摘要:

AbstractA technique is proposed for the selection of stress interpolations for hybrid models. The present paper applies this approach to plane problems. The stiffness matrix is derived using the Hellinger–Reissner variational principle. This formulation uses infinitesimal equilibrium relationships and divides the assumed stress into its lower‐order and higher‐order parts. The patch test can be passed and the resulting elements are generally invariant. A plane four‐node quadrilateral element is described and compared with existing elements. Numerical studies show that the accuracy of the element is general

ISSN:0029-5981    

DOI:10.1002/nme.1620370602

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

摘要:

AbstractSimulated annealing can minimize both profile and fill of sparse matrices. We applied these techniques to a number of sparse matrices from the Harwell–Boeing sparse matrix collection. We were able to reduce profile typically to about 80 per cent of that attained by conventional profile minimization techniques (and sometimes much lower), but fill reduction was less successful (85 per cent at best). We present a new algorithm that significantly speeds up profile computation during the annealing process. Simulated annealing is, however, still much more time‐consuming than conventional techniques and is therefore likely to be useful only in situations where the same sparse matrix is being used repeate

ISSN:0029-5981    

DOI:10.1002/nme.1620370603

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

摘要:

AbstractThe thin‐layer method is a semi‐discrete numerical technique that may be used for the dynamic analysis of laminated solids or fluids. In its classical implementation, the method is normally formulated in the frequency domain and requires the solution of a complex‐valued quadratic eigenvalue problem; in this paper we present an alternative time‐domain formulation which can offer advantages in some cases, such as avoiding the use of complex algebra. The proposed method entails expressing the governing equations in the frequency‐wavenumber domain, solving a linear real‐valued eigenvalue problem in the frequency variable, carrying out an analytical integration over frequencies, and performing a numerical transform over wavenumbers. This strategy allows obtaining the Green's functions for impulsive sources directly in the time domain, even when the system has little or no damping. We first develop the algorithm in its most general form, allowing fully anisotropic materials and arbitrary expansion orders; then we consider a restricted class of anisotropic materials for which the required linear eigenvalue problem involves only real, narrowly banded symmetric matrices and finally, we demonstrate the method by means of a simple problem involving a homogeneous stratum subjected to an antiplane impul

ISSN:0029-5981    

DOI:10.1002/nme.1620370604

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

摘要:

AbstractAn efficient method for structural optimization is presented. Instead of classical direct decomposition methods, Preconditioned Conjugate Gradient (PCG) methods, in conjunction with two proposed starting‐vector generation schemes, are used to solve the systems of linear equations associated with the finite element analysis and behaviour sensitivity analysis problems. These inherently iterative analysis procedures are then used to carry out the analyses needed at the beginning of each stage in an approximation concepts approach to structural optimization. This technique has been implemented in a research program and used to solve a collection of minimum weight truss sizing design problems subject to static deflection and stress constraints. The effectiveness of the PCG methods of analysis in structural optimization is demonstrated. Comparison among different preconditioners is made. The effect of the proposed starting‐vector generation schemes is shown. The comparative merits of analytical sensitivity analysis and finite difference sensitivity analysis, when using PCG methods of analysis, are assessed. The parallel computation potential of PCG methods is discussed. Because of the iterative nature of PCG analysis methods and the prospects they offer for parallel computation, it is found that PCG analysis methods show promise in the context of structural optimizat

ISSN:0029-5981    

DOI:10.1002/nme.1620370605

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

摘要:

AbstractThe paper deals with the discretization of the integral equations arising in the boundary formulation of plane elasticity and plate bending problems. Particular attention is paid to the efficiency of the interpolation used in approximating the boundary quantities and to the precision and computational convenience in evaluating the boundary integrals. The proposed discretization model is based on the use of a quadratic B‐spline approximation to represent the boundary variables and on the results from the analytical integration to compute the boundary coefficients. The advantages are those of accuracy and the saving of computer time. Some numerical results allow an analysis of the performance of the mode

ISSN:0029-5981    

DOI:10.1002/nme.1620370606

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

摘要:

AbstractThe formulation of a curved beam element with 3 nodes for curvature to eliminate the shear/membrane locking phenomenon is presented. The element is based on curvature so that it may represent the bending energy fully, and the shear/membrane strain energy is incorporated into the formulation by the equilibrium equations. To deal with general boundary conditions, a transformation matrix between nodal curvature and nodal displacement vector is introduced. Several examples are presented in order to verify the element formulation and its analytical capability. The solutions obtained reveal that the element describes the curved beam behaviour quite correctly and efficiently, showing no locking phenomena, and that it is also applicable to the analysis of both thin and thick curved beams.

ISSN:0029-5981    

DOI:10.1002/nme.1620370607

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

摘要:

AbstractIn this paper we discuss the theoretical and numerical formulation of 3‐D Trefitz elements. Starting from the variational principle with the so‐called hybrid stress method, the trial functions for the stresses have to fulfil the Beltrami equations, which means also the compatibility equations for the strains. The divergence theorem can be applied, and one arrives at a pure boundary formulation in the sense of the Trefftz method. Besides the resulting variational formulation, different regularizations of the interelement conditions are investigated by numerical tests. Two examples show the numerical efficiency of the derived elements. First, a geometric linear 3‐D example is presented to show the effects on distorted element meshes. The third example shows the geometrically non‐linear analysis of a shallow cylindrical shell segment under a sin

ISSN:0029-5981    

DOI:10.1002/nme.1620370608

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

摘要:

AbstractThe stiffness matrix of a plane four‐node quadrilateral finite element is given in closed form. When expressed as a FORTRAN subroutine and compared with the classical method of forming the stiffness matrix using Gaussian integration, the approach gives a CPU time speed‐up of the order of 2–3 on a vector machine and of the order of 4–5 on a scalar machine. The technique used to generate the terms of the stiffness matrix made use of a computer algebra system which could clearly be extended to generate the matrices for other element

ISSN:0029-5981    

DOI:10.1002/nme.1620370609

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

摘要:

AbstractThe method of Tarantola1based on Bayesian statistical theory for solving general inverse problems is applied to inverse elasticity problems and is compared to the spatial regularization technique presented in Schnur and Zabaras.2It is shown that when normal Gaussian distributions are assumed and the error in the data is uncorrelated, the Bayesian statistical theory takes a form similar to the deterministic regularization method presented earlier in Schnur and Zabaras,2As such, the statistical theory can be used to provide a statistical interpretation of regularization and to estimate error in the solution of the inverse problem. Examples are presented to demonstrate the effect of the regularization parameters and the error in the initial data on the solution.

ISSN:0029-5981    

DOI:10.1002/nme.1620370610

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

摘要:

AbstractWe study the performance of high‐orderh–pfinite clement schemes in approximating the nearly inexlensional deformation state of a thin cylindrical shell roof with both ends free. Severe locking is demonstrated for both quadratic and cubic elements, and even for higher order if the grid is not aligned with the axis of the cylinder.Carefully designed selective reduced integration is shown to improve the accuracy of the finite element approximation at low and moderately high orders. However, so far this technique seems to work well only on aligned gr

ISSN:0029-5981    

DOI:10.1002/nme.1620370611

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY