摘要:

AbstractExact expressions are presented for the potentials, at an arbitrary point in space, due to two quadratic distributions in a triangular disc. These expressions are obtained by means of extensions of the analytical techniques previously developed for evaluating the potential integrals for constant and linear distributions. It is shown that the potential due to any quadratic distribution in a triangle may be obtained by using the two expressions derived here, together with an expression for the potential corresponding to a linear distribution. This latter expression was presented in an earlier paper.1Numerical values obtained through the use of the two expressions are compared with those which result from the numerical evaluation of the potential integrals by triangle quadratures.

ISSN:0029-5981    

DOI:10.1002/nme.1620210202

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractUse of the Green function, for the solution of boundary‐value problems, frequently results in singular integral equations. Algorithms are presented for the accurate and efficient treatment of singular kernels frequently encountered in the boundary element method (BEM). They are based upon the use of appropriately weighted Gaussian quadrature formulae, together with numerical geometrical transformations of the region of integration. The use of high‐order subdomain expansion functions, for interpolation over nonplanar elements, allows boundary curvature to be accommodated. In particular, the handling of Green functions with logarithmic and r−1behaviour are detailed. Volume integrals, with r−2singularity, are outlined. Operations are performed on a simplex, thus resulting in generality and ease of automation. This scheme has been incorporated into boundary element method software and successfully applied to a variety of p

ISSN:0029-5981    

DOI:10.1002/nme.1620210203

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

ISSN:0029-5981    

DOI:10.1002/nme.1620210204

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractThis paper reports a new explicit and conditionally stable finite difference equation for heat conduction. It predicts results with an accuracy comparable with or better than that obtainable by other methods. Stability of operation can be extended to any desired degree by subdividing the basic time step and increasing the number of nodes. Some existing difference equations are special cases of the new equation reported in this paper. The new solution has been tested by calculating the response of a slab to transient and progressive waves whose analytical solutions are known.

ISSN:0029-5981    

DOI:10.1002/nme.1620210205

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractIn a previous paper1, design sensitivity analysis of static response of structural systems when general boundary conditions are imposed during the analysis phase was developed and presented. This paper presents methods for design sensitivity analysis of dynamic response of structural systems when general boundary conditions are imposed during the analysis phase: Eigenvalue as well as transient response problems are discussed. Design sensitivity expression for eigenvalue constraints is derived. For the transient problem, point‐wise as well as the integral‐type constraint functions are treated. Advantages of these design sensitivity analysis procedures for the dynamic problem are the same as for the static problem. Namely, they are compatible with any existing finite element analysis computer code. Also, they can handle general boundary conditions that are design independent or dependent. Three simple examples are presented to show use of the procedures. Based on these applications, general‐purpose numerical procedures can be developed and incorporated into existing computer

ISSN:0029-5981    

DOI:10.1002/nme.1620210206

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractThis paper presents a finite element analysis of laminated bimodulus composite thin shells of revolution using a 48 d.o.f. doubly curved quadrilateral finite element. All the three displacements of the shell element reference surface are expressed as products of one‐dimensional first‐order Hermite interpolation polynomials. The constitutive relationship for a bimodulus composite is assumed to depend on the fibre‐direction strain experienced by each orthotropic layer. Consequently the true state of strain and the corresponding constitutive relationship in a bimodulus composite structure are to be determined iteratively. The true state of stress/strain is obtained by specifying a maximum error in the locations of the two neutral surfaces (one along each of the orthogonal reference axes) in the shell. The use of the quadrilateral shell finite element is validated by solving the problem of (i) a freely supported single layer (0°) bimodulus composite square plate and (ii) a freely supported single layer (0°) cylindrical panel, which are subjected to sinusoidal transverse loading and for which analytical solutions are available. Next, the problems of a single layer (90°) pinched cylindrical shell and a single layer (0°) open crown hemispherical shell are solved to show the ability of the presen

ISSN:0029-5981    

DOI:10.1002/nme.1620210207

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractA new finite element technique for calculating energy release rates is presented. An explicit expression for energy changes due to virtual crack extensions is formulated based on a variation of isoparametric element mappings. Energy release rates are calculated directly from integral expressions evaluated over singular quarter‐point isoparametric elements surrounding the crack tip. Since the energy release rates are expressed in variational form, there is no need for the analyst to select a small finite crack extension to simulate a virtual crack extension. The method is shown to produce very accurate solutions even with fairly coarse element meshes. A similar technique for mixed‐mode fracture based on mutual potential energy release rates is descri

ISSN:0029-5981    

DOI:10.1002/nme.1620210208

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractA geometrically nonlinear formulation for a 48 degrees‐of‐freedom (d.o.f.) quadrilateral shell element is presented. Each of the three displacement functions ofu,vand w is based on the bicubic Hermitian polynomial. The surface of the element is modelled using linearized ratronal B‐spline functions which may be linked to the geometric data bases generated by the computer‐aided design system. The displacement functions and the 48 d.o.f. are expressed in both curvilinear and Cartesian forms, whereas the strain‐displacement equations are expressed in curvilinear co‐ordinates. The use of Cartesian displacement functions and degrees‐of‐freedom allow for the proper representation of the six rigid body motions even for the element with nonzero Gaussian curvature, such as a bellows. Two examples are demonstrated: snap‐through buckling of a spherical cap and large deflection of a semi‐toroidal bellows shell. Results compare well with al

ISSN:0029-5981    

DOI:10.1002/nme.1620210209

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractRecently developed solid modelling systems for the design of complex physical solids using interactive computer graphics offer the exciting possibility of an integrated design/analysis system. Called geometric modellers, these systems build complex solids from primitive solids (cubes, cylinders, spheres, solid patches, etc.) and macro solids (combination of primitives)3, 4, 8, 16, 18, 25, 38. To provide an effective structural analysis capability for these systems, methods must be devised to ease the burden of discretizing the solid geometry into a user controlled (usually locally graded) finite element mesh. The purpose of this paper is to describe an interactive solid mesh generation system capable of generating valid meshes of well‐proportional tetrahedral finite elements for the decomposition of multiply connected solid structures. The system uses a semi‐automatic node insertion procedure to locate element node points within and on the surface of a structure. An independent automatic three‐dimensional triangulator then accepts these nodes as input and connects them to form a valid finite element mesh oftetrahedral elements. Although this report makes use of a modeller based on a constructive solid geometry representation (a so‐called CSG modeller), the mesh generation strategy elaborated herein is completely general and makes no particular use of the CSG represe

ISSN:0029-5981    

DOI:10.1002/nme.1620210210

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractThe two‐dimensional inverse heat conduction problem is solved using the method of dynamic programming. One problem involves determining two unknown heat flux histories imposed on two faces of a slab. Several numerical experiments were performed to ascertain the effects of noise and the weighting parameter

ISSN:0029-5981    

DOI:10.1002/nme.1620210211

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY