摘要:

AbstractIn Part I of this paper,1the conceptual framework of a rate variational least squares formulation of a continuously deforming mixed‐variable finite element method was presented for solving a single evolution equation. In Part II2a system of ordinary differential equations with respect to time was derived for solving a system of three coupled evolution equations by the deforming grid mixed‐variable least squares rate variational finite element method. The system of evolution equations describes the coupled heat flow, fluid flow and trace species transport in porous media under conditions when the flow velocities and constituent phase transitions induce sharp fronts in the solution domain. In this paper, we present the method we have adopted to integrate with respect to time the resulting spatially discretized system of non‐linear ordinary differential equations. Next, we present computational results obtained using the code in which this deforming mixed finite element method was implemented. Because several features of the formulation are novel and have not been previously attempted, the problems were selected to exercise these features with the objective of demonstrating that the formulation is correct and that the numerical procedures adopted converge to the correct solu

ISSN:0029-5981    

DOI:10.1002/nme.1620281203

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractThe performance of group implicit algorithms is assessed on actual concurrent computers. We show that, as the number of subdomains is increased, performance enhancements are derived from two sources: the increased parallelism in the computations; and a reduction in equation solving effort. Moreover, we show that these two performance enhancements are synergistic, in the sense that the corresponding speed‐ups aremultiplied, rather than merelyadded. Our numerical simulations demonstrate that, ifnis the number of degrees of freedom of the structure,pthe number of processors used in the computations, ands⩾pis the number of subdomains in the partition, the net speed‐up is\documentclass{article}\pagestyle{empty}\begin{document}$ O\left({p\sqrt s} \right) $\end{document}in 2D andO(ps) in 3D, asymptotically asn/s→ ∞. In particular, speed‐ups with respect to Newmark's method of\documentclass{article}\pagestyle{empty}\begin{document}$ O\left({p\sqrt s} \right) $\end{document}in 2D andO(s) in 3D are obtained on a single‐processor machine. Finally, simulations on a 32‐node hypercube are presented for which the interprocessor communication efficiencies obtained are consistently in excess

ISSN:0029-5981    

DOI:10.1002/nme.1620281204

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractThis paper presents an efficient numerical integration scheme for evaluating the matrices (stiffness, mass, stress‐stiffness and thermal load) for a doubly curved, multilayered, composite, quadrilateral shell finite element. The element formulation is based on three‐dimensional continuum mechanics theory and it is applicable to the analysis of thin and moderately thick composite shells.The conventional formulation requires a 2 × 2 × 2 or 2 × 2 × 1 Gauss integration per layer for the calculation of element matrices. This method becomes uneconomical when a large number of layers is used owing to an excessive amount of computations. The present formulation is based on explicit separation of the thickness variable from the shell surface parallel variables. With the through‐thickness variables separated, they are combined with the thickness dependent material properties and integrated separately. The element matrices are computed using the integrated material matrices and only a 2 × 2 spatial Gauss integration scheme. The response results using the present formulation are identical to those obtained using the conventional formulation. For a small number of layers, the present method requires slightly more CPU time. However, for a larger number of layers, numerical data are presented to demonstrate that the present formulation is an order‐of‐magnitude economical compared to the conve

ISSN:0029-5981    

DOI:10.1002/nme.1620281205

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractThe structural design sensitivity analysis of a two‐dimensional continuum using conforming (continuous) boundary elements is investigated. Implicit differentiation of the discretized boundary integral equations is performed to obtain design sensitivities in an efficient manner by avoiding the factorization of the perturbed matrices. A singular formulation of the boundary element method is used. Implicit differentiation of the boundary integral equations produces terms that contain derivatives of the fundamental solutions employed in the analysis. The behaviour of the singularity of these derivatives of the boundary element kernel functions with respect to the design variables is investigated. A rigid body motion technique is presented to obtain the singular terms in the resulting sensitivity matrices, thus avoiding the problems associated with their numerical integration. A formulation for obtaining the design sensitivities of the continua under body forces of the gravitational and centrifugal types is also presented. The design sensitivity results are seen to be of the same order of accuracy as the boundary element analysis results. Numerical data comparing the performance of conforming and non‐conforming formulations in the calculation of design sensitivities are also presented. The accuracy of the present results is demonstrated through comparisons with existing analytical resu

ISSN:0029-5981    

DOI:10.1002/nme.1620281206

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractA new element—a partial hybrid stress element—is proposed in this paper for the analysis of thick laminated composite plates. The variational principle of this element can be derived from the Hellinger–Reissner principle through dividing six stress components into a flexural part (σx, σy, σxy, σz) and a transverse shear part (τxy, τyz). The element stiffness matrix can be formulated by assuming a stress field only for transverse shear stresses, while all the others are obtained from an assumed displacement field. Consequently, this new element combines the benefits of the conventional displacement method and the hybrid stress method. A twenty‐node hexahedron element is employed in each layer for the displacement field. For the assumed transverse shear stress field, only the traction‐free boundary conditions and interface traction continuity are satisfied. The equilibrium equation is enforced by the variational principle. Hence, the complicated work of searching an equilibrating stress field for all the six stress components in the hybrid stress method can be avoided. Furthermore, the interlaminar traction discontinuity, especially transverse shear, encountered by the conventional displacement method and higher‐order plate element for laminated plate analysis can also be overcome. Examples are illustrated to demonstrate the accuracy and efficiency of this proposed partial hybr

ISSN:0029-5981    

DOI:10.1002/nme.1620281207

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractThis paper is concerned with the prevention of snow loading on an overhead conductor caused by the mechanism of cylindrical‐sleeve growth. The eccentric snow loading on the windward side of the conductor, having finite torsional stiffness, causes the conductor to rotate and a theoretical study of how this rotation can be controlled on attaching counterweights along the span of the conductor is presented. In the absence of counterweights, the non‐linear rotation equation is solved analytically in terms of elliptic functions, simulating ice loading by a uniform torque density; for large torque density an asymptotic solution is obtained using matched asymptotic expansions. In the rotation equation the counterweights producing torque at discrete points are incorporated as delta functions which enable the discontinuity in the twisting couple at such locations to be accounted for by means of an integral moment balance. A simple algorithm is then presented for integrating the equation of rotation as an initial value problem which can deal with any distribution of counterweights along the span of the conductor. Illustrative numerical results are presented for zero, one, two, three and four counterweights per span; in the absence of counterweights analytical and numerical solutions are in exact agreem

ISSN:0029-5981    

DOI:10.1002/nme.1620281208

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractThe Zienkiewicz–Zhu error estimator is shown to be effective in problems of plate flexure. When used in conjunction with triangular elements and an adaptive mesh generator allowing a prescribed size of elements to be developed, very fast adaptive convergence for results of specified accuracy is achieve

ISSN:0029-5981    

DOI:10.1002/nme.1620281209

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractA 48‐degree‐of‐freedom (d.o.f.) skewed quadrilateral thin shell finite element, including the effect of geometrical non‐linearity, is formulated and appropriate numerical procedures are adopted for the development of an efficient approach for the static and dynamic analysis of general thin 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. The directions of the curvilinear co‐ordinates at each nodal point are uniquely defined to coincide with the directions of the boundaries of the element. In the present case of a skewed quadrilateral with non‐orthogonal curvilinear coordinates, the coupling terms of the metric tensor and curvature tensor of the surface no longer vanish, such as in the case of orthogonal co‐ordinates. The tensor form is used in the setup of the shape functions, geometric derivatives, stiffness matrix and computer code. This allows for the treatment of shells with irregular shapes and variable curvatures. To evaluate the efficiency and accuracy of this formulation, a systematic list of examples is chosen: (i) linear and non‐linear static analysis of square and rhombic plates, cylindrical and spherical shells; (ii) linear vibrations of trapezoidal flat and curved plates; (iii) large amplitude vibrations of a rhombic plate. For the square plate and cylindrical and spherical shell, shewed element meshes with various distortion angles are used to study the effect of the distortion angles on the accuracy of the results and to demonstrate the versatility of the present element. All results are compared with alternative available solutions including those obtained using regular rectangular meshes. Pinched thin cylindrical and spherical shells are studied using different skewed meshes and various Gauss integration meshes, and no membrane locking p

ISSN:0029-5981    

DOI:10.1002/nme.1620281210

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractExact postbuckling stresses usually vary fairly smoothly. Unfortunately, finite element postbuckling stresses tend to be much less well behaved. The result is that second order postbuckling constants determined by the finite element method may be highly inaccurate. The reason is that in finite element solutions transverse displacements associated with the buckling fields furnish too rapidly varying postbuckling strain contributions, while the postbuckling axial or membrane displacements contribute strain components that are sufficiently smooth, thus creating an internal postbuckling strain and stress mismatch.The present study suggests a modified finite element method that handles the problem, which is a special example of membrane locking, by introducing the postbuckling strains as independent variables. In general, the method provides rather complicated finite element expressions. However, by a suitable choice of interpolating functions, the resulting finite element equations themselves may be found to be the usual ones, and yet provide smooth postbucklingstressesand therefore good values of the postbuckling constants.

ISSN:0029-5981    

DOI:10.1002/nme.1620281211

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractThe construction of changing sequences of irregular and nested triangulations, based on the use of conforming refinement/derefinement algorithms for triangulations, is presented and discussed. This strategy is particularly appropriate to combine adaptivity and full multigrid algorithms for dealing with moving fronts or fluid dynamics problems. It is shown that the quality of all the triangulations iteratively generated depends only on the geometric characteristics of the initial grid. A data structure suitable to create, manage and modify series of nested triangulations as well as the main features of the DEREF prototype package are described, and numerical examples are given.

ISSN:0029-5981    

DOI:10.1002/nme.1620281212

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY