bluuebunny/crossref_metadata_2025 huggingface dataset:
Finite plane strain deformations of nonlinear viscoelastic rubber‐covered rolls
Authors: Bapat C. N. , Batra R. C.
Published: August 2005

Finite deformations of a nonlinear viscoelastic rubber layer bonded to a uniformly rotating rigid cylinder and indented by another rigid cylinder are studied by the finite element method. The problem formulation includes both material and geometric nonlinearities. The effect of the change in the thickness of the layer, its speed of rotation and its material properties on the pressure distribution at the contact surface, and other aspects of the deformation of the layer, are studied.
A hybrid algorithm for reducing matrix bandwidth
Authors: Armstrong Bruce A.
Published: August 2005

A hybrid algorithm for reducing the bandwidth of symmetric matrices is described in terms of a finite element grid. The new algorithm produces significantly lower bandwidths than either the commonly‐used Gibbs–Poole‐Stockmeyer (GPS) or Cuthill–McKee (CM) algorithms, with run times comparable to the original CM algorithm. The new hybrid algorithm uses the GPS algorithm as a preprocessor to provide a good initial node numbering for the author's node‐shuffling algorithm, which accounts for variable degrees‐of‐freedom per node (DOF/node). The hybrid algorithm was tested on the 30 benchmark problems that were compiled by Everstine, and on 10 supplemental problems with variable DOF/node. Bandwidths and CPU times are presented for all problems.
A refined finite element model for the analysis of elastic–plastic frames
Authors: Corradi Leone , Poggi Carlo
Published: August 2005

A finite element model for the elastic–plastic analysis of plane frames is proposed. The formulation is based on the independent modelling of the displacement and plastic strain fields; the latter is modelled both over the cross‐section and along the element length as function of a finite number of parameters, which are considered as an extra set of independent variables, in addition to nodal displacements. Stress redistribution is allowed for over the cross‐section, but not over the element length, where the distribution of stress resultants (axial forces and bending moments) is imposed consistently with the assumed displacement model; stress redistribution in terms of stress resultants becomes possible only because of the finite number of redundancies introduced when assembling. It is shown that the model can be formulated in such a way that not only compatibility and elasticity, but also equilibrium (in the sense of beam theory), are fully complied with and only the plastic portion of the constitutive relationship is approximately fulfilled, even if, in principle, to any desired level of accuracy. The model produces accurate results, including a detailed representation of the spreading of plastic zones, with a fairly limited number of elements.
A finite element method for contact problems related to fracture mechanics
Authors: Yagawa G. , Hirayama H.
Published: August 2005

A finite element method for contact problems in crack mechanics is developed on the basis of the penalty function method. The method is successfully applied to three important problems in fracture mechanics: a crack propagated from a pin hole, a two‐point supported specimen with an edge crack loaded by a stamp, and a thick plate with a through‐wall crack under bending force.
A total lagrangian formulation for the geometrically nonlinear analysis of structures using finite elements. Part I. Two‐dimensional problems: Shell and plate structures
Authors: Oliver J. , On̄ate E.
Published: August 2005

A total Lagrangian finite element formulation for the geometrically nonlinear analysis (large displacement/large rotations) of shells is presented. Explicit expressions of all relevant finite element matrices are obtained by means of the definition of a local co‐ordinate system, based on the shell principal curvature directions, for the evaluation of strains and stresses. A series of examples of nonlinear analysis of shell and plate structures is given.
The post‐processing approach in the finite element method—Part 3: A posteriori error estimates and adaptive mesh selection
Authors: Babuška I. , Miller A.
Published: August 2005

This paper is the final in a series of three in which we have discussed a finite element post‐processing technique. Here we shall deal with the questions of adaptive mesh selection and a posteriori error estimation. Some numerical examples computed by the FEARS program will be used to illustrate the approaches taken.
Thin turbomachinery blade design using a finite‐volume method
Authors: Soulis Johannes V.
Published: August 2005

A numerical method is presented for the design of thin turbomachinery blades with specified whirl velocities across the blade span. The numerical scheme involves iteration between the directs solution of a finite‐volume method developed earlier on by Soulis1 and a design solution.

The finite‐volume method, which is a combination of finite elements and finite differences, solves the three‐dimensional, inviscid, steady arid potential flow through turbomachinery blade rows in the incompressible, compressible and transonic flow range. In the design step, the whirl velocity distribution is specified across the blade span (Dirichlet boundary condition). The design procedure yields a new set of co‐ordinates for the blade geometry which are used in the next iteration of the direct solution. However, in the present analysis only thin turbomachinery blades are designed, although a fully three‐dimensional numerical method is used (the whirl velocity components of the flow field are averaged over the blade suction and pressure surface).

The numerical method has been used to design free‐vortex thin turbomachinery blades. Results show that the new numerical procedure is a comparatively economic and reliable method for designing thin turbomachinery blades. It may form the baseline for complete three‐dimensional turbomachinery blade designs.
An improved three‐noded triangular element for plate bending
Authors: Fricker A. J.
Published: August 2005

A new three‐noded triangular element for plate bending is described. The element is based on an earlier stress‐smoothed triangular element due to Razzaque,1 but extra internal ‘bubble’ functions are included to make it more flexible. The accuracy of the new element is compared with that of a number of other high‐performance triangular elements. It is concluded that the present element and that due to Hansen, Bergan and Syvertsen2 are the two most accurate triangular thin plate elements currently available. The extra lines of FORTRAN required to convert Razzaque's shape function subroutine to that for the new element are given, thus making the new element easy to implement in any general‐purpose finite element program.
Analysis of some fully‐discrete algorithms for the one‐dimensional heat equation
Authors: Hughes Thomas J. R. , Tezduyar Tayfun E.
Published: August 2005

A fully discrete stability and accuracy analysis of some algorithms for the one‐dimensional heat equation is presented. Results illustrate that 2‐pass explicit schemes which simultaneously employ lumped and coupled capacity matrices are capable of improved performance over the standard 1‐pass explicit scheme.
Discretization of the expliclt enthalpy method for planar phase change
Authors: Tacke Karl‐Hermann
Published: August 2005

A procedure to discretize explicit enthalpy formulations for one‐dimensional planar phase change problems is derived, which removes numerical oscillations in temperature and phase front position. The technique is based on an enthalpy balance for the control volume containing the phase front in combination with linearized temperature profiles near the phase front. A continuous casting solidification problem and a problem with known analytical solution are applied to demonstrate the effect of the scheme.
Nonlinear static and dynamic analysis of circular plates and shallow spherical shells using the collocation method
Authors: Nath Y. , Dumir P. C. , Bhatiaf R. S.
Published: August 2005

The present work investigates the efficacy and applicability of interior global orthogonal point collocation method to the axisymmetric nonlinear analysis of elastic circular plates and shallow spherical shells subjected to uniformly distributed transverse load. Spacewise discretisation has been carried out using a polynomial expansion with the zeros of a Chebyshev polynomial as collocation points. Timewise integration has been carried out with Newmark k‐β scheme corresponding to average acceleration method. The static response and snap‐through buckling results, as well as, the dynamic response and dynamic buckling results under a uniformly distributed step load have been obtained and found to agree closely with the available results.
Modelling and estimation for a moving boundary problem
Authors: Okuyiga M. O. , Ray W. H.
Published: August 2005

The displacement of a slightly compressible liquid by another in a porous medium has been modelled. This problem, which involves a moving boundary, has been numerically solved for the one‐dimensional case by using the Galerkin method. State and parameter estimation have been carried out using the extended Kalman filter.
A curved quadrilateral element for static analysis of shells with geometric and material nonlinearities
Authors: Yang T. Y. , Saigal Sunil
Published: August 2005

A 48 degrees‐of‐freedom quadrilateral element, including the effect of both material and geometric nonlinearities, is formulated and appropriate numerical procedures are adopted for the development of a systematic and efficient approach for the static nonlinear analysis of general shell structures. The element surface is described by a variable‐order polynomial in curvilinear co‐ordinates. The displacement functions are described by bicubic Hermitian polynomials in curvilinear co‐ordinates. Without being confined to the assumption of axisymmetry, this formulation allows for the treatment of shells with a more general shape and with a complex spread of plastic zones. In the formulation for geometric nonlinearity, the total Lagrangian approach is adopted. Only small strains and small rotations are allowed. In the formulation for plastic deformation, the concept of a layered element model is used. In the inelastic range, the material is assumed to obey the Von Mises yield criterion and the Prandtl–Reuss flow rule. A tangential stiffness formulation is combined with the modified Newton–Raphson iteration method for the solution of nonlinear problems. A systematic choice of examples ranging from fiat plates to cylindrical panels and to spherical caps is solved and compared with available solutions to evaluate the recommended formulations and procedures in terms of their accuracy and efficiency.
The elastic–plastic analysis of frames by the theorems of structural variation
Authors: Majid K. I. , Celik T.
Published: August 2005

The theorems of structural variation for rigidly jointed frames are extended to cover the nonlinear elastic–plastic analysis of frames to collapse. Strain hardening and other material changes are included in the analysis. It is shown that the entire load–deflection history of a frame, following the successive formation of plastic hinges up to and including collapse, is obtained from a single initial elastic analysis.

The manner in which these theorems are used to insert real (or plastic) hinges to a frame is presented and details of the manual calculations involved in the elastic–plastic analysis of a portal is given to demonstrate the simplicity of the method. This is followed by a comparison of the results with those obtained experimentaly by Baker and Charlton. The versatility of the method is then demonstrated by altering the shape of a frame before its elastic–plastic analysis.
Combined convection in an annulus applied to a thermal storage problem
Authors: Zenen S. R. , Collins M. W. , Simonson J. R.
Published: August 2005

In a solar energy application involving thermal storage, one of the heat transfer situations is that of combined convection in vertical annuli for rather complex wall thermal boundary conditions. Predictive data of a high order of reliability are needed for incorporation within the suite of programs treating the whole problem.

The program reported here treats the complete equations for combined free and forced convection in a vertical annulus. It allows for viscosity and density variation with temperature, and a variable heat flux or temperature at the walls. It was developed from a similar program for circular tubes.

Comparisons are made with published data for velocity profiles and heat transfer performance. These are good, and show the step‐wise energy balance method is necessary and valid.

The strategy of generation of the required data is explained, together with sample output. These data are themselves analysed computationally; the performance equations agree with original predictions typically to within ± 11 per cent, with a standard deviation of around 2 per cent.

The working fluid is water with 37 per cent ethylene glycol. Upward heated and downward cooled flows give aided combined convection. For the given design, laminar flow is predicted for the Reynolds number range 1800–2200.
An improved boundary integral equation method for Helmholtz problems
Authors: Adeyeye J. O. , Bernal M. J. M. , Pitman K. E.
Published: August 2005

The eigenvalue problem for the Laplace operator is numerical investigated using the boundary integral equation (BIE) formulation. Three methods of discretization are given and illustrated with numerical examples.
Modelling and state estimation for a two‐dimensional moving boundary problem
Authors: Okuyiga M. O. , Ray W. H.
Published: August 2005

The five‐spot waterflooding problem has been modelled as a two‐dimensional moving boundary problem with a sharp interface separating the water and oil regions. The Galerkin method was used to solve for the shape and movement of the interface, as well as for the pressures in the reservoir. Having obtained a working model, the extended Kalman filter was then used to estimate the interfacial position when using corrupted pressure measurements from a single sensor in the field.
Mixed finite element procedure for soil–structure interaction and construction sequences
Authors: Desai C. S. , Lightner J. G.
Published: August 2005

Mixed 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

The 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

The 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.
Singularity of collapsed Q‐8 finite element
Authors: Banthia Vinod
Published: August 2005

The ability of the collapsed Q‐8 finite element to model strain singularities is studied in this paper. It is shown that its ability to model an r−1 singularity in strains depends strongly on the element size and number of Gauss points used for sampling stresses inside an element.
Finite element analysis of unbounded and incompressible fluid domains
Authors: Sharan Shailendra K.
Published: August 2005

A 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

A 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

In 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

The 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

A 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

The 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

The 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

An 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

The 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

The 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

Analytical 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

A 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

The 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.
Finite strain plasticity in convected frames
Authors: Pegon P. , Guélin P.
Published: August 2005

A rate‐type formulation of quasi‐static boundary value problems using convected material frames is proposed and an associated method of numerical solution is derived. Two numerical problems are presented: the first deals with a significant validation example, the second with a necking bifurcation analysis.
Hydrostatic loading and stability analysis of structures with large displacements
Authors: Bergan P. G. , Mathisen K. M.
Published: August 2005

A 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

In 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

An 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

A 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.
Analysis of spurious eigenmodes in finite element equations
Authors: Bates S. , Cathers B.
Published: August 2005

Numerical analysis of difference schemes often reveals the presence of eigenmodes which do not feature in the continuum solution. An examination of the dispersion relation shows how the spurious and physical modes interact. The behaviour of certain wave‐profiles was predicted using this analysis and the results confirmed by numerical experiment.
Boundary value techniques for finite element solutions of the diffusion‐convection equation
Authors: Evans D. J. , Abdullah A. R.
Published: August 2005

In 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

This 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.
A dynamic finite element preanalyser
Authors: Murti V. , Valliappan S.
Published: August 2005

In a mixed‐mode dynamic crack propagation problem using remeshing, certain elements in the neighbour‐hood of the propagating crack‐tips may have dimensions that do not comform to the allowable limit. Hence, they need to be refined by recursively bisecting the exclusive sides until a global conformity is achieved. ADFEP (a dynamic finite element preanalyser) has been written for this purpose. Apart from this objective, ADFEP has a wide spectrum of salient applications to various discretization related problems, such as automatic irregular generation, adaptive refinement and others. A simple energy criterion to determine the cut‐off frequency of a transient loading, and the concept of preprocessing the input loading using digital filters introduced by Valliappan and Murti1 are employed. They constitute the first module of ADFEP. The second (main) module consists of element splitting procedures where algorithms based on graph theory and element splitting templates have been extensively used. The notion of a ‘cross digraph’ introduced to carry a multiple ‘weights’ and to avoid duplication in node‐generation, is especially useful in three‐dimensional element splitting techniques. Finally, numerical inverse isoparametric mapping techniques presented by Murti and Valliappan2 are also used to interpolate the nodal quantity vectors at the newly generated nodes. These vectors are needed as initial values in subsequent iterations for a dynamic restart. This aspect, together with the node renumbering scheme, is included in the third module of ADFEP. Some illustrative examples are included to elucidate the effectiveness of ADFEP.
A finite element solution method for contact problems with friction
Authors: Chandrasekaran N. , Haisler W. E. , Goforth R. E.
Published: August 2005

A new finite element solution method for the analysis of frictional contact problems is presented. The contact problem is solved by imposing geometric constraints on the pseudo equilibrium configuration, defined as a configuration at which the compatibility conditions are violated. The algorithm does not require any a priori knowledge of the pairs of contactor nodes or segments. The contact condition of sticking, slipping, rolling or tension release is determined from the relative magnitudes of the normal and tangential global nodal forces. Contact iterations are in general found to converge within one or two iterations. The analysis method is applied to selected problems to illustrate the applicability of the solution procedure.
Using eigenvector projections to improve convergence in non‐linear finite element equilibrium iterations
Authors: Eriksson Anders
Published: August 2005

In an earlier paper a method for calculation of non‐linear structural response was described. The method is based on an algorithm, proposed by Bergan, including simultaneous iterations in the load and displacement spaces. A method for selective damping of solution components parallel to critical eigenvectors was proposed reducing the risk for diverging equilibrium iterations.

This method is, in the present paper, shown to be related to the ‘dynamic relaxation’ approach. The method has been further studied for practical problems, and especially adapted for the analysis of plate buckling. A method for variable damping is proposed, and compared to existing methods. The conclusions are that damping, based on eigenvector projection, is an efficient way to improve the stability in the iterations, and in this an alternative to other methods for choice of optimum corrections in N–R schemes. The extra computational effort is considered worth while in cases where restarts in the calculation are not desired.

In the paper, suitable criteria for reformulation of the tangential relation during iterations in a step are also discussed.
An improved computational technique for perturbations of the generalized symmetric linear algebraic eigenvalue problem
Authors: Bickford William B.
Published: August 2005

A technique is developed and presented which improves the accuracy of the predictions for the eigenvalues of the usual first order perturbation scheme for the generalized symmetric linear algebraic eigenvalue problem. The improved method very simply replaces the usual B‐norms appearing in the denominator of the expressions for the first order changes in the eigenvalues by BP‐norms where BP is the perturbed B matrix. With increasing sizes for the perturbations the improved technique produces results whose accuracy approaches those of the usual second order predictions. Numerical studies are presented to support the analysis.
The tanh transformation for the solution of singular integral equations
Authors: Tsamasphyros G. , Androulidakis P.
Published: August 2005

Using a tanh transformation a quadrature formula for the evaluation of singular integrals is obtained. The formula has the same step length h as the formula for regular integrals derived by F. Stenger. These quadrature formulae are valid for end point singularities of any order and their error exhibits an exponential decay when the number of integrations tends to infinity.

Using these formulae the solution of singular integral equations does not depend on the order of the end point singularities. Furthermore the collocation points are given by a very simple equation and, in the case of constant coefficients, by a closed‐form formula.
BEM simulation of cathodic protection systems employed in infinite electrolytes
Authors: Zamani N. G. , Chuang J. M. , Porter J. F.
Published: August 2005

This paper describes the proper external potential formulation of a cathodic protection system employed for corrosion prevention of structures in infinite electrolytes. The boundary condition associated with the mathematical formulation is not of the standard type encountered in hydrodynamic, electrostatic or heat transfer applications. The developed mathematical model is discretized by the boundary element technique, which is then solved iteratively by the Newton–Raphson method.
A hybrid model for prismatic solids
Authors: Cannarozzi Mario
Published: August 2005

A finite prism approach for the approximate analysis of three‐dimensional solids is proposed. The approach is based on a semi‐algebraic assumed stress hybrid model, according to Pian's scheme. Prismatic solids with various end conditions can be analysed with a traditional matrix‐displacement procedure, thus enlarging the possibilities offered by analogous compatible models.
Practical stability analysis of finite difference equations by the matrix method
Authors: Sucec James
Published: August 2005

It is shown how the various norms of the coefficient matrix of a set of finite difference equations can, in many cases, be employed in an easy, straightforward fashion to find sufficient conditions for stability in situations involving non‐periodic boundary conditions and variable coefficients. With the aid of the easily computed norms, particularly the infinite norm, one does not have to rely on the necessary condition provided by the spectral radius, which has been the main basis of criticism of the matrix method in the past.
The dynamic analysis of a flat plate under a moving load by the finite element method
Authors: Wu Jong‐Shyong , Lee Ming‐Ling , Lai Tser‐Shyong
Published: August 2005

The object of this paper is to analyse by the finite element method the dynamic responses of a flat plate subjected to various moving loads. First of all the actual continuous flat plate was replaced by a discrete system composed of isoparametric rectangular plate elements. And then the elementary and overall stiffness and mass matrices were determined and the natural frequencies and mode shapes of the flat plate were solved. Next, the Newmark direct integration method was used to find the dynamic responses of the flat plate.

The effects of eccentricity, acceleration and initial velocity of the moving load, and the effect of span length were the key points of study. The dynamic behaviour of a multi‐span flat plate supported by the beam members of rigid plane frames and subjected to the action of a series of moving loads (in identical or opposite directions) were also investigated.
Least‐squares finite element method and preconditioned conjugate gradient solution
Authors: Carey G. F. , Jiang B. N.
Published: August 2005

A least‐squares variational procedure for first‐order systems of differential equations and an approximate formulation based on finite elements are developed. Error estimates, a condition number bound and analysis of weighting factors are given. Steepest descent and conjugate gradient solution procedures are examined, and an appropriate preconditioner constructed which is demonstrated to yield rapid convergence and to be insensitive to problem size. Numerical studies of rates of convergence for a test problem are given.