摘要:

AbstractThe paper presents an extended approach to non‐linear first‐order approximation of non‐linear programming problems and it explains how to transform an approximate problem into a strictly convex one. The essence of the proposed approximation technique is to rewrite each given function hjas a composite gjoΨj. The function Ψjhas to be chosen—the paper explains how to do this—while gjis linear approximated withgj. The approximation of hjis then obtained asgjoΨj.This approach enables one to obtain approximate functions with variable conservativeness, which implies an adjustable approximate problem. A solution procedure, which replaces the original problem with a sequence of approximate problems, can therefore adjust each succeeding approximate problem to improve the convergence properties.The theory is illustrated with a three parameters controlled approximation. This technique represents, together with an optimality criteria based solution procedure, a powerful and economic tool for solving nonlinear programming problems. The three parameters, which influence to a great extent the conservativeness of the approximate functions, are under full control of the optimizer. They are varied automatically during the process of optimization to speed‐up the convergence or to prevent oscillations.The benefits gained from the proposed approach are demonstrated on several numerical examples involving structures and a dynamic mu

ISSN:0029-5981    

DOI:10.1002/nme.1620330202

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractA theory is presented for the determination of the free vibration characteristics of anisotropic thin cylindrical shells, partially or completely filled with liquid, for two circumferential wave numbers,n= 0, axisymmetric andn= 1, beam‐like. The method used was a combination of finite element analysis and classical shell theory. The shell was subdivided into cylindrical finite elements and the displacement functions were obtained using the shell equations. Expressions for the mass and stiffness matrices for a finite element and for the whole structure were obtained. A finite element was developed for the liquid in cases of potential flow. The natural frequencies of the shell, both empty and partially filled, were obtained and compared with existing experiments and other theorie

ISSN:0029-5981    

DOI:10.1002/nme.1620330203

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractTo overcome numerical difficulties in highly non‐linear materials Crisfield6proposed a solution procedure involving the use of a constant arc length solution scheme with line searches and accelerations. This paper uses the arc length method with line searches to increase the stability and substantially reduce the cpu time required for convergence in the finite element modelling of reinforced concrete. The arc length method is compared with the modified Newton–Raphson solution scheme and it was found that substantial savings in computer resources are obtained by using the arc length method. On difficult iterations the use of line searches is shown to lead to substantial improvement, with the best results occurring when using a slack tolerance of ψ =

ISSN:0029-5981    

DOI:10.1002/nme.1620330204

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractA novel method of mesh generation is proposed which is based on the use of fractal concepts to derive contractive, affine transformations. The transformations are constructed in such a manner that the attractors of the resulting maps are a union of the points, lines and surfaces in the domain. In particular, the mesh nodes may be generated recursively as a sequence of points which are obtained by applying the transformations to a coarse background mesh constructed from the given boundary data. A Delaunay triangulation or similar edge connection approach can then be performed on the resulting set of nodes in order to generate the mesh. Local refinement of an existing mesh can also be performed using the procedure. The method is easily extended to three dimensions, in which case the Delaunay triangulation is replaced by an analogous 3‐D tesselatio

ISSN:0029-5981    

DOI:10.1002/nme.1620330205

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractTime finite element methods are developed for the equations of structural dynamics. The approach employs the time‐discontinuous Galerkin method and incorporates stabilizing terms having least‐squares form. These enable a general convergence theorem to be proved in a norm stronger than the energy norm. Results are presented from finite difference analyses of the time‐discontinuous Galerkin and least‐squares methods with various temporal interpolations and commonly used finite difference methods for structural dynamics. These results show that, for particular interpolations, the time finite element method exhibits improved accuracy and st

ISSN:0029-5981    

DOI:10.1002/nme.1620330206

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractA technique is presented whereby the standard finite element approximations used in vibration analysis are modified in order to allow them to accurately predict the frequencies of the higher modes. This is done by using the results of dispersion analysis of the numerical approximations. The method is applied to the longitudinal vibration of a bar, and is shown to give good results for a uniform bar, a bar with continuously varying properties, and a bar with a step change in properties. Dispersion correction gives improved accuracy for the flexural vibration of a beam. The results of the method are also applied to the mode superposition method of dynamic analysis, and again a marked improvement in performance is obtained.

ISSN:0029-5981    

DOI:10.1002/nme.1620330207

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractIn this paper the necessary requirements for the good behaviour of shear constrained Reissner–Mindlin plate elements for thick and thin plate situations are re‐interpreted and a simple explicit form of the substitute shear strain matrix is obtained. This extends the previous work of the authors presented in References 18 and 31. The general methodology is applied to the re‐formulation of some well known quadrilateral plate elements and some new triangular and quadrilateral plate elements which show promising features. Some examples of the good behaviour of these elements are

ISSN:0029-5981    

DOI:10.1002/nme.1620330208

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractA new comprehensive acoustic 2‐D interface element capable of coupling the boundary element (BE) and finite element (FE) discretizations has been formulated for fluid–structure interaction problems. The Helmholtz equation governing the acoustic pressure in a fluid is discretized using the BE method and coupled to the FE discretization of a vibrating structure that is in contact with the fluid. Since the BE method naturally maps the infinite fluid domain into finite node points on the fluid–structure interface, the formulation is especially useful for problems where the fluid domain extends to infinity. Details of the BE matrix computation process adapted to FE code architecture are included for easy incorporation of the interface element in FE codes. The interface element has been used to solve a few simple fluid–structure problems to demonstrate the validity of the formulation. Also, the vibration response of a submerged cylindrical shell has been computed and compared with the results from an entirely finite element form

ISSN:0029-5981    

DOI:10.1002/nme.1620330209

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractA plate formulation, for the inclusion of warping and transverse shear deformations, is considered. From a complete thick and thin plate formulation, which was derived withoutad hocassumptions from the three‐dimensional equations of elasticity for isotropic materials, the bending solution, involving powers of the thickness co‐ordinatez, is used for constructing a quadrilateral finite plate bending element. The constructed element trial functions, for the displacements and stresses, satisfy,a priori, the three‐dimensional Navier equations and equilibrium equations, respectively. For the coupling of the elements, independently assumed functions on the boundary are used. High accuracy for both displacements and stresses (including transverse shear stresses) can be achieved with rather coarse meshes for thick and thin p

ISSN:0029-5981    

DOI:10.1002/nme.1620330210

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractA finite element method for stress and vibration analysis of laminated composite beams was investigated. The analysis was based on a multilayered theory presented by Lu and Liu. This theory accounts for the continuity of interlaminar shear stress. The principle of minimum potential energy was used in the finite element formulation. The interlaminar shear stress was obtained directly from the constitutive equations. It was verified that the present technique was able to give excellent results for displacements, stresses and vibration frequencies for both thin and thick composite beams. The effects of the number of layers and the number of elements on the convergence were also discussed.

ISSN:0029-5981    

DOI:10.1002/nme.1620330211

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY