摘要:

AbstractThis paper describes an efficient formulation, based on a discrete Fourier series expansion, for the analysis of axi‐symmetric solids subjected to non‐symmetric loading. In contrast to the commonly adopted continuous Fourier series approach, the discrete Fourier series representation has largely overcome problems such as the presence of Gibb's phenomenon and the lack of conformity of elements. The computational advantage over a fully three‐dimensional formulation is illustrated. Finally, the method is demonstrated through a finite element study of rigid caissons founded in both elastic and elasto‐plasti

ISSN:0029-5981    

DOI:10.1002/nme.1620310402

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractThis paper presents a hierarchical three dimensional curved shell finite element formulation based on thep‐approximation concept. The element displacement approximation can be of arbitrary and different polynomial orders in the plane of the shell (ξ, η) and the transverse direction (ξ). The curved shell element approximation functions and the corresponding nodal variables are derived by first constructing the approximation functions of orders pξ, pηand pξand the corresponding nodal variable operators for each of the three directions ξ, η and ξ and then taking their products (sometimes also known as tensor product). This procedure gives the approximation functions and the corresponding nodal variables corresponding to the polynomial orders pξ, pηand pξ. Both the element displacement functions and the nodal variables are hierarchical; therefore, the resulting element matrices and the equivalent nodal load vectors are hierarchical also, i.e. the element properties corresponding to the polynomial orders pξ, pηand pξare a subset of those corresponding to the orders (pξ+ 1), (pη+1) and (pξ+1). The formulation guaranteesC° continuity or smoothness of the displacement field across the interelement boundaries.The geometry of the element is described by the co‐ordinates of the nodes on its middle surface (ξ = 0) and the nodal vectors describing its bottom (ξ = −1) and top (ξ = +1) surfaces. The element properties are derived using the principle of virtual work and the hierarchical element approximation. The formulation is equally effective for very thin as well as very thick plates and curved shells. In fact, in many three dimensional applications the element can be used to replace the hierarchical three dimensional solid element without loss of accuracy but significant gain in modelling convenience. Numerical examples are presented to demonstrate the accuracy, efficiency and overall superiority of the present formulation. The results obtained from the present formulation are compared with those available in the literature as w

ISSN:0029-5981    

DOI:10.1002/nme.1620310403

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractCalculation of the scalar electric potential of an earthing grid in heterogeneous soil is obtained by the finite element technique combining differential and integral formulations of the problem. Such a combined formulation made it possible to generate easily the mesh of finite elements and to divide the problem domain into a sufficiently small number of large finite elements. The unbounded domain of calculation is solved by using mapped infinite elements. The contribution of singular sources is represented by the analytical expression, and included in the approximation function of the potential. A sufficiently satisfactory approximation is realized with a small number of singular source images, obtained by local imaging of sources within a finite element on its boundary surfaces. The calculation accuracy is tested on examples solvable by an average potential method which is based on an integral formulation of the problem.

ISSN:0029-5981    

DOI:10.1002/nme.1620310404

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractA general and efficient remeshing algorithm is presented for the discretization of arbitrary planar domains into triangular elements in consistency with the given node spacing function.The contour lines of the node spacing function at suitable calculated levels provide the natural lines of division of the problem domain into subregions, where finite element meshes of different element sizes are generated using the available general‐purpose mesh generators.1, 2Examples of remeshing for various node spacing functions are given to illustrate that high‐quality gradation meshes can be generated automatically without any user's intervention by this simple contour line met

ISSN:0029-5981    

DOI:10.1002/nme.1620310405

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractThis paper presents a new boundary element approach to transform domain integrals into equivalent boundary integrals. The technique, called the Multiple Reciprocity Method, is applied to 2‐D elasticity problems and operates on domain integrals resulting from different types of body forces such as gravitational and centrifugal forces, as well as loadings due to linear and quadratic temperature distributions. Numerical examples are presented to demonstrate the accuracy and efficiency of the metho

ISSN:0029-5981    

DOI:10.1002/nme.1620310406

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractThe governing non‐linear finite element equations for the spatial stability analysis of curved beams, using a simple two‐noded model, are derived based on the incremental form of a mixed variational principle with independent discretization for its generalized strain field and the reference line displacements as well as cross‐sectional warping and bending/twisting rotations. The formulation is valid for both open‐and closed‐type thin‐walled sections, and this is accomplished by the use of a kinematic description based on a generalized beam theory in which shear deformation due to both flexural‐and warping‐torsional actions is accounted for. The effect of finite rotations in space is included, resulting in a second‐order accurate geometric stiffness matrix and ensuring that all significant instability modes can be predicted. Finally, the results obtained in a number of numerical simulations for lateral‐torsional bifurcation buckling of circular arches are presented to illustrate the model effectiveness and practical usefulness, and to provide explanations for the source of discrepancies noted in the results obtained in prev

ISSN:0029-5981    

DOI:10.1002/nme.1620310407

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractSeveral simple and accurate C° two‐node arch/beam and four‐node cylindrical shell/plate finite elements are presented in this paper. The formulation used here is based on the refined theory of thick cylindrical shells and the quasi‐conforming element technique. Unlike most C° elements, the element stiffness matrix presented here is given explicitly. In spite of their simplicity, these C° finite elements posseses linear bending strains and are free from the deficiencies existing in curved C° elements such as shear and membrane locking, spurious kinematic modes and numerical ill‐conditioning. These finite elements are valid not only for thick/thin beams and plates, but also for arches/straight beams and cylindrical shells/plates. Furthermore, these C° elements can automatically reduce to the corresponding C1beam and plate elements and give the C° beam element obtained by the reduced integration as a special case. Several numerical examples indicate that the simple two‐node arch/beam and four‐node cylindrical shell/plate elements given in this paper are superior to the existing C° elements with the same element degrees of freedom. Only the formulation of the rectangular cylindrical shell and plate element is presented in this paper. The formulation of an arbitrarily quadrilateral plate element will be presented in a

ISSN:0029-5981    

DOI:10.1002/nme.1620310408

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractThe correspondence between the homogeneous and particular solutions of differential equations and the related solutions of the discrete equations is brought to light in this study. Guided by this correspondence, the trial functions for finite elements are written in two parts—one the homogeneous and the other a prescribed particular solution. It is shown that this approach allows one to simplify the computations of element matrices and also yields better results, throughout the element, than those obtained by the conventional approach. Two simple examples are provided for illustratio

ISSN:0029-5981    

DOI:10.1002/nme.1620310409

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractThe scattering problem of elastic waves by a crack with spring‐mass contact is investigated. Such a crack may be regarded as a simplified model of a thin elastic inclusion. Boundary integral equations are formulated for both displacement and traction on crack faces and are solved numerically. Numerical results are presented for stress intensity factors, crack‐opening displacements and scattering cross‐sections. Our results are in good agreement with other published solutions. It is also found that the effect of a mass can not be neglected in evaluation of scattering cross‐sections, even if the mass i

ISSN:0029-5981    

DOI:10.1002/nme.1620310410

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractBoundary representation by straight lines and circular arcs is described, and the error introduced through the common representation of circular arc boundaries by quadratic geometrical shape functions is investigated. This error is shown to be in some cases the major contributor to the total error. An even more significant advantage of exact boundary representation is that it permits many of the required integrations to be performed analytically, rather than by using Gaussian quadrature. For example, all integrations in any rectilinear domain can then be evaluated analytically. This generally produces an increase in accuracy, and a saving in the computing time required to assemble the coefficient matrices. In slender domains both this increase in accuracy and saving in computing time are very marked, as analytical integrations permit the use of very much coarser discretization than would be required for numerical quadrature.

ISSN:0029-5981    

DOI:10.1002/nme.1620310411

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY