International Journal for Numerical Methods in Engineering

doi: 10.1002/nme.1620371101pmid: N/A

Saitoh, T. S.; Nakamura, M.; Gomi, T.

doi: 10.1002/nme.1620371102pmid: N/A

In this paper, the time–space method (TSM) for multidimensional melting and solidification problems is proposed. In the proposed TSM, the timewise co‐ordinate is incorporated into one of the spatial co‐ordinates, thereby transforming the usual transient 2‐D (or 3‐D) problems into steady 3D (or 4‐D) boundary‐value problems. Since time integration is not necessary, the TSM has a feature that eliminates the so‐called numerical instability which has been a great concern in the principal numerical methodologies in the past. That is, no error propagation in the timewise direction occurs in the TSM calculation. The TSM is applicable to almost all transient heat transfer and flow problems. The computer running time will be reduced to only 1/100th–1/1000th of the existing schemes for 2‐D or 3‐D problems. The sample calculations are presented for a 2‐D melting problem in a square cavity and the validity of the present method is examined.

Sygulski, R.

doi: 10.1002/nme.1620371103pmid: N/A

Vibrations of open membrane structures including interaction with air are presented in the paper. Free and forced linear harmonic vibration problems are considered in the analysis. It is assumed that the air is compressible and inviscid. The aerodynamic pressure associated with structure deformations is described by boundary integral equation. The finite element method for the structure and the boundary element method for the air are used. To discretize the surface of the structure, triangular curvilinear 6‐node elements are applied. The effects of the air compressibility and the aerodynamic radiation damping are investigated. The considerable decrease of the lowest natural frequencies in consequence of considering the effect of the surrounding air is observed. Numerical examples are given.

Power, Henry; Partridge, Paul W.

doi: 10.1002/nme.1620371104pmid: N/A

This paper presents a boundary element formulation for the permanent Navier–Stokes equations in which the well‐known closed‐form fundamental solution for the steady Stokes equations is employed. In this way, from the integral representation formulae for the Stokes' equations, an integral equation is found in which the original non‐linear convective terms of the Navier–Stokes equations appear as a domain integral. Additionally, the method of dual reciprocity is used to transform the domain integral to boundary integrals (this method is closely related to the method of particular integrals also used in the literature to transform domain integrals to boundary integrals). Numerical results are presented for the three‐dimensional internal flow in a cylindrical container with a rotating cover, in which the accuracy of the method is shown.

Wright, Julian P.; Jack, Alan G.

doi: 10.1002/nme.1620371105pmid: N/A

Presented in this paper are the theoretical aspects of node addition to a non‐convex, multiboundary mesh of tetrahedral elements as used in finite element modelling. The method used is derived from Watson1 and Shenton and Cendes2 and is extended to deal with node addition on inter‐material boundaries. Several situations are identified that result in an illegal insertion polyhedron (IP), these could be caused by the ‘constrained’ nature of the mesh, adjacent objects with different material properties, or degenerate node configurations. A new Delaunay algorithm is described that checks for illegal cases of the IP and then corrects them, this checking relies on the consistent ordering of the element nodes. It is shown that a particular type of illegal IP can easily be identified and corrected using this technique. The Delaunay algorithm is then applied to automatic mesh generation, and modification to the basic Delaunay algorithm is described so that previously meshed edges and faces of the current object being meshed are not deleted during the addition of subsequent nodes. This ‘protection’ method only becomes viable by recognizing the node ordering sense of the IP faces.

Poots, G.; Skelton, P. L. I.

doi: 10.1002/nme.1620371106pmid: N/A

Current three‐dimensional, time‐dependent mathematical models for (dry) rime‐ice and snow accretion on Overhead Line Conductors (OHLC), of finite span and finite torsional stiffness, assume that the airflow past the iced OHLC is given by Attached Potential Flow (APF) and that the effect of aerodynamic moment on the rotation of the OHLC during ice evolution can be neglected. In the present numerical study a CFD code is employed to simulate the turbulent airflow past an iced OHLC and used to validate APF predictions for icing particle impactions, ice evolution and rotation of the OHLC. Comparisons are made for the following: (a) icing particle impaction velocities determined using the CFD code and APF when, for example, the iced surface is fixed at an attitude experiencing lift; (b) the aerodynamic moment, for a chosen ice shape at a range of attitudes, predicted using the CFD code and AFT; (c) the aerodynamic moment, for natural ice shapes, given by APF and measured in wind‐tunnel tests; (d) the effect of aerodynamic moment, predicted using the CFD code and APF, on ice evolution during a short period of icing. Finally, on employing aerodynamic moments calculated using APF modified values, the sensitivity of the ice‐accretion process, across the span of the OHLC, to conductor rotation and various meteorological and physical data for the icing particles is discussed.

Du, H.; Lim, M. K.; Lin, R. M.

doi: 10.1002/nme.1620371107pmid: N/A

This paper presents the first endeavour to exploit a generalized differential quadrature method as an accurate, efficient and simple numerical technique for structural analysis. Firstly, drawbacks existing in the method of differential quadrature (DQ) are evaluated and discussed. Then, an improved and simpler generalized differential quadrature method (GDQ) is introduced to overcome the existing drawback and to simplify the procedure for determining the weighting coefficients. Subsequently, the generalized differential quadrature is systematically employed to solve problems in structural analysis. Numerical examples have shown the superb accuracy, efficiency, convenience and the great potential of this method.

Crisfield, M. A.; Shi, J.

doi: 10.1002/nme.1620371108pmid: N/A

New procedures are proposed for implicit dynamic analysis using the finite element method. The main aim is to give stable solutions with significant rigid‐body motions, in particular rotations. In contrast to most conventional approaches, the time‐integration strategy is closely linked to the ‘element technologies’ with the latter involving a form of co‐rotational procedure. For the undamped situation, one of the solution procedures leads to an algorithm that exactly conserves energy when constant external forces are applied (i.e. with gravity loading).

Ghazzawi, N. A.; Rabadi, N. J.

doi: 10.1002/nme.1620371109pmid: N/A

Similarity solutions for incompressible axisymmetric jets using a k–ϵ and a constant eddy diffusivity turbulence models are considered. For the k–ϵ model, the governing equations are very complex. Therefore, a transformation that simplifies these equations and makes them amenable to efficient numerical solution is used. Results for the velocity, turbulent kinetic energy and dissipation rate are obtained. Also, velocity decay rate, growth rate, entrainment and kinetic energy decay rate are determined. A comparison with experimental data and other works utilizing a parabolic marching asymptotic solution to the full partial differential equations is made. This comparison shows that similarity solutions are more accurate than solutions using numerical marching procedures.

Arnold, S. M.; Saleeb, A. F.; Tan, H. Q.; Zang, Y.

doi: 10.1002/nme.1620371110pmid: N/A

The issue of developing effective and robust schemes to implement a class of the Ogden‐type hyperelastic constitutive models is addressed. To this end, special purpose functions (running under MACSYMA) are developed for the symbolic derivation, evaluation, and automatic FORTRAN code generation of explicit expressions for the corresponding stress function and material tangent stiffness tensors. These explicit forms are valid over the entire deformation range, since the singularities resulting from repeated principal‐stretch values have been theorectically removed. The required computational algorithms are outlined, and the resulting FORTRAN computer code is presented.