bluuebunny/crossref_metadata_2025_split huggingface dataset:
Mixed finite element procedure for soil–structure interaction and construction sequences
Authors: Desai C. S. , Lightner J. G. 
Published: August 2005

AbstractMixed finite element procedures with triangular and quadrilateral elements are evaluated and applied for nonlinear elastic and elastic–plastic analysis of some engineering problems. The elastic–plastic analysis involves implementation of von Mises, Drucker–Prager and Cap models. A number of special techniques such as symbolic programming, utilization of dihedral symmetry and the frontal solution are used to achieve computational economy. The procedure is also adopted for simulation of construction sequences in geomechanics such as excavation involving stress‐free surface. The proposed procedures are evaluated and verified with respect to closed‐form solutions, other finite element (displacement) procedures and field observations.
The dual variable method for finite element discretizations of Navier/Stokes equations
Authors: Hall C. A. , Peterson J. S. , Porsching T. A. , Sledge F. R. 
Published: August 2005

AbstractThe numerical solution of two‐dimensional, transient, incompressible Navier–Stokes problems is considered. The dual variable method, originally developed in the context of a finite difference discretization, is a technique to considerably reduce the size of the linear system to be solved at each time step. The steps involved in the method are (1) the determination of the rank of the discrete divergence operator, A, (2) the determination of a basis for the null space of A, N(A), and (3) the calculation of a particular solution of the discrete continuity equation.A finite element implementation of the method is presented using quadrilateral piecewise bilinear velocity/constant pressure elements. Algorithms for the determination of a basis for N(A) and a particular solution are presented. Numerical comparisons of primitive versus dual variable formulations on several problems demonstrate the advantage of the dual variable method, in terms of both execution speed and memory requirements.
Inelastic finite strain analysis of structures subjected to nonproportional loading
Authors: Tseng N. T. , Lee G. C. 
Published: August 2005

AbstractThe inelastic behaviour of elasto‐plastic materials is nonlinear, path‐dependent, and is a function of the total plastic strain. For finite strain problems, the total inelastic strain in Lagrangian co‐ordinates cannot be decomposed additively. A generalized logarithmic strain which is formulated in ‘updated’ Lagrangian coordinates and obtained by numerical integration of the Lagrangian strain rate is therefore introduced in this paper. By the use of this strain measure, which is additively decomposable, the plasticity model proposed by the authors can be extended to the finite strain range. It is shown that by correlating the generalized plastic modulus in the constitutive relations with the experimental uniaxial true stress‐logarithmic strain diagrams, the inelastic behaviour of steel structures subjected to nonproportional loading can be analyzed numerically by using the finite element method.
Finite element analysis of unbounded and incompressible fluid domains
Authors: Sharan Shailendra K. 
Published: August 2005

AbstractA finite element technique of analysing the hydrodynamic pressure, resulting from the vibration of a structure submerged in an unbounded fluid domain, is presented. A suitable boundary condition is proposed for the surface where the unbounded fluid domain is truncated. Pressure is assumed to be the nodal unknown and the fluid is treated as being incompressible and inviscid. The proposed method is computationally very efficient and its implementation in a finite element program is quite straightforward. The efficiency of the method is demonstrated by analysing some two‐dimensional problems.
Improved difference approximations to the heat equation
Authors: Lick Wilbert 
Published: August 2005

AbstractA method for obtaining difference equations from differential equations which has previously been applied to ordinary differential equations is here applied to the time‐dependent heat conduction equation as a representative example of parabolic partial differential equations. Explicit difference equations are derived which are stable for all values of αΔt/Δ2 and are also accurate. Implicit‐algorithms with improved accuracy are also derived. Problems in cartesian and cylindrical co‐ordinates are treated.
On an alleged philosophers' stone concerning variational principles with subsidiary conditions
Authors: Mang Herbert A. , Hofstetter Günter , Gallagher Richard H. 
Published: August 2005

AbstractIn general, the Lagrange multiplier method (LMM) is used to incorporate subsidiary conditions into variational principles. The Lagrange multipliers represent an additional field of independent variables. The attempt to satisfy subsidiary conditions without employing additional independent unknowns has led to the development of simplified variational principles (SVP). They are characterized by expressing Lagrange multipliers in terms of original field variables by means of the Euler‐Lagrange equations for the multipliers, providing their physical interpretation.In the first part of the theoretical investigation, systems with infinitely many degrees‐of‐freedom are studied. It is shown that the Euler‐Lagrange equations of a LMM based on a modification of the principle of minimum of potential energy (PMIPE) do not hold unconditionally, that is, for arbitrary subsidiary conditions, for the corresponding SVP. The second part of the theoretical investigation is concerned with systems with a finite number of degrees‐of‐freedom. The finite element method (FEM) is employed to discuss and compare the characteristics of the LMM and of the corresponding SVP. Contrary to the former, the latter are found to be problem‐dependent. Several shortcomings of the SVP are listed, including the possibility of obtaining an infinite sequence of singular coefficient matrices in the process of a systematic mesh refinement. Consequently, convergence of finite element solutions to the true solution in the limit of finite element representations is not guaranteed. The theoretical findings are corroborated by the results of a detailed numerical study.
Fixed‐point iteration to nonlinear finite element analysis. Part II: Formulation and implementation
Authors: Zeid Ibrahim 
Published: August 2005

AbstractThe finite element formulation and implementation of the Fixed‐Point Iteration (FPI) to linear/nonlinear structural static or dynamic analysis are developed. The direct and tangent formulations are presented and compared with the Newton–Raphson method (NRM). ‘Modified’ FPI algorithms have also been derived. A graphical interpretation of the method is introduced and suggested to call the FPI ‘the Saw method’. Mixing both the FPI and NRM is shown to be possible and may be useful in some applications. The overall strategies, iterative algorithms, and the appropriate norm convergence criteria necessary to implant the FPI into existing finite element programs are also included in the development.The superiority of the FPI over the NRM as seen from the development and the formulation lies in three major factors. First, the existing assembly process of element matrices is eliminated completely from the nonlinear finite element analysis. Secondly, the Gauss elimination or Crout's method is also eliminated. In the finite element terminology, this means that nonlinear structural static or dynamic responses can he obtained without recourse to the inverse of the structural stiffness matrix. Thirdly, the FPI can also be applied equally to linear structural analysis. Hence, the assembly process and the programming and storage associated with it can be removed from the existing finite element programs.While the FPI can solve problems that the NRM can, it will also be able to handle some engineering problems where the latter cannot. Buckling problems and problems where the force–displacement curve changes curvature are examples where the FPI is expected to be efficient.
Automated computer simulation of two‐dimensional elastostatic problems by the finite element method
Authors: Yokoyama Masaaki 
Published: August 2005

AbstractA software system for the automated computer simulation of two‐dimensional elastostatic problems by the finite element method is described. This system consists of two parts, automated mesh generation and automated stress analysis. The mesh generation is based on a method in which equilateral triangles are generated successively in the unmeshed region. Automated mesh refinement is carried out in the latter part of the simulation process. The stress analysis is based on the assumed stress hybrid method and the successive over relaxation method. The computer program developed for this paper can generate a succession of increasingly refined triangular meshes until a certain mesh convergence criterion is achieved. The mesh convergence criterion is based on a comparison of nodal stresses in successive analyses until all the stress differences are within a specified tolerance.
A study on the linear elastic stability of Mindlin plates
Authors: Cheung Y. K. , Chan A. H. C. , Tham L. G. 
Published: August 2005

AbstractThe debate on the performance of Lagrangian and Serendipity elements in Mindlin's plate theory has been going on for quite some time. Limited published results for static and vibration analysis based on exact integration demonstrated a drastic deterioration in accuracy as the thickness of the plate decreases, and reduced/selective integration schemes have been suggested to improve their performance. Appreciable improvement for Lagrangian elements has been recorded, but it is only marginal for the Serendipity elements. On the strength of such observations one would then be tempted to rule out the exact integration schemes and Serendipity elements.In this paper, the above problem is reviewed for stability analysis of plates. Two elements are chosen from each family, one representing the higher order and the other the lower order element. Contrary to published results, all elements can attain very accurate solutions independent of the integration schemes for a sufficiently restrained plate, although in general the Serendipity elements will require a more refined mesh than the Lagrangian ones. However, for loosely restrained plates, the solution failed when integration is performed by reduced/selective schemes. The failure marks the limitation of the reduced/selective schemes which have somehow introduced spurious modes into the system, but on the other hand it is ironical that these spurious modes in fact contribute to the improvement of performance of the restrained cases. Therefore, one can equally improve the Serendipity elements by a selective scheme which can introduce additional zero modes. A scheme based on (5 × 5) integration points for flexural stiffness and (3 × 3) integration points for shear stiffness improved the 17SE (Serendipity elements) remarkably. However, because of the lack of bounds in most cases, the use of reduced/selected schemes is still not recommended. Finally, this paper also proposed an approximate formulation of the geometric stiffness matrices to replace the full formulation. Such an approximate formulation reduces the number of variables considerably in the eigenvalue search and can still give reasonably accurate results for thin plates with a/t > 15.
An assessment of the semiloof shell element
Authors: Hellen T. K. 
Published: August 2005

AbstractThe semiloof shell element is the final product of years of research by Professor Irons and his colleagues, during which period the three‐dimensional quadratic displacement isoparametric elements were successively modified into Ahmad thick shells, then eventually, using discrete Kirchhoff hypotheses, into the thin semiloof shells. The retention of curved sides and midside nodes retains the familiar appearance of the two‐ and three‐dimensional isoparametric families, which enables ease of use with existing pre‐ and post‐processing facilities. The element has been widely adapted and used frequently for elastic analyses of wide‐ranging structures. It has also been developed for nonlinear geometric and material behaviour. However, despite the unparalleled generality in performance of this element, some unresolved problem areas still exist, particularly with use of reduced integrating rules. Such problems are highlighted in the paper and rectified where possible. A variety of problems are described to illustrate the above points and other interesting features, such as the treatment of thermal loading, and to emphasize the importance of this contribution to finite element technology by Professor Irons.
Relations between incompatible displacement model and hybrid stress model
Authors: Pian Theodore H. H. , Tong Pin 
Published: August 2005

AbstractAn examination of the variational formulations confirms the similarity between the incompatible displacement model and the assumed stress hybrid model that was pointed out by Irons in 1972. But the basic differences between the two are also identified. For 8‐node solid elements the assumed stress terms obtained through a rational procedure also agree with those deduced by Irons purely from his physical insight.
A study of the efficiency of iterative methods for linear problems in structural mechanics
Authors: Samuelsson A. , Wiberg N‐E. , Bernspång L. 
Published: August 2005

AbstractThe efficiency of iterative methods in linear structural mechanics is studied. The efficiency concerns the calculation time, the numerical accuracy and the core storage needed. We state that iterative methods are effective in connection with hierarchical improvement of a primary approximation. Three iterative methods are studied: the conjugate gradient method preconditioned by a modified incomplete factorization matrix, the same method preconditioned by a matrix obtained from natural factors on elemental level, and a Jacobi integration preconditioned by viscous relaxation split in an element‐by‐element way. We make comparisons with direct methods, Gaussian elimination and factorization by use of natural factors.
Finite element methodology for elastic‐plastic fracture problems in three dimensions
Authors: Moyer E. T. , Liebowitz H. 
Published: August 2005

AbstractThe governing finite element system for elastic‐plastic analysis of fracture specimens in three dimensions is formulated. The formulation accounts for mixed material hardening, finite strains, finite rotations and plastic incompressibility. The implementation of these aspects into a computational formula is presented and alternative formulations are compared. Small strain theory is recovered as a special case of the present formulation.Analysis is performed on a finite thickness centre‐cracked specimen. The grid characteristics required for converged solutions are discussed. The effects of material hardening model and specimen thickness are studied. The local yield state is examined as a gauge of the local deformation processes. The implications for the fracture behaviour of the specimen are discussed.Local surface displacements are compared to experimentally measured yield surfaces. The formulation is shown to predict extremely accurate local deformation in the neighbourhood of the crack front. Contrary to the few three‐dimensional fracture studies carried out to date, this analysis concentrates on the local deformation behaviour which ultimately controls fracture. Accurate resolution of this behaviour is essential before meaningful fracture criteria in three dimensions can be developed.
Analytical tools for systematic transonic design
Authors: Sobieczky Helmut 
Published: August 2005

AbstractAnalytical flow models in the near sonic domain of compressible flow are discussed as a supplementary background to elliptic continuation and fictitious gas design methods, to extend shock‐free design into choked flow design, shock‐wave construction, with the aim of developing new analysis programs and of developing experience for three‐dimensional configuration design.
Inverse design of multiholed internally cooled turbine blades
Authors: Kennon Stephen R. , Dulikravich George S. 
Published: August 2005

AbstractA methodology is described for the inverse design and/or analysis of coolant flow passage shapes in multiholed internally cooled turbine blades. The user of this technique may specify the temperature (or heat flux) distribution along the aerofoil outer surface. In addition, the temperature on the surface of each of interior coolant flow passages (holes) may be specified. The numerical solution of the outer hot gas flow field determines the remaining unspecified aerofoil outer surface quantity—surface heat flux if temperature was originally specified or vice versa. The position and shape of each turbine blade coolant hole is then found iteratively by solving the heat conduction problem within the solid portions of the blade. This solution procedure involves satisfying the dual Dirichlet and Neumann specified boundary conditions of temperature and heat flux on the outer boundary of the aerofoil. The inner hole geometry is then modified using an optimization procedure in such a way as to minimize the error in satisfying the specified Dirichlet temperature boundary condition on the surface of each of the evolving interior holes. Results are shown for single‐hole and double‐hole configurations that have analytic solutions and for a realistic turbine blade design problem.
Optimization in design processes: An informatics point of view
Authors: Van Den Dam R. F. , Boerstoel J. W. , Daniëls H. A. M. 
Published: August 2005

AbstractThe purpose of this paper is to outline the optimization‐system development at NLR. The paper starts with a discussion of the potential of mathematical optimization techniques in aeronautical engineering. Subsequently, the main requirements to be met by a general‐purpose optimization system are given. Following this, the implementation at NLR is described, and some examples of applications are presented to illustrate the optimization capabilities.
Hydrostatic loading and stability analysis of structures with large displacements
Authors: Bergan P. G. , Mathisen K. M. 
Published: August 2005

AbstractA method for the computation of hydrostatic forces on cable, truss, beam, plate and shell type structures is presented. A general large displacement formulation is assumed which allows for displacements and rotations of unlimited size. Equilibrating forces for nodal points as well as incremental force‐displacement relationships are given. Various ways of making the geometric load matrix symmetric for incremental analysis is discussed. Alternative strategies for the incremental–iterative solution is also treated. A method for the determination of the hydrostatic stability of floating structures is suggested. Metacentres and centres of buoyancy for rotations about principal axes in the water plane are automatically computed. The paper presents three examples of applications: a pipe which is partially submerged, a full overturning of a floating space frame and, finally, a hydrostatic stability analysis of a ship.
Influence of rate of porepressure generation on the stress–strain behaviour of soils
Authors: Hicks M. A. , Smith I. M. 
Published: August 2005

AbstractIn a previous publication1 it was suggested that the most fruitful area for the deployment of ‘complicated’ soil models—i.e. those involving more than, say, 6 parameters—lay in analyses of undrained and partially drained problems. The present paper extends previous drained and undrained analyses to the partially drained state, for two rather simple boundary value problems.
Nonlinear analysis and elastic–plastic load‐carrying behaviour of thin‐walled spatial beam structures with warping constraints
Authors: Wunderlich W. , Obrecht H. , Schrödter V. 
Published: August 2005

AbstractAn analysis of the elastic–plastic load‐carrying behaviour of thin‐walled spatial beam structures is presented. It is based on a beam theory valid for large displacements and rotations, which admits arbitrary cross‐sections, curved axes, initial imperfections, a general material description, and which fully accounts for the influence of warping constraints as well as the stress‐history dependence of the elastic–plastic shear moduli. An incremental updated Lagrangian viewpoint is adopted in the derivation of the basic beam equations from a generalized variational principle, and in the numerical solution procedure the displacement–finite element approach is followed. The associated tangential stiffness matrices are obtained by direct numerical integration of the governing incremental differential equations rather than through the use of shape functions in connection with a virtual work principle. Applications of the theory are given in which the influence of the loading configuration, material parameters, geometric nonlinearities and warping constraints on the load‐carrying behaviour and on the bifurcation and ultimate loads of thin‐walled beam structures is explored.
An integral formulation applied to the diffusion and Boussinesq equations
Authors: Taigbenu Akpofure , Liggett James A. 
Published: August 2005

AbstractA new integral method is proposed here to solve the diffusion equation (confined flow) and the Boussinesq equation (unconfined flow) in a two‐dimensional porous medium. The method, based on Green's theorem, derives its integral representation from the portion of the original differential equation with the highest space derivatives so that the resulting kernel of the integral representation is not time dependent. Compared to an earlier integral formulation, namely the direct Green function, based on the same theorem, the kernel is simpler so that the present theory provides a more efficient numerical model without compromising accuracy. An iterative scheme is employed along with the theory to achieve solutions to the non‐linear Boussinesq equation. Concepts used in the finite difference and finite element methods enable simplification of the temporal derivative. The method is tested with success on a number of numerical examples from groundwater flow.
Boundary value techniques for finite element solutions of the diffusion‐convection equation
Authors: Evans D. J. , Abdullah A. R. 
Published: August 2005

AbstractIn this paper, the formulation of six‐point and nine‐point finite element equations for the solution of the diffusion‐convection equation is presented. The six‐point equation requires the solution of a tridiagonal system of equations and the nine‐point centred equation is treated as a solution of a boundary value problem which leads to a large linear system of equations.Some numerical experiments are presented and the comparison with existing methods is included.
On the performance of Mindlin plate elements in modelling plate‐elastic medium interaction: A comparative study
Authors: Rajapakse R. K. N. D. , Selvadurai A. P. S. 
Published: August 2005

AbstractThis paper discusses the finite element analysis of the flexural interaction between an elastic plate and an elastic half‐space. The applicability of certain Mindlin‐type plate elements, based on reduced integration techniques, to this class of interaction problem is investigated. A series of numerical computations reveal that those elements which possess spurious zero‐energy modes are deficient in modelling properly the interaction phenomenon. It is also found that the ‘heterosis’ plate element reported in the literature is capable of modelling the plate‐elastic medium interaction very efficiently.