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The diffraction of waves due to the presence of submerged objects in the ocean environment is solved by a relatively novel approach involving the direct boundary integration method (DBIM). Firstly, the method is tested for the case of a submerged circular cylinder and compared with the conventional boundary element method (BEM) results. The agreement between the results using this method and the BEM is good. Further, the DBIM has been applied to the case of a submerged horizontal plate for which the horizontal and vertical force coefficients are computed and compared with a semi-analytical solution using the matched eigenfunction expansion method (EFEM). It is found that the computed results using DBLM are in good agreement with those of EFEM and BEM. Further, the DBIM is found to be computationally more efficient than the BEM for the water wave diffraction problems presented in this paper. [ABSTRACT FROM AUTHOR]

The paper presents a probabilistic boundary element method for analysis of structural responses to static loading, when the shape parameters of structures are considered as random variables. We can use this method to evaluate the mean values and standard deviations of the responses, and estimate the stochastic errors of structural character resulting from manufacturing errors. [ABSTRACT FROM AUTHOR]

We present in this paper a nine-point, fourth-order difference scheme for the numerical solution of the quasilinear Poisson equation in polar co-ordinates, [This equation can not be represented in ASCII.TXT] with appropriate boundary conditions. A separate difference scheme of order four valid at r = 0 has also been obtained. The method is based on five evaluations of the function f. The numerical results of two problems obtained using this scheme are listed. The numerical results demonstrate the fourth-order accuracy of the scheme. [ABSTRACT FROM AUTHOR]

In the paper the experimental results considering the effects of temperature on the elastic modulus and creep of concrete arc introduced into the mathematical models of the three-dimensional finite-element method to improve the calculation of creep stresses in mass concrete structures. The Unite-element implementation of the exponential algorithm for concrete creep at variable temperatures is studied. The numerical solution procedure for thermal creep stresses in mass concrete structures with temperature effects is presented and a three-dimensional finite-element program is developed. [ABSTRACT FROM AUTHOR]

In the paper a computation code based on the finite-element method for temperature evolutions in composite elements with internal cavities is presented. It is suitable for the analysis of various thermal problems encountered in mechanical and civil engineering such as fire risk assessment. It is based on a plane isoparametric triangular element with six nodes allowing the modeling of curved boundaries. In order to analyze composite steel-concrete elements and to take into account the non-linearities coming from the temperature-dependent material properties and from the boundary conditions, an implicit integration scheme is used. Another advantage of the program is the possibility of describing internal cavities with convection and radiation exchanges. In order to show the capacity of the program two examples are presented. Comparisons have been made with experimental and other numerical results, exhibiting very good agreement. [ABSTRACT FROM AUTHOR]

In this paper we present numerical experiments made to investigate the behaviour of the Newmark time- stepping scheme applied to non-linear dynamic systems. Our attention is focused on the instability and chaos in the Newmark scheme when it is applied to the equation ü + P(u) = 0, representing a non-linear elastic spring. Some unusual modes of behaviour, which are of substantial interest, have been observed. In the first case, a stable but chaotic solution is found. In the second case, while a stable solution is obtained with a certain time step, an unstable solution is found by decreasing the time step. In the third case, instability is triggered by neglecting the initial acceleration. A simple modification of the Newmark scheme is proposed which keeps the energy constant for the equation ü + P(u) = 0 and thereby guarantees unconditional stability. Numerical examples in support of such an energy-conserving scheme are presented. [ABSTRACT FROM AUTHOR]

We propose in this paper a nine-point, fourth-order difference method for the numerical solution of the quasilinear Poisson equation Auzz + &frac1r; ur + Burr = f(r, z, u, ur, uz) with appropriate boundary conditions. The method is based on five evaluations of f. The numerical results of four problems obtained using this method are listed. The results demonstrate the fourth-order accuracy of the method. [ABSTRACT FROM AUTHOR]

In the paper we present a superconvergent patch recovery technique for obtaining higher-order-accurate finite-element solutions and thus a postprocessed type of L2 norm error estimate. Two modifications make our procedure different from the one proposed by Zienkiewicz and Zhu (1992), in which higher- order-accurate derivatives of the finite-element solution at nodes are determined. Firstly, the recovery process is made for elements, not for nodes. An 'element patch', which represents the union of an element under consideration and the surrounding elements, is introduced. Secondly, the local error estimate is calculated directly from the improved solution for this element. Numerical tests on both 1D and 2D model problems show that this method can provide an asymptotically exact a posteriori L2 norm error estimate if the used element possesses superconvergent points for the solutions. [ABSTRACT FROM AUTHOR]

A numerical method, based on neural-network-based functions, for solving partial differential equations is reported in the paper. Using a 'universal approximator' based on a neural network and point collocation, the numerical problem of solving the partial differential equation is transformed to an unconstrained minimization problem. The method is extremely easy to implement and is suitable for obtaining an approximate solution in a short period of time. The technique is illustrated with the aid of two numerical examples. [ABSTRACT FROM AUTHOR]

In the paper we have developed a new formulation for solution of structural-acoustic coupling problems by boundary elements using the multiple reciprocity method. It is assumed that the structure is composed of plate components and is excited by the external or the internal noise source. The efficiency of the proposed formulation becomes especially remarkable if the boundary-value problem is to be solved repeatedly for different values of frequency. The accuracy of the numerical computations has been compared with the analytical solution in a test example. [ABSTRACT FROM AUTHOR]

In this paper we consider an explicit finite-element method, with elements adaptively oriented in space-time, for the solution of one-dimensional conservation laws, extending previous work dealing with linear convection-diffusion and incompressible flow. In particular we consider Burgers' equation and the compressible Euler equations. [ABSTRACT FROM AUTHOR]

In the paper the use of a truncated envelope technique is discussed as a preconditioning for the conjugate gradient method for solving large linear systems of equations with symmetric positive-definite matrices. An algorithm to generate a truncated envelope is introduced. Computational experience with systems of linear equations from the Harwell-Boeing collection is presented to highlight the efficiency of this approach. [ABSTRACT FROM AUTHOR]

Standard isoparametric finite elements can be used as singular crack-tip elements in fracture mechanical computations by placing the middle nodes in the neighbourhood of the crack tip. Such elements have already been applied to several plane and three-dimensional problems, so this method can be considered as commonly well accepted. The paper shows that a singularity of order r(1-m)/m is obtained with an nth-order isoparametric element. [ABSTRACT FROM AUTHOR]

In this paper, an iterative method of statistic linearization (IMSL) is presented to solve non-linear stochastic vibration equations. This method represents an improvement over the classical linearization method. The method uses the solution of the corresponding linear vibration equation as an initial value in an iterative procedure. To obtain information about essential statistical average values, the method uses a `boot-strapping' procedure, which defines a pseudorandom process based on the statistical characteristics of the linear solution and then uses samples from the process to estimate them. For Gaussian input excitation, the statistical average values are obtained by theoretical analysis. [ABSTRACT FROM AUTHOR]

Reduction of reheating time saves on energy input and increases the production rate in the steel-making process. Reductions can be achieved by allowing the centre temperature of a steel bar to be lower than the surface temperature by a small margin, before starting with the hot rolling process. This can only be done if the temperature difference does not adversely affect the quality of the final product or the rolling equipment. The paper presents numerical simulations to investigate the savings that can be obtained for various temperature differences between surface and centre temperatures to evaluate the feasibility of the concept. The results presented include the cross-sectional temperature distribution in a typical steel bar during reheating at hourly intervals as well as the effect of various differences between centre and surface temperatures on reheating time. The reheating time predicted for various steel bar sizes as well as for various differences between surface and centre temperatures are then compared against measured reheating times. To indicate the practical applicability of the concept to the hot rolling process the detailed temperature distribution in a typical steel bar, with an initial temperature difference between the surface and centre of the bar, was simulated numerically. This was compared to a similar simulation for a well soaked steel bar for which experimental measurements are also available. The numerical method used to obtain the simulations is also presented. Boundary conditions account for radiation, convection and conduction inside the steel bar. It is concluded that the concept of allowing differences between surface and centre temperatures of a steel bar during reheating holds great potential for energy savings in the steel-making process. [ABSTRACT FROM AUTHOR]

An arbitrary Lagrangian--Eulerian model is described for the prediction of metal flow in a steady-state forming process. The formulation is shown to be capable of dealing with free surface and boundary friction; the coupling with thermal effects is also considered. The numerical techniques are based on the finite elements for spatial discretization of the momentum equation and on an explicit integration scheme for discretization relative to time. The mass and energy equations are integrated by a finite-volume method. Details on the application to an orthogonal cutting process are given in the final Section of the paper. [ABSTRACT FROM AUTHOR]

The paper deals with the solution of the quasi-harmonic equation by the finite element method in a domain with corners on its boundary. A mapping technique, which can be used for locating the nodes of standard isoparametric elements in a subgrid (patch) of finite elements in the vicinity of a corner singularity point, is presented. The equations of the mapping are based on the analytical singular solution of the problem. Some analytical and numerical results to show the efficiency of the technique are presented. [ABSTRACT FROM AUTHOR]

The use of micromechanically based constitutive equations for contact interfaces leads to technically relevant parameters to ill-conditioned finite-element equations. In the paper an augmented Lagrangian technique is employed to overcome this difficulty and to provide a good converging algorithm. [ABSTRACT FROM AUTHOR]

Structural models of large space structures have a substantial number of degrees of freedom (DOF) and possess semi-positive-definite stiffness matrices. The paper presents an efficient co-ordinate reduction procedure for structural dynamic analysis of large space structures. The method is based on the superposition of load-dependent Ritz vectors, which are computed in block form using a shifted stiffness matrix. Comparative transient dynamic analyses are performed on a 2803 DOF model of the space station Freedom using the load-dependent method (LDM) and the mode-displacement method (MDM) based on the superposition of eigenvectors. It is shown that the LDM is able to provide convergence of displacements with a small number of vectors. The acceleration response is found to be more sensitive to vector truncation than the displacement response. Error norms based on the representation of the dynamic load by the vector basis are developed to provide an indication of the effect of vector truncation on the structural response. [ABSTRACT FROM AUTHOR]

In the paper the BEM and FEM results have been compared in the context of 2D electromagnetic field analysis in a zoned medium with eddy current subregions. The practical problem concerning the turbo- generator end region has been discussed. The magnetic flux density over the surface of the end package and the current density in the non-magnetic pressure plate have been analysed. [ABSTRACT FROM AUTHOR]

The paper presents two complementary variational formulations of Trefftz-type elements wherein the piece-wise assumed displacement approximations a priori fulfil the governing differential equations over the element subdomain. The two formulations are such that either the displacement conformity or the reciprocity of the conjugate tractions is enforced at the element interfaces, one more strongly than the other. This is achieved through linking the piece-wise approximations either through an auxiliary displacement or a boundary traction frame. The two formulations concern solid mechanics and structures. Although for hybrid elements monotonic convergence in energy cannot be warranted, in practice the two presented formulations yield opposite bounds on the energy provided that the number of internal Trefftz functions is sufficiently large. [ABSTRACT FROM AUTHOR]

The paper reports some numerical experiments on the effectivity of the Zienkiewicz-Zhu error estimate (1987) and comparisons of two adaptive mesh generators: ADMESH, developed by Jin and Wiberg (1990) and MAD2D by Peraire et al. (1987) and Zhu et al. (1990-91). From the experiments we observe that: (1) without any empirical correction, the effectivity of the error estimate for linear triangular elements is good if post-processed continuous stresses are obtained by adequately using an iterative stress recovery procedure (Zienkiewicz et al., 1985), and is also acceptable by using a simple `averaging' procedure; (2) these two mesh generators are basically comparable. [ABSTRACT FROM AUTHOR]

The multiple reciprocity method is based on using higher-order fundamental solutions to eliminate domain integrals encountered in transient boundary integral formulations. The paper considers the numerical stability of this approach through an eigenvalue decomposition of the system matrix. We demonstrate that the multiple reciprocity method for transient heat conduction is stable only for appropriately chosen time steps. [ABSTRACT FROM AUTHOR]

In this paper a new method has been presented to determine the optimum number of knots for cubic splines. The knot-finding process is based on the numerical integration of the input curve. The number and the location of the knots is determined automatically. The method has been applied to a test case and the performance has been compared with two other existing methods. It is shown that fewer knots are retained for the portions of the curve having small curvature whereas a larger number of knots is retained for highly curved portions. The computer time required by our method depends only upon the number of points in the input curve and does not depend upon the shape of the curve or the desired accuracy. [ABSTRACT FROM AUTHOR]

When a forging is machined to its net shape, unacceptably large distortions can occur if the final part shape is complex. Such distortions can be predicted with the application of the finite-element method. However, numerical errors associated with the finite element technique can render such predictions unreliable. This paper presents benchmark problems for verifying the accuracy of machining distortions predicted by any prospective finite-element code. Also, a comparison between two industry-standard general-purpose codes, ANSYS and ABAQUS, is presented. [ABSTRACT FROM AUTHOR]

In the present paper numerical solutions of the one-dimensional Burger equation are obtained. The technique of finitely reproducing non-linearities introduced by Bazley is used. This technique when applied to Burger's equation gives a method where a system of non-linear ordinary differential equations is to be solved. The present method produces very accurate results in comparison to finite-difference of finite-element methods. [ABSTRACT FROM AUTHOR]

This paper presents an algorithm for obtaining the inverse of a tridiagonal matrix numerically. The algorithm does not require diagonal dominance in the matrix and is also computationally efficient. [ABSTRACT FROM AUTHOR]

It is known that the boundary-element coefficient matrices in steady-state elastodynamics are frequency- dependent. For a multifrequency run, the coefficient matrices have to be reformed at each different frequency. This procedure usually involves heavy numerical integration, and hence is very time consuming. In this paper, two interpolation schemes are initially introduced to accelerate the process of matrix reformation without sacrificing the solution accuracy. In the first scheme, the coefficient matrices are first slightly transformed and then interpolated in the frequency domain. In the second scheme, the Green function is interpolated in the spatial domain. Comparison between these two schemes both in terms of accuracy and efficiency is presented. Finally, a hybrid scheme that takes advantage of the best of both interpolation schemes is proposed. Numerical examples are given to demonstrate the three different interpolation schemes. [ABSTRACT FROM AUTHOR]

Explicit finite-element programs, such as DYNA3D, are frequently used to solve large structural problems, such as automobile impacts, that involve tens of thousands of shell elements. Since the explicit finite-element programs do not use a stiffness matrix, the major cost of the calculation is the evaluation of the force vector. A significant part of that cost is the evaluation of the constitutive models. The standard algorithm for integrating J2 plasticity at the stress points is the radial return method. An iterative variation of radial return is commonly used to impose the zero normal stress condition within the shell elements. In this paper we explore several different non-iterative methods that impose the zero normal stress condition in an approximate manner. We show that the cost of the constitutive evaluation can be reduced by 25 per cent without introducing significant errors. [ABSTRACT FROM AUTHOR]

Recently a bicubic transformation was introduced to numerically compute the Cauchy principal value (CPV) integrals. Numerical results show that this new method converges faster than the conventional Gauss-Legendre quadrature rule when the integrand contains different types of singularity. Assume &ηsline; is the singular point of a CPV integral. The point &ηsline; divides the interval [-1, 1] into two parts: [-1, &ηsline;] and [&ηsline;, 1]. The bicubic transformation maps the intervals [-1, &ηsline;] and [&ηsline;, 1] to the interval [-1, 1] with the following constraints: it maps the point &ηsline;-∊ to μn and &ηsline; + ∊ to - μn where μn is the largest Gaussian point of an n-point Gauss-Legendre quadrature rule, and e is a user-supplied constant. The n-point Gauss-Legendre quadruture rule is then applied. In contrast to ordinary expectation, further numerical experiment shows that smaller ∊ does not always produce better results. In this paper we are concerned with the selection of e to yield rapid convergence of numerical integration when the bicubic transformation method is applied. [ABSTRACT FROM AUTHOR]

The symmetric boundary-element method for mixed boundary-value problems is currently gaining increasing interest as it permits the derivation of symmetric matrices. It is even possible to obtain positive-definite finite-element stiffness matrices for BEM subregions, and therefore the method provides a very straightforward coupling to the finite-element method (FEM). The BEM subregions can be handled like FEM substructures in a domain decomposition context. The symmetric BEM uses the full set of integral representations for the 2n types of boundary data for self-adjoint problems of order 2n and solves them in a weighted residual (Galerkin) sense. The main difficulty of the method is caused by the need to compute hypersingular integrals arising from the integral representations of the Neumann boundary data. It is the object of the paper to show that, for 2-D problems on polygonal domains, these hypersingular integrands pose no problem at all, even for higher-order approximations. The present approach makes use of analytical integrations as far as possible. The integrals of the hypersingular expressions are derived completely within the framework of simple engineering mathematics. The problem is reduced to the computation of weakly singular integrals even for C0 continuous approximations. [ABSTRACT FROM AUTHOR]

The static bifurcation criterion, i.e. singularity of the tangential stiffness matrix, is discussed in the sense of non-linear dynamics since it is sometimes used in the engineering literature. In this paper the connection between static stability, i.e. that the tangential stiffness matrix is positive-definite, and insensitivity, i.e. local damping of small perturbations, is proved. Since, in general, there is no connection between insensitivity and asymptotic stability, the concept of sensitivity cannot replace the classical stability theory of motion [ABSTRACT FROM AUTHOR]

In the Eulerian description of metal forming operations usually rigid/incompressible viscoplastic material models are used. In this paper a quadrilateral 2-13 finite-element formulation for incompressible viscoplastic flow analysis is developed. The element (QMITC) is based on mixed interpolation of tensorial components, and the incompressibility constraint is imposed via the penalty method. It is shown that the resulting element does not lock either in plane strain rate flows or in axisymmetric flows, that the oscillations in the pressure predictions (checkerboard) tend to zero when the mesh is refined and that the solutions for some typical benchmark problems are very accurate. [ABSTRACT FROM AUTHOR]

This paper compares two formulations of Lax-Wendroff TVD methods. The basis of comparison is to the results of several test problems providing both qualitative and quantitative results. Results show that using an upwind biased limiter provides higher resolution of both smooth and discontinuous solutions from a lower amount of induced numerical viscosity. The conclusion is that a limiter should have as small a support as possible in order to limit its effects if high resolution is the object. [ABSTRACT FROM AUTHOR]

This paper deals with the solution of the one-dimensional advection-diffusion equation. The method of solution is based on the process-splitting technique. The transport equation is split up into the advection part and the diffusion part at every time step. The advection transport equation is solved by a method of characteristics using a spline function for interpolation. This solution approach proves to be very effective because it reduces numerical dispersion and wiggles. The diffusion equation is solved by the standard Galerkin finite-element method. A comparison of calculations with the results of Holly and Preissmann and with analytical solutions demonstrates the great accuracy of the proposed method. [ABSTRACT FROM AUTHOR]

The paper is concerned with the solution of non-linear wave distribution in structural fibre members subjected to dynamic kinematic forcing. The development of reliable and efficient techniques for numerical handling of wave distribution based on the application of combined finite-element and transfer matrix approaches is emphasized. Illustrative numerical solutions are presented. [ABSTRACT FROM AUTHOR]

To obtain accurate gas-bearing lifts and moments, finite-difference and conventional finite-element techniques often require excessively large degrees of freedom. In this paper we avoid this problem by solving the compressible gas-bearing solution by the p-version finite-element method. The lubrication finite-element equation is formulated based on the weighted residual approach, and the resulting non- linear equations are solved iteratively by the Newton-Raphson procedure. To achieve higher-order solutions the formulation utilizes the C0 hierarchical shape functions to describe the element pressure field. A numerical example is included to demonstrate the simplicity of modeling and the rapid convergence characteristics of the present p-formulation. An efficient numerical strategy, which utilizes the most recent polynomial pressure solution available as an estimate for the next higher polynomial level calculations, shows a 50 per cent reduction in the required computational effort for the low-flying Winchester air-bearing slider presented here. When compared against results obtained from conventional h-version finite-element models, the p-formulation yields better accuracy with fewer degrees of freedom required. [ABSTRACT FROM AUTHOR]

There has been considerable effort put into determining the motion of a single bubble in a fluid in a variety of different situations. The boundary integral method has proved to be a convenient tool in such studies as it reduces the unbounded, three-dimensional fluid-filled domain of the governing partial differential equation to the finite, two-dimensional surface of the bubble. In this paper the author's work, which considered the motion of a bubble close to a fixed rigid structure, is extended to the case where the structure may be moving.

This paper examines the behavior of various time-stepping schemes used in structural dynamic analysis when applied to models with negative stiffness. It is found that under such circumstances the accuracy of the numerical solution is greatly affected by the choice of integration parameters of the scheme. Optimal parameters for the Newmark family and the SS32 family have been investigated. [ABSTRACT FROM AUTHOR]

In this paper an algorithm for generating pure triangular or pure quadrilateral meshes for arbitrary polygonal domains is presented. The first part shows a triangulation procedure being as suitable for local mesh refinement as for local mesh coarsening. In the second part an algorithm for transformation of triangular grids to quadrilateral meshes of the same relative mesh density is introduced. Two simple strategies are shown which can easily be implemented into any existing triangulation algorithm. [ABSTRACT FROM AUTHOR]

The paper describes the numerical method for calculating the crack propagation in the tooth root of a case-hardened and hardened gear. The method is based on the linear elastic fracture mechanics taking into account the total values of loadings and properties of the individual layers of the gear material. The main points are the determination of the stress intensity factor and the numerical calculations of the crack propagation, crack speed and path. [ABSTRACT FROM AUTHOR]

An isoparametric plate shell element of 16 nodes and 40 degrees of freedom is developed in this paper directly from 3-D elastic theories. In order to overcome the difficulties caused by straightforward use of a 3-D formulation, the relative displacement method is introduced. For curved shell elements, the use of the orthogonal curvilinear co-ordinate system greatly reduces the computer effort. The new element can conveniently solve shell problems with variable thicknesses and also easily link with other finite elements using displacement d.o.f. such as 8-node to 21-node 3-D elements. Numerical examples demonstrate the efficiency of the element. [ABSTRACT FROM AUTHOR]

The multiple reciprocity method (MRM) is known as a method for elimination of domain integrals appearing in the integral equation in the framework of the direct-type boundary-element formulation. The method employs the fundamental solution of a part of the adjoint operator corresponding to the original differential equation. In this paper we discuss the relation between the conventional integral equation formulation of the Helmholtz equation and that derived by means of the MRM formulation. The latter, formulated in terms of real-valued variables, is proved to be a special case of the general complex-valued formulation. [ABSTRACT FROM AUTHOR]

Presents an announcement about the 9th Annual Robert J. Melosh Medal Competition for the best student paper on finite element analysis, at Duke University in Durham, North Carolina, on April 4, 1997.

The journal "Communications in Applied Numerical Methods" (CANM) will have a change of title effective from this issue and henceforth will be known as "Communications in Numerical Methods in Engineering." The reason for the title change is to further strengthen the already existing bond between this journal and the "International Journal for Numerical Methods in Engineering" (IJNME). It was originally intended that CANM would be the vehicle for the publication of short papers which had been submitted to IJNME and which merited rapid publication. The growth of the IJNME prohibited such rapid turnaround and for this reason the new journal was launched in 1985.