摘要:

AbstractThe inelastic flexural behaviour of reinforced concrete beams is described, as usual, by a trilinear (or, in general, multilinear) moment–rotation relationship. The analysis of beams and frames subject to given external actions is formulated as a ‘linear complementary problem’ and, in two dual ways, as a ‘quadratic programming problem’. These problems are solved by means of classical and recent algorithms in use in operations research. By the procedures pointed out it is also possible to calculate the distribution of plastic deformations along the beams. Two methods are proposed for the evaluation of the safety factor against local failure due to limited rotation capacity: the solution technique of the direct one essentially consists of an application of the simplex method for linear programming. Finally, a procedure is established for determining, allowing for the irreversibility of plastic rotations, the structural response to non‐proportional loading histories which consist of individually proportional stages. Illustrative example

ISSN:0029-5981    

DOI:10.1002/nme.1620040302

出版商:John Wiley&Sons, Ltd    

年代:1972

数据来源: WILEY

摘要:

AbstractAn iterative procedure of structural optimization is discussed that combines finite element analysis with the use of explicit optimality conditions. The procedure is illustrated by examples concerning sandwich beams with constraints on the deflection at a specified section, the maximum deflection or the sum of the maximum deflection in all spans of a continuous beam. The examples suggest that, starting from a uniform beam, by far the greatest saving in weight is obtained in the first two or three iterations.

ISSN:0029-5981    

DOI:10.1002/nme.1620040303

出版商:John Wiley&Sons, Ltd    

年代:1972

数据来源: WILEY

摘要:

AbstractThe finite element technique is extended to an ideal gaseous mixture to study diffusion of several gaseous species in a carrier gas under various geometries and flow conditions. This is accomplished by obtaining the finite element analog of the balance of mass for each species, along with the corresponding equations for the balance of mass, momentum and energy for the mixture. Numerical results are obtained for a steady‐state, incompressible, isothermal, viscous mixture of two gases for several boundary conditions. Favourable agreement is obtained between the finite element results and analytical solution

ISSN:0029-5981    

DOI:10.1002/nme.1620040304

出版商:John Wiley&Sons, Ltd    

年代:1972

数据来源: WILEY

摘要:

AbstractA method is proposed for the inclusion of stochastic parameters, using a Monte Carlo simulation technique, in the lower bound plastic analysis of a structural continuum by non‐linear mathematical programming. The particular example chosen is a circular, cylindrical concrete silo subject to loading by its content

ISSN:0029-5981    

DOI:10.1002/nme.1620040305

出版商:John Wiley&Sons, Ltd    

年代:1972

数据来源: WILEY

摘要:

AbstractThis paper formulates the viscoelastic problem so as to allow the use of higher‐order differential equation solution techniques. Viscoelastic models describing the functional relationships of stress and strain for the material are used. However, the procedure outline is valid for more general relationships. The advantages of using Runge–Kutta integration formulae are indicated and an example demonstrates the excellent results obtainable. The computational efficiency of the method is emphasized and error prediction is discus

ISSN:0029-5981    

DOI:10.1002/nme.1620040306

出版商:John Wiley&Sons, Ltd    

年代:1972

数据来源: WILEY

摘要:

AbstractA method is presented for the derivation of displacement fields which satisfy compatibility of normal slopes at inter‐element boundaries and the condition of internal equilibrium. The displacement field is obtained by integrating the governing partial differential equation over the element, using the initial value approach. The method is applied to calculate the stiffness matrix of a triangular bending element with nine degrees of freedom. Comparison with published solutions based on various element models shows a high degree of accuracy and convergence of the method. The advantage of internal equilibrium is illustrated by an example involving slab‐column interaction. The solution correlates satisfactorily with existing experimental resu

ISSN:0029-5981    

DOI:10.1002/nme.1620040307

出版商:John Wiley&Sons, Ltd    

年代:1972

数据来源: WILEY

摘要:

AbstractA generalized eigenvalue algorithm is presented herein along with the complete listing of the associated computer program, which may be conveniently utilized for the efficient solution of certain broad classes of eigenvalue problems. Extensive applications of the procedure are envisaged in the analysis of many important engineering problems, such as stability and natural frequency analysis of practical discrete structural systems, idealized by the finite element technique. The procedure based on the Sturm sequence method is accurate and fast, possessing several significant advantages over other known methods of such analysis. Numerical results are also presented for two representative structural engineering problems.

ISSN:0029-5981    

DOI:10.1002/nme.1620040308

出版商:John Wiley&Sons, Ltd    

年代:1972

数据来源: WILEY

摘要:

AbstractIt is shown that the Helmholtz equation in three dimension leads to finite element approximations on tetrahedral elements that closely resemble the corresponding two‐dimensional treatment on triangle. For each polynomial order, there exist two numeric universal matrices independent to tetrahedron size and shape; the element matrices are always given as linear combinations of row and column permutations of these. Numeric matrices are given up to third‐order, and the permutation schemes are shown in detail. Experimental computer programs using these elements have shown fast matrix assembly times; convergence rates are essentially similar to those obtained with the corresponding triangular eleme

ISSN:0029-5981    

DOI:10.1002/nme.1620040309

出版商:John Wiley&Sons, Ltd    

年代:1972

数据来源: WILEY

摘要:

AbstractA finite element incremental stiffness formulation for determining finite displacement flexure behaviour of thin elastic plates is presented. The solution of the finite displacement problems is based on a piecewise linear incremental approach. The procedural aspects of the incremental approach, the control of incremental sizes and the accuracy of the incremental approximation are investigated. The details concerning how to obtain in‐plane stresses and how to treat edge conditions are discussed. Results include rectangular plates under lateral pressure with various edge conditions and aspect ratios. The laterally loaded plate with edges movable in the plane of the plate is also treate

ISSN:0029-5981    

DOI:10.1002/nme.1620040310

出版商:John Wiley&Sons, Ltd    

年代:1972

数据来源: WILEY

摘要:

AbstractThe problem of the elastica is generalized to include the effect if shear as well as axial strain. This leads to a non‐linear two‐point boundary‐value problem composed of five first‐order differential equations. At first the problem is linearized to study the way in which the bucking loads are modified by the combination of effects. For a simple column, the eigenvalues are found to be zeros of a third‐order polynomial, and these are evaluated by a straightforward Newton–Raphson technique using a digital computer. The postbucking behaviour is then studied by using the computer and a ‘shooting’ method to solve the non‐linear problem. For the special case of the prismatic column, graphs plotted by the computer are displayed to show the variation of load with both lateral and axial deflection for various combinations of axial compressibility and shear deformability. For one particular case, the deflected center line at various loa

ISSN:0029-5981    

DOI:10.1002/nme.1620040311

出版商:John Wiley&Sons, Ltd    

年代:1972

数据来源: WILEY