摘要:

AbstractA series of direct‐integration and model‐expansion finite element algorithms for a geometrically and materially nonlinear elastodynamic problem are constructed and analysed. The algorithms are constructed by temporally approximating the individual nonlinear stiffness terms such that discrete conservation laws are obtained. This conservative property has a positive effect in providing a stable appromixation, and in addition allows the stability properties of the algorithms to be easily assessed. Stability and convergence criteria for the algorithms are rigorously established using an energy met

ISSN:0029-5981    

DOI:10.1002/nme.1620210602

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractConventional error analyses norms in the finite element method are based on the percentage error or its equivalent in some computed value as compared to the theoretically predicted value. In problems where two or more field variables are coupled, it is possible that if the field interpolation functions do not ‘consistently’ reproduce limiting situations of physical behaviour, there may be very large errors which are exaggerated enormously when some structural parameters become indefinitely large in a penalty limiting sense. The percentage error norms therefore saturate quickly to a value approaching 100 per cent and do not sensibly reflect the relationship between error and the structural parameter, even on a logarithmic plot.Errors due to these spurious constraints have recently been recognized as belonging to a special class described as ‘errors of the second kind’. A new error norm, called the additional stiffening parameter, helps to recognize the manner in which errors of the second kind can be blown out, of propprtion by a large variation in some structural parameter. Recent investigations in some multi‐field problems are summarized here to demonstrate the usefulness of thi

ISSN:0029-5981    

DOI:10.1002/nme.1620210603

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractThe complex variable boundary element method (CVBEM) is used to approximate several potential problems where analytical solutions are known: A modelling result produced from the CVBEM is a measure of relative error in matching the known boundary condition values of the problem. A CVBEM error‐reduction algorithm is used to reduce the relative error of the approximation by adding nodal points in boundary regions where error is large. From the‐test problems, overall error is reduced significantly by utilizing the adaptive integration algori

ISSN:0029-5981    

DOI:10.1002/nme.1620210604

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractThis analysis presents a procedure that can reliably debug computer programs. The central idea lies in creating a fictitious problem whose exact solution exists and is known, and in obtaining the numerical solution for comparison with the exact solution. If the two solutions are found identical, it is safe to assume that the computer program computing the fictitious problem is free of bugs. Then, conversion of the program computing the ficititious problem to that computing the real problem generally involves changing only one single statement. This procedure may be jointly used with all the existing numerical schemes.

ISSN:0029-5981    

DOI:10.1002/nme.1620210605

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractA new hourglassing control technique for quadrilateral and hexahedral elements used in dynamic finite element codes is presented. Based on expansion of the strees in a Taylor series and retention of additional terms beyond the usual constant stress term, this technique has the advantage that actual rather than artificial material properties are used. Simplifications that render this technique competitive with artificial viscosity and stiffness procedures in terms of additional storage and computation requirements are described.

ISSN:0029-5981    

DOI:10.1002/nme.1620210606

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractA structure is defined by a set of governing points. These points can be used to define lines, surfaces and solids. A governing point can be connected to a design variable. The values of the design variables are determined in order to minimize the weight of the structure subject to a number of stress constraints. Three simple structures are then designed.

ISSN:0029-5981    

DOI:10.1002/nme.1620210607

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractThe pressure pattern of nonlinear airflow through a filled grain bin is obtained by numerically solving the partial differential equation modelling the flow. The finite element method as implemented in an IMSL package—TWODEPEP—is used to obtain the numerical approximation to the solution. The predicted isopressure lines are compared with other published computational results and with the experimentally measured values. It is shown that some features of the experimental isopressure patterns can be obtained computationally by using solution techniques that are more accurate than the ones used so

ISSN:0029-5981    

DOI:10.1002/nme.1620210608

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractTwo generalized finite difference representations of then‐dimensional Laplacian operator are obtained vectorialiy by extensions of the techniques previously developed for three‐dimensional space. Each representation is presented in a form which can readily be applied at the nodes generated in an automatic decomposition of ann‐dimensional region. The finite difference expressions for the Laplacian are applied to the n‐dimensional sphere, as well as to certain important polytopes for which detailed algebraic descriptions are p

ISSN:0029-5981    

DOI:10.1002/nme.1620210609

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractNon‐stationary, behaviour of statistical moments up to the second order, of solutions of linear one‐dimensional diffusion equations having random initial conditions and random external excitations the latter of which is represented by non‐stationary Gaussian white noises, is considered. Three approaches are presented: the first is concerned with the analytical solution procedure based on separation of variables together with the superposition principle; the second deals with a semi‐analytical approach by the use of finite element and finite difference approximations in space; and the third is related to numerical analysis using the simplest explicit and implicit finite differences. Comparison is made for the results obtained by these three solution procedures. Convergence behaviour of the analytical solutions is investigated, and the consideration of stability of the finite difference solutions is als

ISSN:0029-5981    

DOI:10.1002/nme.1620210610

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractThe developments of an existing 48 degrees‐of‐freedom (d.o.f.), curved, quadrilateral, thin shell element, for materially and geometrically nonlinear static analysis of shell structures, are extended for the study of dynamic responses of nonlinear shells. The variable‐order polynomial representations of the shell surface and the non‐axisymmetric definition of the shell boundaries allow the study of the dynamic behaviour of a class of shell structures more general than those treated by using flat plate elements and elements with assumptions of axisymmetry. The equations of motion are based on a Lagrangian frame of reference. A combination of step‐by‐step and iterative procedures is used for the solution of nonlinear equations. The incremental equations of motion are linearized for computation purposes, and an algorithm for numerical integration based on Newmark's generalized operator for dynamic analysis, using optional iteration, is adopted. The flow theory of plasticity is used in the inelastic range, and perfectly plastic or isotropic strain hardening materials are considered. The spread of plastic zones in the thickness direction is treated by using a layered model. Numerical examples presented include the dynamic analyses of a square plate, a circular annulus, a cylindrical panel and a spherical cap. Comparisons with existing solutions demonstrate the validity and accuracy of the present d

ISSN:0029-5981    

DOI:10.1002/nme.1620210611

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY