ISSN:0029-5981    

DOI:10.1002/nme.1620040102

出版商:John Wiley&Sons, Ltd    

年代:1972

数据来源: WILEY

摘要:

AbstractTwo methods for the numerical evaluation of orthogonal damping matrices are developed. The first relates the modal damping ratios to the coefficients of the Caughey series. The second is a direct approach which expresses the damping matrix as a sum of a series of matrices each of which produces damping in a particular mode. It is found that the direct approach is more convenient to apply and is less numerically sensitive than the series approach.

ISSN:0029-5981    

DOI:10.1002/nme.1620040103

出版商:John Wiley&Sons, Ltd    

年代:1972

数据来源: WILEY

摘要:

AbstractThe constitutive equation is assumed in a very general form which includes as special cases non‐linear creep, incremental elasto‐plasticity as well as viscoelasticity represented by a chain ofnstandard solid models. Subdividing the structure intoNfinite elements, the problem of structural analysis is formulated with a system of 6N(n+ 1) ordinary non‐linear first‐order differential equations in terms of the components of stresses and strains in the elements. This formulation enables one to apply Runge–Kutta methods or the predictor–correc

ISSN:0029-5981    

DOI:10.1002/nme.1620040104

出版商:John Wiley&Sons, Ltd    

年代:1972

数据来源: WILEY

摘要:

AbstractSome elements commonly used for analysis are examined for examined for completeness of polynomial interpolation and computational efficiency. Extensions ton‐dimensional space are shown to be natural consequences of the interpolation, thus all elements considered here allow for finite element approximation in higher than three‐dimensional spaces (e.g. space–time interpolations). From the study it is concluded that ‘serendipity’ class elements from the most efficient elements up to third‐degree polynomial approximations. The method used here to develop the serendipity shape functions allows for different orders of interpolation along each edge. Thus, in zones where high accuracy is required meshes can now be easily changed from linear to quadratic or higher‐order elements. Computations on some simple problems have demonstrated this to be a superior method than using large numbers of low ord

ISSN:0029-5981    

DOI:10.1002/nme.1620040105

出版商:John Wiley&Sons, Ltd    

年代:1972

数据来源: WILEY

摘要:

AbstractA computer program for surge tank analysis, which gives a complete history of the water level in the tank and the fluid velocity in the pressure conduit from the time of initiation of value closure, is described and presented. The governing equations are solved by third‐order Runge–Kutta procedure and losses in head in the pressure conduit and surge tank constriction. A major aspect in the paper is the non‐dimensional from of the governing parameters, facilitating the use of the program in preliminary design situa

ISSN:0029-5981    

DOI:10.1002/nme.1620040106

出版商:John Wiley&Sons, Ltd    

年代:1972

数据来源: WILEY

摘要:

AbstractA numerical method for the direct computation of the particle densities, mass density, enthalpy and specific heat at constant pressure of a monatomic ionized gas in thermodynamic equilibrium is presented. This method permits calculation of the thermodynamic properties without iteration or numerical differentiation of any of the formulae.

ISSN:0029-5981    

DOI:10.1002/nme.1620040107

出版商:John Wiley&Sons, Ltd    

年代:1972

数据来源: WILEY

摘要:

AbstractThe application of the high precision triangular plate bending element to problems with curved boundaries is considered. Appropriate edge conditions for nodal points on these boundaries are derived. The error inherent in representing the shape of a curved boundary by a series of straight segments is found to be the limiting factor on accuracy, while the effect of approximations in the actual boundary conditions is minor. To overcome the first type of error, the high precision element is modified to include one curved edge. Substantial improvements in accuracy are obtained, as demonstrated in example calculations for circular and elliptical plates.

ISSN:0029-5981    

DOI:10.1002/nme.1620040108

出版商:John Wiley&Sons, Ltd    

年代:1972

数据来源: WILEY

摘要:

AbstractA mixed triangular finite element model has been developed for plate bending problems in which effects of shear deformation are included. Linear distribution for all variables is assumed and the matrix equation is obtained through Reissner's variational principle. In this model, interelement compatibility is completely satisfied whereas the governing equations within the element are satisfied ‘in the mean’. A detailed error analysis is made and convergence of the scheme is proved. Numerical examples of thin and moderately thick plates are presen

ISSN:0029-5981    

DOI:10.1002/nme.1620040109

出版商:John Wiley&Sons, Ltd    

年代:1972

数据来源: WILEY

摘要:

AbstractBy formulating the potential boundary value problems in terms of physical (in contrast to purely mathematical) variables, the existence of dual energy principles may be clearly distinguished. In direct analogy with elasticity, two possible energy methods present themselves giving rise to two possible finite element procedures. General upper and lower bounds on an energy quantity may be obtained, which in the case of seepage become the total seepage rate for a certain class of seepage problem. For this case of seepage the derivation of the finite element procedure and the computing of the bounds is described.

ISSN:0029-5981    

DOI:10.1002/nme.1620040110

出版商:John Wiley&Sons, Ltd    

年代:1972

数据来源: WILEY

摘要:

AbstractThis paper deals with the stability of the numerical solutions of a dynamic finite element analysis. The solutions are obtained through a stepwise integration of the equations of motion. Upper bounds on the steplength of the integration are obtained from a stability analysis of using a simple finite difference approximation for the equations of motion, and are shown to depend strongly on the particular element is use and on how the mass of the element is distributed at its nodes.As an example, the two‐dimensional wave propagation in a semi‐infinite plate subjected to a suddenly applied moment along its edge is studies. Through the example, we show that the bound on the steplength, obtained from the simple analysis, can provide a useful guide on choosing the steplength in other higher order integration methods. In particular, we show that, for stability considerations, the upper bound on the steplength should also hold for a fourth order explicit method. In order to achieve an acceptable accuracy of the solution, we show that the steplength should be approximately one half of the bound for the higher order explicit method as well as a higher order implicit method.Solution of the example has been compared with that of the Timoshenko the

ISSN:0029-5981    

DOI:10.1002/nme.1620040111

出版商:John Wiley&Sons, Ltd    

年代:1972

数据来源: WILEY