monomial method.
Control of the freezing interface motion in two‐dimensional solidification processes using the adjoint method
Authors: Kang Shinill , Zabaras Nicholas 
Published: August 2005

AbstractThe aim of this work is to calculate the optimum history of boundary cooling conditions that, in two‐dimensional conduction driven solidification processes, results in a desired history of the freezing interface location/motion. The freezing front velocity and heat flux on the solid side of the front, define the obtained solidification microstructure that can be selected such that desired macroscopic mechanical properties and soundness of the final cast product are achieved.The so‐called two‐dimensional inverse Stefan design problem is formulated as an infinite‐dimensional minimization problem. The adjoint method is developed in conjunction with the conjugate gradient method for the solution of this minimization problem. The sensitivity and adjoint equations are derived in a moving domain. The gradient of the cost functional is obtained by solving the adjoint equations backward in time. The sensitivity equations are solved forward in time to compute the optimal step size for the gradient method. Two‐dimensional numerical examples are analysed to demonstrate the performance of the present method.
On the robustness and efficiency of the SAM algorithm for structural optimization
Authors: Stander Nielen , Snyman J. A. , Coster J. E. 
Published: August 2005

AbstractA parameter study involving a feasibility factor, adaptive tolerance refinement and active set and move limits is conducted on the interior feasible direction method with successive approximations (SAM). The study involves the sizing design of five structural problems of which one is a large power transmission tower to be designed in adherence with a standard design code. It is concluded that a move limit is dispensable for this application while adaptive tolerance refinement makes the algorithm more efficient. Optimal ranges for the feasibility factor and active set limits are suggested. This study reaffirms and quantifies the exceptional stability and robustness of the SAM algorithm.
Sequential quadratic programming for non‐linear elastic contact problems
Authors: Björkman Gunnar , Klarbring Anders , Sjödin Björn , Larsson Torbjörn , Rönnqvist Mikael 
Published: August 2005

AbstractThe physical problem considered in this paper is that of a non‐linear elastic body being indented by a rigid punch. The treatment is based on finite element discretization and sequential quadratic programming (SQP). The finite element formulation is obtained through a variational formulation, which generalizes to frictionless contact a three‐field principle which involves deformation, volume strain and hydrostatic pressure as independent fields. We compare an incremental load method and a method where the indentation for the final load is sought directly. Crucial for the second method is the use of a line search with respect to a merit function which measures the infeasibility in the optimality criteria for the problem; this line search also includes a check of the orientation‐preserving condition of a positive determinant of the deformation gradient. Each iteration within an SQP method requires the solution of a quadratic programming (QP) subproblem, and four different methods for the solution of these subproblems are compared. The performance of the overall procedure is also compared to that of a commercially available system. Test examples ranging from 23 to 770 displacement degrees of freedom are treated. The computational results show that the proposed solution concept is feasible and efficient. Furthermore, it can be applied to general non‐linear elastic contact problems, since it does not include any ad hoc rules.
A unified set of resequencing algorithms
Authors: Souza Luiz T. , Murray David W. 
Published: August 2005

AbstractA general algorithm for resequencing equations and finite element meshes is presented. This algorithm incorporates, in a unified form, the most successful resequencing schemes, namely: the Sloan, Gibbs–King (GK) and Gibbs–Poole–Stockmeyer (GPS) algorithms. As well it provides a context within which the development of new algorithms may take place with a minimum of change. It is easily programmed and has been shown to speed up the execution of the original GK algorithm.
Application of high‐order quadrature rules to time‐domain boundary element analysis of viscoelasticity
Authors: Lee Sang Soon , Westmann R. A. 
Published: August 2005

AbstractThis paper presents an accurate and efficient method for the treatment of time integrals in time‐domain boundary integral equations for viscoelastic problems. First, the integral equations in space and time are derived for linear viscoelastic and thermo‐viscoelastic problems. Then various quadrature rules are discussed for the computation of time integrals. A modified Simpson's rule is proposed as an effective integration scheme. The proposed procedure requires a small computational effort and it is applicable even in time‐domain boundary element analysis of many different problems. Numerical results of example problems show the accuracy and effectiveness of the proposed method.
Unified and mixed formulation of the 4‐node quadrilateral elements by assumed strain method: Application to thermomechanical problems
Authors: Zhu Y. Y. , Cescotto S. 
Published: August 2005

AbstractIn this paper, a class of ‘assumed strain’ mixed finite element methods based on the Hu–Washizu variational principle is presented. Special care is taken to avoid hourglass modes and shear locking as well as volumetric locking. An unified framework for the 4‐node quadrilateral solid and thermal as well as thermomechanical coupling elements with uniform reduced integration (URI) and selective numerical integration (SI) schemes is developed. The approach is simply implemented by a small change of the standard technique and is applicable to arbitrary non‐linear constitutive laws including isotropic and anisotropic material behaviours. The implementation of the proposed SI elements is straightforward, while the development of the proposed URI elements requires ‘anti‐hourglass stresses’ which are evaluated by classical constitutive equations. Several numerical examples are given to demonstrate the performance of the suggested formulation, including static/dynamic mechanical problems, heat conduction and thermomechanical problems.