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The article invites submissions for research papers about numerical methods in engineering.

The spatial oscillation of values in the consolidation analysis when using small time increments has been a common problem for most existing methods. In this paper, the numerical characteristics of a simple finite element formulation for 1-D consolidation analysis recently proposed by the authors have been examined in detail. This paper proves that the commonly encountered phenomenon of spatial oscillation due to small time increments does not occur in the simple finite element formulation. The criterion of minimum time step used in most existing methods can be eliminated at least for linear situations by using the simple formulation proposed by the authors. Thus, the consolidation analysis can be carried easily for many situations, such as the one involving a relatively impermeable clay layer sandwiched between sandy layers. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Dynamics response of systems to impact or loading may be effectively treated by direct integration. However, it is often difficult to select the time-step of integration properly, especially in the case where the system is badly stiff. Zhong presented an explicit direct integration scheme, HPD, for the homogeneous systems. This paper extends HPD scheme to analyse systems with loading or impact, through Fourier expansion and homogenizing the initial system. Compared with other methods, the new scheme named homogenized high-precision direct integration (HHPD) has a higher precision and wider application and is less time-consuming, and several examples in this paper show HHPD's effectiveness in engineering. Copyright © 2002 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

When solving parabolic partial differential equations using finite difference non-overlapping domain decomposition methods, one often uses the stripwise decomposition of spatial domain and it can be extended to the rectangular decomposition without further analysis. In this paper, we analyze the rectangular decomposition when the modified implicit prediction (MIP) algorithm is used. We show that the performance of the rectangular decomposition and the stripwise decomposition is different. We compare spectral radius, maximum error, efficiency, and total operations of the rectangular and the stripwise decompositions. We investigate the accuracy of the interface of the rectangular decomposition and the effects of the correction phase of the rectangular decomposition. Numerical experiments have been done in both two and three spatial dimensions and show that the rectangular decomposition is not better than the stripwise decomposition. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A simplified method for analysing lateral response of suspension bridges under wind loads is proposed in this paper. The geometric non-linearity in the deflection theory and the three components of displacement-dependent wind loads are taken into account in the method. The analytical formulas for calculating the torsional, vertical, and lateral responses of suspension bridges under wind loads are derived. An iterative procedure, which has a high convergence rate for solving the problem, is developed. The proposed method is sufficient and simple to use. Wind-induced lateral response analysis of a long-span suspension bridge demonstrates the proposed method's efficiency and accuracy. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, incorporating the hybrid method and the mixed interpolation method into a unified optimization framework, a 4-node quadrilateral plate element with bilinear displacement approximations is proposed. By an energy optimization tactic, among all of assumed linear bending moment modes, a 5-parametric optimal bending moment mode is selected. Using the optimal bending moment mode to improve the well-known plate element MITC4, the optimized plate element numerically possesses high accuracy at the coarse meshes in the analysis of thin/thick plates. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In the context of composite parametric surface meshing using a direct or an indirect (via the meshing of parametric domains) method, the discretization of interface curves joining patches plays a central part. In the case of an indirect method, the discretization of interface curves must be taken back to parametric spaces. This is usually done using root finding techniques for generally non-linear parametric functions. This paper presents a new linearization technique to determine the above correspondence. In addition, this linearization of interface curves makes it possible to obtain their discretization without explicitly computing the arc length. This method has been implemented in a surface mesh generator and an example from Fluid Mechanics is given to illustrate the pertinence of the proposed approach. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, a new scheme for designing the penalty factor in 3-D penalty-equilibrating mixed elements based on the Hu–Washizu three-field variational functional is proposed to improve the performance of the elements when applied to beam, plate and shell structures. In order to construct this new scheme, the role played by the penalty factor is first discussed in detail by comparing it with the selective reduced factor designed by Sze for overcoming the so-called ‘trapezoid locking’. The reason of the poor performance of the penalty-equilibrating element for the distorted elemental geometry is investigated thoroughly. Furthermore, the penalty factor is designed to alleviate the influence of false strain/stress in elements by considering the geometrical characteristics of beam, plate and shell structures. The new scheme is applied to the penalty-equilibrating 3-D mixed element proposed by the present authors previously. Some challenging numerical examples are selected to demonstrate the effectiveness of the present approach. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper proposes an improvement on the DYNAMIC-Q method for optimization of applications requiring expensive and (often) noisy numerical simulations for function evaluations. The original DYNAMIC-Q method requires the selection of a step size and a move limit by the user. For noisy responses, the success of the original method depends on the correct choice of step size and move limit. The improved version uses the adaptive trust region features of an existing successive response surface method (SRSM) algorithm to replace the selection of the step size and move limit with one parameter, the initial trust region size. For the testing of the new method, DYNAMIC-Q(RSG), an arbitrary selection from the well-known Hock and Schittkowski problems as well as a non-linear structural engineering problem are used. It is shown that for problems where the gradient information is reliable, the original DYNAMIC-Q method is superior as expected. However, where noisy responses cause inaccurate and unreliable gradient information, the SRSM and DYNAMIC-Q(RSG) methods are proven to be more robust with SRSM superior in its ability to converge more stably. The performance of DYNAMIC-Q(RSG) is encouraging as it maintains the robustness and minimum user input of SRSM, but has faster convergence for analytical problems. Copyright © 2003 John Wiley & Sons, Ltd [ABSTRACT FROM AUTHOR]

This paper presents a new scheme of time stepping for solving non-linear dynamic problems. By expanding variables in a discretized time interval, FEM-based recurrent formulae are derived leading to a self-adaptive algorithm for different sizes of time steps. There will be no requirement of iteration for the non-linear solutions. Numerical validation shows satisfactory results. Copyright © 2001 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The theorem of minimum potential energy is not valid for an incompressible material. A new variational principle, called splitting elastic modulus variational principle, is introduced. Splitting elastic modulus finite element which is based on the new principle is established. There is a splitting factor in the variational principle. Potential energy and complementary energy components in the finite element model are changed with the change of the splitting factor, so stiffness of the finite element model can be adjusted, precision of solutions of the finite element model can be improved. The paper shows that the minimum potential energy variational principle and Herrmann's principle are special cases of the splitting elastic modulus variational principle. Finally, two examples show that the splitting elastic modulus finite element not only can calculate compressible material but also can calculate incompressible or nearly incompressible material, and precision of the solutions is higher. Copyright © 2000 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A triangular differential quadrature method (TDQM) is proposed in the paper. The partial derivative of a function with respect to space variables at a given point is approximated by a weighted linear summation of the function values at all discrete points in the triangular domain. The weighting coefficients are determined with the aid of area coordinates in the triangular domain. Two simple examples are provided to validate the new numerical method. It is shown that the method is accurate and reliable. Copyright © 2000 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, the existence, uniqueness and uniform convergence of the solution of the Carey non-conforming element with non-quasi-uniform partitions is proved for non-self-adjoint and indefinite second-order elliptic problems under a minimal regularity assumption. Furthermore, the optimal error estimate for the solution of Carey non-conforming element method is obtained only under an H2 smoothness hypothesis. Finally, a two-level Schwarz method which suits non-quasi-uniform partitions is proposed and optimal convergence for the pre-conditioned GMRES method is shown. Copyright © 2000 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The so-called enhanced strain finite elements are based on the enrichment of the standard compatible strain field by the introduction of additional, non-compatible strains. This class of elements can be derived starting from a partial Hu–Washizu variational principle. However, since in the original enhanced strain formulation the stress field is eliminated from the formulation, a separate least-squares procedure had to be implemented for a variational derivation of the stress field. A three-field generalized variable approach incorporating strain enhancement is proposed in the present paper within the context of linear elastic structural problems. It is shown how the original two-field enhanced strain method can be naturally recovered by suitably choosing the strain model. For this case a straightforward, but still variationally consistent stress recovery is proposed. Copyright © 2000 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, Lanczos and Arnoldi reduction methods as the special cases of the generalized Hessenberg method are briefly reviewed. Attention is paid to the effect of symmetry of matrices on the behaviour of the reduction schemes, such as serious numerical breakdown. Based on the summation decomposition of matrices, two structures of the upper Hessenberg form of a general unsymmetric matrix and their relationship are revealed, in terms of which, Arnoldi reduction schemes for unsymmetric matrices can be reformulated in two respective forms. The relationship between the reformulated reduction scheme and the current Lanczos schemes for skew and symmetric matrices are also discussed. Copyright © 1999 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Developing an efficient algorithm for solving a large linear system in a parallel computing environment is the major problem associated with the application of parallel processing to the numerical solution of large-scale engineering problems. This paper presents a new algorithm called Multiple Sequential Staging of Tasks (MSST) to speed up the solution of a large linear system. The technique of Sequential Staging of Tasks (SST) is a highly efficient approach to the parallel solution of a large linear system, but it is not suitable for middle- and large-scale parallel computers due to the idle periods of processors. The MSST technique partitions processors into groups and makes each group start its operation from a different row of a large linear system to remove the idle period. Therefore, MSST can be performed effectively on middle- and large-scale parallel computers and achieves a higher speed-up. Numerical results were obtained from computer experiments performed with a numerical solution method of the Poisson equation on a Dawning-1000 supercomputer (a distributed-memory MIMD architecture). The parallel speed-up is satisfactory. Copyright © 1999 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper discusses implementation strategies for second-order finite difference discretizations of advection. Purely explicit and implicit methods both have disadvantages, and we consider semi-implicit schemes in which the flux is split into a primary implicit part and a secondary explicit correction. One-dimensional scalar advection is used as a model problem to analyse the leading order error terms and the stability of the schemes. Some of the splittings turn out to be unconditionally stable, but accuracy or monotonicity may deteriorate for large time steps. © 1998 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, an attempt is made to show the usefulness of computational quantifier elimination (CQE) techniques in computer algebra inside classical numerical methods in engineering for the derivation of feasibility (consistency) conditions in problems with weakly parametric linear inequality constraints (with the parameters appearing only in their right-hand sides). A simple, but non-trivial, straight edge-crack problem in fracture mechanics under linear inequality constraints both on the applied loading along the crack faces and on the value of the stress intensity factor at the crack tip (associated with the Green/weight function method, numerical approximations and classical numerical integration) is used for an elementary illustration of the proposed approach. In this application, the method used tries to imitate the theoretical principle of the linear programming methods. The manually obtained related result is expressed as a disjunction of conjunctions of inequalities (as is frequently the case in similar CQE problems), and concrete numerical results are also displayed. The related influence of various approximations and the application of the trapezoidal quadrature rule are also considered in some detail. Further possibilities could concern the application of the approach to other numerical methods in engineering (such as to the finite and the boundary element methods, to singular and hypersingular integral equation methods, etc.) combined with efficient algorithms for linear inequality constraints such as the old Fourier and the recent Weispfenning elimination methods. © 1998 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper proposes a new family of special Trefftz elements in which the boundary conditions on an internal curve (stiffener, hole, etc.) are fulfilled by the least squares procedure. The author anticipates difficulties with conditioning of such elements and therefore proposes a method to improve the aspect. © 1997 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper it is shown that, from the expression of the internal electric and magnetic fields, we can express the electric and magnetic energy stored inside a cavity in the form of a simple sum. This proposed method has the advantage of avoiding the calculation of a double integral which needs an appropriate numerical method. The knowledge of the radiating power can lead to the evaluation of the internal impedance at the desired frequency. Also it is shown that the electric and magnetic energy stored in a cavity can be expressed with the internal electric and magnetic fields in the form of the presented expression at resonance frequency. There is excellent agreement with the cavity method that has been confirmed by experimental results. ©1997 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The purpose of the paper is twofold: firstly to show that a very large range of finite element linear and non-linear computations have been conducted without the use of quadrature; secondly to present some of the prerequisites that have been used in order to accomplish this task. Although some of the rules stated here have been well known in the scientific literature and may have been applied for separate subtasks, to our knowledge they have not been put in practice for the conduction of numerous large-scale practical engineering computations and the estimation of nearly all important elemental matrices. © 1997 by John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents an improved approximation technique for gradient based approximation methods of mathematical programming. The proposed technique prevents oscillations of the sequence of approximate solutions in the optimization process efficiently and preserves the relatively simple form of the approximating functions. The improvement is achieved by adding an appropriate convex term to each conventional approximating function. The theory is illustrated with several numerical examples. © 1997 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The modal superposition method is often used for computing the perturbation of eigenvectors in structural modification and model correction. However, it will bring about significant errors in the solution when the high-frequency modes are truncated. This paper presents a new method, which uses known modes construct a new basis of the N-dimensional Euclidean space (say, the mixed-basis), to calculate the first and second order perturbations of the known eigenvectors. In the present method only the known modes are used. The accuracy of this method not only has no relation to number of the truncated modes but is better than the truncated modal superposition method, in which only the known modes are employed. A numerical example of a truss structure with 36 degrees of freedom is given to illustrate the effectiveness of the method. [ABSTRACT FROM AUTHOR]

This paper presents an automatic sliding interface algorithm for intense impulsive loading computations due to high velocity impact and explosive detonation. This algorithm allows the user to perform computations involving complex sliding interfaces without having to predetermine the sliding interfaces; everything is automated. The interface determination algorithm, the searching algorithm and the contact algorithm are included. [ABSTRACT FROM AUTHOR]

The fundamental solution of the temperature field in an infinite three-dimensional body under the periodic unit thermal source is given in the present paper. According to the indirect boundary element method (IBEM) with fictitious heat sources, the problem of 3-D periodic heat conduction in a finite body is solved. By use of a quadratic inharmonic element, the problem of the corner region and the indetermination of the normal direction at boundary points can be solved in the numerical process. The validity of the present method is checked with two examples of which analytical solutions exist. It offers a useful method for the actual simulated calculation of the 3-D temperature field in engineering. [ABSTRACT FROM AUTHOR]

The present paper deals with the shape design optimization of bodies subjected to a non-homogeneous Helmholtz equation. Using the adjoint variable method the material derivative of a general integral functional is obtained analytically. Boundary integral equations defined only on the boundary are derived using auxiliary fundamental solutions to be used in the boundary element method. Some constrained shape design optimization problems are solved by the proposed numerical procedure. [ABSTRACT FROM AUTHOR]

The paper attempts to improve the efficiency of a general method developed previously for computing nearly singular kernel integrals. Three new formulations are presented by following an approach similar to that used in the previous method. Their numerical efficiency is compared with the previous method. The results indicate that these new formulations are substantially more efficient than the previous method. In particular, the new formulation in which the same sampling points for all n values are used is the most efficient. This new formulation remains highly efficient even when the field point is as close to the panel surface as 0-1 per cent of the panel diagonal. [ABSTRACT FROM AUTHOR]