摘要:

AbstractNew requirements for finite element model convergence are defined. It is shown that the presence of constant strain states in an element is not sufficient to guarantee convergence.Numerical tests are proposed to assess convergence, direction of convergence, monotonicity of convergence, convergence rate and monotonicity of convergence rate. The proposed tests are mathematically stronger and more general than existing tests.

ISSN:0029-5981    

DOI:10.1002/nme.1620240502

出版商:John Wiley&Sons, Ltd    

年代:1987

数据来源: WILEY

摘要:

AbstractThe one‐dimensional freezing problem can be solved numerically for the temperature distribution accompanied by explicit reference to the position of the freezing front at each time interval. A new front‐tracking scheme provides accurate determination of the phase front, which is an essential requirement for the temperature distribution in the different phases of such problems. The front is made to coincide with a grid‐node throughout the analysis. The scheme uses a combination of the finite difference and the finite element methods for obtaining the solution of the freezing pro

ISSN:0029-5981    

DOI:10.1002/nme.1620240503

出版商:John Wiley&Sons, Ltd    

年代:1987

数据来源: WILEY

摘要:

AbstractThe paper presents various ways of fitting the boundary conditions in the T‐complete functions method. The authors point out the distinct advantages of the orthogonal collocation in comparison to the equidistant collocation and the integral fit. The convergence of the Collatz error measures and the conditioning of the solution matrices are investigated in detai

ISSN:0029-5981    

DOI:10.1002/nme.1620240504

出版商:John Wiley&Sons, Ltd    

年代:1987

数据来源: WILEY

摘要:

AbstractThis paper describes two substepping schemes for integrating elastoplastic stress–strain relations. The schemes are designed for use in finite element plasticity calculations and solve for the stress increments assuming that the strain increments are known. Both methods are applicable to a general type of constitutive law and control the error in the integration process by adjusting the size of each substep automatically. The first method is based on the well‐known modified Euler scheme, whereas the second technique employs a high order Runge–Kutta formula. The procedures outlined do not require any form of stress correction to prevent drift from the yield surface. Their utility is illustrated by analysis of typical boundary value pro

ISSN:0029-5981    

DOI:10.1002/nme.1620240505

出版商:John Wiley&Sons, Ltd    

年代:1987

数据来源: WILEY

摘要:

AbstractA simple computational procedure is presented for reducing the size of the analysis model for a symmetric structure with asymmetric boundary conditions to that of the corresponding structure with symmetric boundary conditions. The procedure is based on approximating the asymmetric response of the structure by a linear combination of symmetric and antisymmetric global approximation vectors (or modes). The key elements of the procedure are (a) restructuring the governing finite element equations to delineate the contributions to the symmetric and antisymmetric components of the asymmetric response, (b) successive application of the finite element method and the classical Rayleigh–Ritz technique. The finite element method is first used to generate a few global approximation vectors (or modes). Then the amplitudes of these modes are computed by using the Rayleigh–Ritz technique.A tracing parameter is introduced which identifies all the contributions to the antisymmetric response. The global approximation vectors are selected to be the solution corresponding to a zero value of the tracing parameter and the various‐order derivatives of the solution with respect to this parameter, evaluated at zero value of the parameter. The size of the analysis model used in generating the global approximation vectors is identical to that of the corresponding structure with symmetric boundary conditions.The effectiveness of the computational procedure is demonstrated by means of numerical examples of linear static problems of shells, and its potential for solving non‐linear problems is di

ISSN:0029-5981    

DOI:10.1002/nme.1620240506

出版商:John Wiley&Sons, Ltd    

年代:1987

数据来源: WILEY

摘要:

AbstractHaving established the non‐uniqueness, in general, of quadratic–linear functionals in elasticity, the investigative work on this topic is reviewed, whence it is noted that there is no existing formal approach for the identification of either the causes of singular solutions or suitable remedial measures that might ensure their elimination. A comparison of the weighted averages obtained from the single field and Reissner's principles is then used to identify a higher order uniqueness criterion for the latter. A detailed consideration of the application of the new condition to the arch equations demonstrates how and why singular solutions can be obtained, and thence how suitable forms of remedial action can often be identified. Finally, several other classes of problem are briefly investigated in order to show how the criterion can be used to explain the full range of known behaviour of the mixed meth

ISSN:0029-5981    

DOI:10.1002/nme.1620240507

出版商:John Wiley&Sons, Ltd    

年代:1987

数据来源: WILEY

摘要:

AbstractA damper technique is proposed to model the effects of radiation damping in the finite element analysis of hydrodynamic pressures generated due to the vibration of a structure submerged in a compressible fluid. The proposed damper is suitable for a time‐domain analysis. It is assumed that the fluid is inviscid and its vibration is of small amplitude. The structure–fluid system is assumed to be two‐dimensional, and the fluid domain is considered to be unbounded along the direction of structural vibration. In the finite element analysis, pressure is assumed to be the nodal unknown, and the discretized equations of motion are solved by using a direct integration procedure. As a result of the analysis of several cases, the proposed damper is found to be very effective and efficient for a wide range of the period of excitation. The only exception is the case when the period of excitation is near the natural period of vibration of the fluid domain. For this case, the pressure becomes infinitely large and there is no requirement for any damper. The implementation of the proposed damper in the finite element analysis requires practically no extra computational effort. With the use of the suggested technique, an unbounded fluid domain may be truncated at a relatively very short distance from the structure, as compared to the distance required when the Sommerfeld damper is used. As a result of these advantages of the proposed technique, the cost of computation is greatly re

ISSN:0029-5981    

DOI:10.1002/nme.1620240508

出版商:John Wiley&Sons, Ltd    

年代:1987

数据来源: WILEY

摘要:

AbstractAlmost all general purpose boundary element computer packages include a curved geometry modelling capability. Thus, numerical quadrature schemes play an important role in the efficiency of programming the technique. The present work discusses this problem in detail and introduces efficient means of computing singular or nearly singular integrals currently found in two‐dimensional, axisymmetric and three‐dimensional applications. Emphasis is given to a new third degree polynomial transformation which was found greatly to improve the accuracy of Gaussian quadrature scheme's within the near‐singularity range. The procedure can easily be implemented into existing BE codes and presents the important feature of being self‐adaptive, i.e. it produces a variable lumping of the Gauss stations toward the singularity, depending on the minimum distance from the source point to the element. The self‐adaptiveness of the scheme also makes it inactive when not useful (large source distances) which makes it very safe for gene

ISSN:0029-5981    

DOI:10.1002/nme.1620240509

出版商:John Wiley&Sons, Ltd    

年代:1987

数据来源: WILEY

摘要:

AbstractThis paper presents the development of an automatic design algorithm for gears. The criterion on which the design performance is assessed is the maximum tensile stress induced in the gear tooth fillet under service conditions. Starting from an initial set of design parameters the stresses in the gear tooth fillet are calculated. The maximum value of the stress is then expressed as a function of the design variables. By minimizing this function, the objective function, subject to both equality and inequality constraints a new set of design parameters, is produced. Iterative application of the analysis and minimization stages forms a sequence of non‐linear optimization problems which converges to yield the optimal design.Finite element techniques employed to calculate accurately the stresses in the gear tooth are again used to compute the design derivatives. This process is very economical, owing to its efficient reuse of the factorized stiffness matrix.The algorithm is illustrated by its application to a spur gear tooth of involute profile. Both linear and non‐linear forms of the objective function are used and a comparison made between the solutions obtai

ISSN:0029-5981    

DOI:10.1002/nme.1620240510

出版商:John Wiley&Sons, Ltd    

年代:1987

数据来源: WILEY

摘要:

AbstractNew algorithms which improve the finite element solution on a fixed mesh of the domain are developed. For this, objective functions which depend on a positive parameter to be determined are proposed. These functions lead to criteria which combine in several ways the residual of the solution, the approximation in the Euclidean norm of the value of the solution at the nodes, and the approximations in the energy andHknorms. Some aspects of optimality are studied and, finally, numerical results are given.

ISSN:0029-5981    

DOI:10.1002/nme.1620240511

出版商:John Wiley&Sons, Ltd    

年代:1987

数据来源: WILEY