bluuebunny/crossref_metadata_2025_split huggingface dataset:
Discrete orthogonalization of parameter lines on curved surfaces for finite element analysis of thin shells
Authors: Eberhardsteiner J. , Mang H. A. 
Published: August 2005

AbstractOrthogonal curvilinear co‐ordinates represent the logical choice for description of the middle surface of the majority of shells in engineering practice. By means of orthogonalization of originally skew parameter lines at integration points for shell analysis by the finite element method (FEM), the remaining minority can be treated without having to resort to skew curvilinear co‐ordinates. Therefore, it does not seem to be worth while to extend existing computer codes for shell analysis by the FEM, restricted to orthogonal curvilinear co‐ordinates, to general curvilinear co‐ordinates. Depending on the structure of such a code, this extension may require a substantial amount of recoding. (However, it is advisable to consider general curvilinear co‐ordinates if a new computer code for shell analysis by the FEM, based on thin‐ or thick‐shell theory, is written).Based on these considerations, the concept of ‘discrete orthogonalization of parameter lines’ has been developed. It is presented in this paper and applied to the analysis of a hyperbolic paraboloid groined vault subjected to dead load. In the numerical investigation it is demonstrated that treating skew parameter lines incorrectly as orthogonal has a significant effect on the results for the displacements and the internal forces.
A comparison of Galerkin and streamline techniques for integrating strains from an Eulerian flow field
Authors: Agrawal Ajay , Dawson Paul R. 
Published: August 2005

AbstractTwo methods are compared for integrating the strains that can arise in finite element solutions for Eulerian velocity fields associated with large strain material forming processes. With the Galerkin formulation, partial differential equations for the deformation gradient are solved over the entire domain based on a weighted residual; with the streamline integrated technique, the corresponding ordinary differential equations are integrated along characteristic lines. Both methods have yielded accurate integrations for the radial flow and planar rolling problems studied. A finite element technique is also presented for ensuring that the free surfaces of the fluid flow are streamlines. This technique has been used for ensuring proper boundary conditions in the rolling analysis.
A study of mathematical programmingmethods for structural optimization. Part II: Numerical results
Authors: Belegundu Ashok D. , Arora Jasbir S. 
Published: August 2005

AbstractVarious mathematical programming methods for structural optimization are studied. In a companion paper, these methods have been studied based on certain theoretical considerations. In this paper, the methods are studied based on solving a set of test problems. The methods that are studied include recursive QP, feasible directions, gradient projection, SUMT and multiplier methods. Various computer codes have been developed, and are studied together with some existing programs such as CONMIN and OPTDYN. The test problems considered have 3–47 design variables and 3–252 constraints. The evaluation criteria consist of studying the accuracy, reliability and efficiency of a code. It turns out that globally convergent algorithms (multiplier methods, in particular) are very reliable but not efficient. Primal algorithms (like CONMIN), which are not proved to be globally convergent, are efficient but not reliable.
A finite element method for analysing skin effect in conductors with unknown values of surface boundary conditions
Authors: Gasiorski A. K. 
Published: August 2005

AbstractThis paper presents a method of analysing the distribution of a two‐dimensional electromagnetic field in a conducting medium of known cross‐section carrying sinusoidal current and of unknown numerical values of boundary conditions on conductors surfaces. The method combines the finite element and separation of variables methods. An example is given of application of the method to calculation of impedance and electrodynamic forces of two thick, full and round conductors carrying oppositely directed sinusoidal currents. On the basis of numerical computation, graphs of resistance, reactance and electrodynamic forces are plotted.
Comparison of some single‐step methods for the numerical solution of the structural dynamic equation
Authors: Penry S. N. , Wood W. L. 
Published: August 2005

AbstractThis paper compares the performance of the SS22 and SS23 (References 1 and 2) single step algorithms for the numerical solution of the second‐order structural dynamic equation and a related new algorithm SS32B applied to the equivalent first‐order system, with sine and step forcing functions. Various aspects of stability relevant to these equations are discussed.
A consistent finite element technique for recovery of distributed reactions and surface tractions
Authors: Haber Robert B. 
Published: August 2005

AbstractAn effective technique is presented for recovering surface tractions and distributed reaction forces from finite element displacement solutions of structural mechanics problems. Nodal values of surface tractions and assumed trial functions are used to represent the distribution of surface stresses. Equations obtained from the familiar Galerkin formulation are used to compute the nodal traction values. The method is demonstrated to be efficient and highly accurate, even in the presence of jump conditions or singularities. Extensions of the method are possible for recovering secondary solution variables in non‐structural finite element applications.
Continuously deforming finite elements
Authors: Mueller Alan C. , Carey Graham F. 
Published: August 2005

AbstractA general class of time‐dependent co‐ordinate transformations is introduced in a variational formulation for evolution problems. The variational problem is posed with respect to both solution and transformation field variables. An approximate analysis using finite elements is developed from the continuous variational form. Modified forms of the variational functional are considered to ensure the deforming mesh is not top irregular. ODE system integrators are utilized to integrate the resulting semidiscrete systems. In Part I we consider the formulation for problems in one spatial dimension and time, including, in particular, convection‐dominated flows described by the convection‐diffusion, Burgers' and Buckley–Leverett equations. In Part II the extension of the method to two dimensions and supporting numerical experiments are presented.
A generalized displacement method for the finite element analysis of thin shells
Authors: Kui Li Xi , Liu Guo Qiang , Zienkiewicz O. C. 
Published: August 2005

AbstractThe shear locking problem for the bilinear degenerated thick shell elements, when used in the context of thin shell structures, can be overcome by a generalized displacement method presented in this paper. The transverse shear energy in the degenerated thick shell elements is totally suppressed by introducing discrete Kirchhoff constraints in each element. The constrained variational problem based on the nodal displacement space is transformed into an unconstrained one based on a so‐called generalized displacement subspace. It is shown that shear looking phenomena completely disappear and no degradation of results is observed as the ratio of thickness to span approaches zero.
On the implementation of iterated defect correction to finite difference methods for elliptic boundary‐value problems
Authors: Hertling JÖRg 
Published: August 2005

AbstractWe present a method which makes it possible to apply the idea of iterated defect correction to finite difference methods for the numerical treatment of partial differential equations. The method yields numerical approximations of very high accuracy for the solution, while the corresponding algebraic systems of equations still have ‘reasonable’ size.
An approach for undrained geotechnical problems accounting for the development of partial saturation
Authors: Genna Francesco , Gioda Giancarlo 
Published: August 2005

AbstractA mathematical programming approach is discussed for the finite element‐analysis of two‐phase undrained problems in the field of geomechanics. This approach enables us to account for the possible development of partially saturated zones in the geotechnical medium, due to the attainment of a given lower limit in the pore pressure distribution. Two alternative formulations are presented, both of them in terms of linear complementarity and quadratic programming problems, and the computational advantages of one of them are illustrated. The main characteristics of a step‐by‐step solution technique are presented. Finally, the solutions of some test problems are discussed and compared with those deriving from the traditional analyses in which the development of partial saturation is neglected.
Unilateral buckling of thin elastic plates by the boundary integral equation method
Authors: Bezine G. , Cimetiere A. , Gelbert J. P. 
Published: August 2005

AbstractThe unilateral buckling of thin elastic plates, according to Kirchhoff's theory, is studied by using a boundary integral method. A representation for the second member of the equation is given. In the matrix formulatiea, boundary unknowns are eliminated; therefore, the unilateral buckling problem reduces to compute the eigenvalues and the eigenvectors of a matrix depending on the contact zone with the rigid foundation. An iterative process allows this zone and the buckling load to be computed. The capacities of the proposed method are illustrated by four examples.
Analysis of laminated composite plates using a higher‐order shear deformation theory
Authors: Phan N. D. , Reddy J. N. 
Published: August 2005

AbstractA higher‐order shear deformation theory is used to analyse laminated anisotropic composite plates for deflections, stresses, natural frequencies and buckling loads. The theory accounts for parabolic distribution of the transverse shear stresses, and requires no shear correction coefficients. A displacement finite element model of the theory is developed, and applications of the element to bending, Vibration and stability of laminated plates are discussed. The present solutions are compared with those obtained using the classical plate theory and the three‐dimensional elasticity theory.
Nonlinear subincremental method for determination of elastic–plastic–creep behaviour
Authors: Ottosen Niels Saabye , Gunneskov Ole 
Published: August 2005

AbstractThe frequently used subincremental method has so far been based on a linear interpolation of the total strain path within each main step. This method has proven successful when elastic–plastic behaviour and secondary creep is involved. The present paper proposes a nonlinear subincremental method applicable to general elastic–plastic–creep behaviour including problems with a highly nonlinear total strain path caused by the occurrence of creep hardening. This nonlinear method degenerates to the linear‐approach for elastic–plastic behaviour and when secondary creep is present. It is also linear during step loadings and it becomes increasingly more nonlinear, the more creep hardening deformations dominate the behaviour. A wide range of structures are analysed and the results from both subincremental methods are compared; the nonlinear strategy increases the accuracy by a factor of typically 3–5 without affecting the computer time. Moreover, the implementation of the nonlinear method is extremely simple. The optimum number of substeps in each main step is found to be around 5. For such a choice, the advantage of using the subincremental method as compared to the more conventional solution technique, where only one type of time step is used, is a significant reduction in computer time without, in practice, affecting the accuracy.
On the heat‐flow distribution from and the temperature profile on an equally heated rectangle, calculated by series development
Authors: Nieuwenhuizen J. K. 
Published: August 2005

AbstractA method is proposed to approximate the solutions of a certain class of differential equations, linear or nonlinear, in two or three, dimensions, provided that the boundary conditions are given on a rectangle or a parallelepiped, respectively. For other boundary shapes the co‐ordinate system must be transformed to meet that requirement. As in illustration, an example is given for the solution of Poisson's equation in two dimensions with a constant heat source, giving the temperatures on the rectangle together with the heat‐flow distribution along its edges. The basis of the method is a Taylor‐series development around one point; the result is given in terms of as many partial derivatives in that point as is desired. A similar method has already been described by Small2 for the ‘heat equation’ ∂θ/∂t = ∂2θ/∂x22. Compared with finite difference and finite element solutions, these methods have the advantage that the solution is continuous, whereas first and second derivatives such as heat fluxes are available at hardly any effort. The results are compared with those of the exact solution. Even if the size of the determinant is limited to 4 × 4, the accuracy is already better than 98.98 per cent. When more effort is spent to solve a system of 10 equations, the accuracy is better than 99–95 per cent.
Exact Bernoulli–Euler dynamic stiffness matrix for a range of tapered beams
Authors: Banerjee J. R. , Williams F. W. 
Published: August 2005

AbstractBernoulli‐Euler theory and Bessel functions are used to obtain explicit expressions for the exact dynamic stiffnesses for axial, torsional and flexural vibrations of any beam which is tapered such that A varies as yn and GJ and I both vary as y(n + 2), where A, GJ and I have their usual meanings; y = (cx/L) + 1; c is a constant such that c > − 1; L is the length of the beam; and x is the distance from one end of the beam. Numerical checks give better than seven‐figure agreement with the stiffnesses obtained by extrapolation from stepped beams with 400 and 500 uniform elements. A procedure is given for calculating the number of natural frequencies exceeded by any trial frequency when the ends of the member are clamped. This enables an existing algorithm to be used to obtain the natural frequencies of structures which contain tapered members.
Implicit modelling and mesh refinement for complex structures
Authors: Taig Ian C. 
Published: August 2005

AbstractWhen analysing complex structures it is rarely feasible to represent explicitly all the structural features which may contribute significantly to local or global structural performance. This paper presents a variety of methods for representing features which are below the economic analysis scale. Two approaches are described—referred to as implicit stiffness calculation and implicit mesh refinement. The former is essentially approximate and uses relatively simple formulae and computations. The latter involves quite extensive subsidiary calculation, but can lead to numerically exact simulation of fine mesh behaviour in so far as it affects neighbouring structure. Stiffness equivalence principles are stated and a number of computation schemes are presented and illustrated with simple two‐dimensional examples.
The patch test for elements
Authors: Razzaque Abdur 
Published: August 2005

AbstractThe main purpose of this paper is to emphasize the necessity of convergence tests in general and the patch test in particular. Following a brief introduction, the patch test is described with examples. This, it is hoped, will help to remove any lingering misunderstanding of this very useful convergence test. Some positive contributions of the test in the formulation and improvement of elements are also discussed.
TRUNC for shells—an element possibly to the taste of Bruce Irons
Authors: Argyris J. , Haase M. , Mlejnek H.‐P. , Schmolz P. K. 
Published: August 2005

AbstractIn his delightful and original textbook,18 Bruce Irons introduces the chapter of plate bending with the remark ‘History of disasters, but the pioneering days are past’. This is certainly true. On the other hand, we learn in the same context from Irons: ‘We believe that the world has not yet exhausted the older formulations.’ In this paper we present a review of theoretical aspects of the plate‐bending triangle TRUNC (Reference 4), together with extensive tests in linear statics, dynamics, buckling and nonlinear large deformations both for plates and shells. The unconventional TRUNC model is based on the patch test, which was originated by Irons.1 In spite of its limited theoretical foundation, the performance of this element on a fairly broad field of applications appears at least from the practical point of view very satisfactory.
A study of the influence of hierarchical nodes on the performance of selected parametric elements
Authors: Delpak R. , Peshkam V. 
Published: August 2005

AbstractA number of programs have been developed and tested to enable the routine addition of elements with internal nodes into most finite element packages. A subsequent examination was carried out to assess the effect of those nodes on (a) the accuracy of the displacements and stresses using parametric elements with varying formulation complexities, and (b) the possible additional cost in processing, owing to adequacy of representation. It was found in general that, by including the internal nodes, the representation of both the displacement and the stress fields improved dramatically. It was also found that having hierarchical nodes could lead to a reduction in the processing cost.
Optimal design in elasticity and plasticity
Authors: Strang Gilbert , Kohn Robert V. 
Published: August 2005

AbstractA direct weight minimization subject to compliance constraints or plastic yielding constraints leads to a non‐convex variational problem. Both the theoretical and the numerical analysis are unsatisfactory: the minimum weight is not achieved by any design, and the approximate designs oscillate as the element mesh is refined. We look for equivalent ‘relaxed problems’ with the same minima. They come from allowing composite materials constructed in an optimal way from the original materials. The constructions are different for elasticity and plasticity, but surprisingly the final relaxed problems are in some cases the same.
Ultimate load behaviour of reinforced concrete plates and shells under dynamic transient loading
Authors: Liu G. Q. , Owen D. R. J. 
Published: August 2005

AbstractThis paper considers a layered thick shell finite element procedure for determining the dynamic transient nonlinear response of plates and shells. The degenerated three‐dimensional isoparametric shell element with independent rotational and translational degrees‐of‐freedom is employed and a layered formulation is adopted to represent the steel reinforcement and to simulate progressive concrete cracking through the thickness. The dynamic yielding function is assumed to be a function of the current strain rate, in addition to being total plastic strain or work dependent. The concrete model also simulates both compressive crushing and tensile cracking behaviours and an implicit Newmark algorithm is employed for time integration of the equations of motion. Several numerical examples are presented for both slab and shell structures and the results obtained compared with those from other sources wherever available.
Continuous stress fields by the finite element–difference method
Authors: Cook Robert D. , Huang Xianrui 
Published: August 2005

AbstractStandard finite elements yield a stress field that is discontinuous across interelement boundaries. In this paper, results given by standard finite elements are postprocessed by an efficient iterative scheme that makes use of nodal strains, finite difference operations and interpolations that augment (and may differ from) the shape functions used to generate the element stiffness matrix. Various types of interpolation are considered. Each leads to a continuous stress field that is more accurate than the unprocessed stress field.
Penalty‐function iterative procedures for mixed finite element formulations
Authors: Felippa C. A. 
Published: August 2005

AbstractIterative methods for solving mixed finite element equations that correct displacement and stress unknowns in ‘staggered’ fashion are attracting increased attention. This paper looks at the problem from the standpoint of allowing fairly arbitrary approximations to be made on both the stiffness and compliance matrices used in solving for the corrections. The resulting iterative processes usually diverge unless stabilized with Courant penalty terms. An iterative procedure previously constructed for equality‐constrained displacement models is recast to fit the mixed finite element formulation in which displacements play the role of Lagrange multipliers. The penalty function iteration is shown to reduce to an ordinary staggered stress‐displacement iteration if the weight is set to zero. Convergence conditions for these procedures are stated and the potentially troublesome effect of prestress modes noted.
The design of transonic aerofoils by a well‐posed inverse method
Authors: Volpe G. , Melnik R. E. 
Published: August 2005

AbstractThis paper describes a numerical method for designing closed aerofoils that correspond to given surface speed distributions including flows with shock waves. The prescribed surface speed distribution in general contains three parameters whose values are found as part of the solution. The inverse aerofoil design problem is not well posed unless the prescribed speed satisfies three constraints that can be used to fix the value of the three adjustable parameters. The computational method is based on the numerical solution of the full potential equation in conservation form by an approximate factorization–multigrid scheme. The nature of the constraints and several strategies for introducing the necessary freedom in the prescribed speed are discussed along with typical solutions illustrating the method.
Application of elliptic continuation method for transonic aerofoil design and experimental verification
Authors: Redeker G. , Wichmann G. , Oelker H.‐Chr. 
Published: August 2005

AbstractWith the aid of the elliptic continuation method, transonic aerofoils for two different purposes have been optimized. The design process is described and it is shown that the optimization is more difficult for higher design Mach numbers. The results of experimental investigations confirmed the good aerodynamic performances of the designed aerofoils, although no real shock‐free pressure distributions could be achieved in the experiments and the highest aerodynamic efficiencies occurred always at higher lift coefficients, with pressure distributions already having shock waves.
Shallow water problems: A general explicit formulation
Authors: Peraire J. , Zienkiewicz O. C. , Morgan K. 
Published: August 2005

AbstractWe present in this paper a general formulation for shallow water equations which is capable of solving problems of induced harbour oscillation, tidal flow, tsunami propagation, dispersion of pollutant, etc.The shallow water equations are written in a novel fully conservative form. The solution algorithm is based on an explicit time integration procedure which exploits the conservative properties of the governing equations and incorporates accurate treatment of convective terms without introduction of artificial damping. Its accuracy and low cost of computation make it attractive vis‐à‐vis existing procedures.