摘要:

AbstractA geometrically nonlinear formulation using total Lagrangian approach is presented for the axisymmetric shell elements. The basic element is formulated using the co‐ordinates of the mid‐surface nodes and the mid‐surface nodal point normals. An important aspect of the formulation presented here is that the restriction on the magnitude of the nodal rotations is eliminated. This is accomplished by retaining true nonlinear nodal rotation terms in the definition of the displacement field and the consistent derivation of the element properties based on this displacement field. The element properties are derived and presented in detail. Numerical examples are also presented to demonstrate the element behaviour and the acc

ISSN:0029-5981    

DOI:10.1002/nme.1620180402

出版商:John Wiley&Sons, Ltd    

年代:1982

数据来源: WILEY

摘要:

AbstractA method for the numerical solution of singular integro‐differential equations is proposed. The approximate solution is sought in the form of the sum of a power series with unknown coefficients multiplied by a special term which controls the appropriate solution behaviour near and at the edges of the interval. The coefficients are to be determined from a system of linear algebraic equations. The method is applied to the solution of a contact problem of a disk inserted in an infinite elastic plane. Exact analytical solution is obtained for the particular case when the disk is of the same material as the plane. Comparison is made between the exact and the approximate solutions as well as with the solutions previously available in literature. The stability and the accuracy of the present method is investigated under variation of the parameters involved. The applicability of the method to the case when the boundary conditions for the unknown function are nonzero is discussed along with an illustrative example. A FORTRAN subroutine for the numerical solution of singular integro‐differential equations is also provi

ISSN:0029-5981    

DOI:10.1002/nme.1620180403

出版商:John Wiley&Sons, Ltd    

年代:1982

数据来源: WILEY

摘要:

AbstractFinite element analysis of engineering structures commonly requires the use of inter‐nodal displacement constraints. Current algorithms for this facility—elimination, Lagrange multipliers and penalty function methods—are briefly reviewed. An alternative approach is proposed which avoids some of the problems of these methods. This technique uses solution of the unconstrained stiffness equation with an extended number of right‐hand sides. The resulting solutions are then combined to satisfy the constraints. This method has application in the synthesis of sub‐structures with incompatible boundary variables. It is particularly efficient when the constraint affects many variables but the kinematics of the constraint can be expressed in terms of few independent variables, e.g. rigid body motion of part of the structure. In common with the Lagrange method, it produces data for use in a nonlinear analysis with constraints. The formulation of ‘rigid body’ constraints in geometric nonlinearity is detailed and

ISSN:0029-5981    

DOI:10.1002/nme.1620180404

出版商:John Wiley&Sons, Ltd    

年代:1982

数据来源: WILEY

摘要:

AbstractThe author's recent work on thermodynamically consistent numerical methods for the simulation of inviscid, adiabatic flow is extended to handle transonic flow problems of practical interest. The basic Singhal–Spalding scheme is developed and tested on two problems. The first one is the standard transonic nozzle flow. The computational results are shown to be in good agreement with the analytical solution. The second problem is a flow situation studied experimentlly by Sieverding. The inviscid results are in surprisingly good agreement with the principal qualitative features of the real folws. There are important quantitative discrepancies which are believed to be due to the inadequacies of the inviscid model rather than failings of the scheme itself. Arguments in support for this view are presente

ISSN:0029-5981    

DOI:10.1002/nme.1620180405

出版商:John Wiley&Sons, Ltd    

年代:1982

数据来源: WILEY

摘要:

AbstractThree competing finite element techniques are applied to a simple flow problem in a region with curved boundaries. Only three‐sided elements are considered. The techniques are (1) straight‐sided elements, (2) isoparametric elements, both of which use polynomial bases, and (3) curved elements using rational basis functions. The broad conclusions are that both curved‐edge techniques are much superior to their straight‐sided equivalent and that rational basis functions are quite successful in practice but require slightly more effort to implement, and cost a little more in computer time. From the point of view of efficiency, isoparametric elements seem to be the best

ISSN:0029-5981    

DOI:10.1002/nme.1620180406

出版商:John Wiley&Sons, Ltd    

年代:1982

数据来源: WILEY

摘要:

AbstractAll physical process change with time and although physicists and engineers often freeze them to simplify their model studies, this is not always possible. Add to this the existence of several subregions within the modelling domain with different physical properties, the size and number of which change with time, and one has produced what might appear to be an intractable problem. Previous studies have shown that adaptive grids are an inconvenient way of modelling such moving interface problems and suggested that the use of a fixed grid with special discontinuous elements affords an efficient solution technique.This work presents and develops the characteristic matrices for two such elements, namely a quadratic triangle with an internal interface modelled by two straight lines and a quadratic isoparametric element. Both these elements are tested against an analytical solution to a simple Poisson equation. Such tests reveal the performance of the proposed elements to be satisfactory except for the definition of gradients near the interface.

ISSN:0029-5981    

DOI:10.1002/nme.1620180407

出版商:John Wiley&Sons, Ltd    

年代:1982

数据来源: WILEY

摘要:

AbstractAn algorithm is presented and discussed which gives 40 per cent reduction in the cost of the basic subspace iteration for eigenvalues.

ISSN:0029-5981    

DOI:10.1002/nme.1620180408

出版商:John Wiley&Sons, Ltd    

年代:1982

数据来源: WILEY

摘要:

AbstractTo account for plastic deformation in plate and shell structures an elasto‐viscoplastic solution algorithm is considered based on Perzyna's model for material behaviour. This algorithm can be employed to solve for time‐dependent elasto‐viscoplastic situations and by allowing steady‐state conditions to be reached, elasto‐plastic problems can also be considered.For the large displacement elasto‐viscoplastic analysis of thin shells, an incremental stiffness procedure is employed together with a Lagrangian description of the stress and strain vectors. The Semiloof plate and shell elements are used for finite element space discretization.The procedures developed are applied to the solution of several numerical examples and the solutions compared with results from other sources wher

ISSN:0029-5981    

DOI:10.1002/nme.1620180409

出版商:John Wiley&Sons, Ltd    

年代:1982

数据来源: WILEY

摘要:

AbstractA semi‐implicit direct time integration procedure is presented which avoids factorization of the implicit difference solution matrix. The procedure, if properly implemented, requires only vectorial calculations and hence needs the same computer core space as explicit integration procedures. Guidelines for splitting the stiffness matrix into upper and lower matrices are established, which among other things are designed to satisfy a correct transmission of rigid‐body motions from element (or grid) to its adjacent eleme

ISSN:0029-5981    

DOI:10.1002/nme.1620180410

出版商:John Wiley&Sons, Ltd    

年代:1982

数据来源: WILEY

ISSN:0029-5981    

DOI:10.1002/nme.1620180411

出版商:John Wiley&Sons, Ltd    

年代:1982

数据来源: WILEY