Showing papers in "Computer Methods in Applied Mechanics and Engineering in 1972"

TL;DR: In this article, it is shown how the analytical relations can be satisfied in a stabilized manner in order to improve the numerical accuracy of the solution of the differential equations, which leads to a modified differential system which is often stable in the sense of Ljapunov.

TL;DR: In this article, a general theory for obtaining asymptotic estimates of the form ∥ u − Πu ∥ Hm ( K ) = O ( h k + 1− m ).

TL;DR: In this paper, two finite-difference procedures are described for the computation of steady, three-dimensional boundary layers in ducts, one method uses pressure as the fourth dependent variable, while the other uses vorticity.

TL;DR: In this article, a simplified analog (the finite Hilbert transform) or the equation of two-dimensional incompressible thin wing flow, is studied and several important points concerning this discretization proved.

TL;DR: In this paper, two recently developed numerical procedures have been used to predict some laminar, three-dimensional flows in rectangular-sectioned ducts, compared with experimental data and theoretical analyses.

TL;DR: It is shown that implicit schemes are best suited for the particular problem and the successive under-relaxation method (SUR) is appropriate for the solution of the implicit equations.

TL;DR: The hypermatrix Cholesky approach is presented, as implemented by the authors and their colleagues as a part of the ASKA structural analysis package, in order to reduce both the time spent in performing the arithmetical operations as well as the required number of data transfers between core and external storage.

TL;DR: In this paper, the minimum weight design of both perfectly plastic and elastic grillages of given strength as well as elastic grillage of given stiffness and fibre-reinforced plates with given strength is considered.

TL;DR: In this paper, the application of the SHEBA triangular thin shell element with variable curvature initiated in [2] is discussed and a number of examples are presented illustrating the appropriate mapping procedures and the pertinent rules for the boundary conditions; it is also shown how singularities can be simulated.

TL;DR: In this paper, a Boussinesq response of a homogeneous, isotropic supporting media is used for the formulation of an elastic half space stiffness matrix, assuming full bond between plate and half space.

TL;DR: In this article, a second order accurate difference method is presented for systems of first order hyperbolic differential equations, analogous to the Courant, Isaacson, Rees (CIR) method.

TL;DR: In this article, a numerical procedure based on Floquet's theorem is presented which answers the stability question in full detail and reveals indeed the analytical representation of the fundamental system of solutions of the variational equations.

TL;DR: Two symmetric decompositions based on the QR factorization are suggested, and these are in general more accurate than the Cholesky decomposition and only slightly more time-consuming.

TL;DR: In this article, the authors show that the range of validity of a single segment solution is increased by a factor of six to ten over what has previously been suggested in the literature for two-point boundary value problems exhibiting boundary layer behavior.

TL;DR: The combination of matrix exponential method and the APL language provides a fast and accurate interactive means for solving this class of ordinary differential equations.

TL;DR: In this article, the problem of finding the natural frequencies and the appropriate modes of vibration of tuning-forks of quite general geometry is investigated, where the tuning-fork is first discretized, and then the method of transfer matrices is applied.