摘要:

AbstractA diagonal lumped mas formulation with non−zero inertia terms is presented for Ahmad's general shell element. The effect of co−ordinate transformation of the mas matrix is demonstrated. Due to arbitray co−ordinate transformation on nodal variables, the diagonal lumped mas matrix becomes a banded matrix of half bandwidth three. It is shown that with some approximations this matrix can be made diagnoal without effecting the results appreciably. Numerical examples are presented to illustrate the accuracy of the formulation. Similar lumped mass matrix formulation is also given for axisymmetric shell ele

ISSN:0029-5981    

DOI:10.1002/nme.1620121102

出版商:John Wiley&Sons, Ltd    

年代:1978

数据来源: WILEY

摘要:

AbstractA Procedure is presented for generating a class of conformal mappings useful in the formulation of finite−difference problems involving curved boundaries. The method provides a systematic approach that is capable, in principle, of reducing the geometry to a nearly−rectangular domain for a wide variety of partical problems. The introduction of sheared co−ordinates in this computational domain then provides for solution of the problem in a nearly−orthogonal (in fact, nearly−conformal) co−ordinate system, with its boundaries corresponding to co−ordinate lines. The method is based upon the Schwarz−Christoffel transformation and is quite simple to apply. Several examples illustrating the types of geometries which can be treated in this manne

ISSN:0029-5981    

DOI:10.1002/nme.1620121103

出版商:John Wiley&Sons, Ltd    

年代:1978

数据来源: WILEY

ISSN:0029-5981    

DOI:10.1002/nme.1620121104

出版商:John Wiley&Sons, Ltd    

年代:1978

数据来源: WILEY

摘要:

AbstractThis paper presents a thin plate element formulated along parallel lines to the general three−dimensional Semiloof shell element. This plate version possesses only one half of the total number of degrees−of−freedom of the shell element and has the advantqage that the formulation of the strains and other terms is very much simplified. The element is first assessed in static situations and then its performance in the solution of eigenvalue problems is consi

ISSN:0029-5981    

DOI:10.1002/nme.1620121105

出版商:John Wiley&Sons, Ltd    

年代:1978

数据来源: WILEY

摘要:

AbstractThe paper presents a classification of mathematical commonly encountered in connection with solution of non−linear finite element problems. The principal methods for numerical solution of the non−linear equations are surveyed and discussed. Special emphasis is placed upon the description of an automatic load incrementation procedure with equilibrium iterations. It is shown how this algorithm can be adapted for solving problems involving instabilities, snap−through and snap−back. A simple scalar quantity denoted the current stiffness parameter is suggested; this parameter is used to characterize the overall behaviour of non−linear problems. It can also be used as a steering parameter in the solution process. The use of the present technique is illustrated by several

ISSN:0029-5981    

DOI:10.1002/nme.1620121106

出版商:John Wiley&Sons, Ltd    

年代:1978

数据来源: WILEY

摘要:

AbstractThis paper analyses the oscillatory nature of central difference approximations to the heat transport equation when convection is the important mechanism of heat transport. The effects of three different boundary conditions, various heat source profiles, the Peclet Number and the parity of the number of meshes on the amplitudes of these oscillations are described. A boundary condition is presented which suppresses the oscillations to insignificant amplitudes in the one−dimensional situatio

ISSN:0029-5981    

DOI:10.1002/nme.1620121107

出版商:John Wiley&Sons, Ltd    

年代:1978

数据来源: WILEY

摘要:

AbstractA new and efficient method of dynamic condensation is presented. It reduces the order of dynamic matrices without intoroducing further approximation by representing the passive co−ordinates in terms of the active ones exactly. The resulting frequency dependent eigenvalue problem is solved by a combined technique of Sturm sequence and subspace iteration. Examples are given for a space frame and a substructure problem. Results are compared to the complete solutio

ISSN:0029-5981    

DOI:10.1002/nme.1620121108

出版商:John Wiley&Sons, Ltd    

年代:1978

数据来源: WILEY

摘要:

AbstractThe Zienkiewicz three− and four−time level schemes as proposed for vibration problems1and adapted for the numerical integration of the diffusion equation after finite element discretization. Conditions are found for A0stability and the methods are studied for their representation of the solution of y1=−λy. Methods used by various authors for linear and non−linear parabolic problems are compared. For the three time−level scheme a Liniger exponential fit of e−λ0Δtwith a larger value of λ0Δtand the fully implicit scheme give the most promising results. The four time−level scheme is so much less amenable to control as to make it unsuitable

ISSN:0029-5981    

DOI:10.1002/nme.1620121109

出版商:John Wiley&Sons, Ltd    

年代:1978

数据来源: WILEY

摘要:

AbstractFor the 12−node quadrilateral isoparametric elements, it is shown that the inverse square root singularity of the strain field at the crack tip can be obtained by the simple technique of collapsing the quadrilateral elements into triangular elements around the crack tip and placing the two side nodes of each side of the triangles at 1/9 and 4/9 of the length of the side from the tip. This is analogous to placing the mid−side nodes at quarter points in the vicinity of the crack tip for the quadratic isoparametric elements. The advantages of this method are that the displacement compatibility is satisfied throughout the region and that there is no need of special crack tip elements. The stress intensity factors can be accurately obtained by using general purpose programs having isoparametric elements such as NAST

ISSN:0029-5981    

DOI:10.1002/nme.1620121110

出版商:John Wiley&Sons, Ltd    

年代:1978

数据来源: WILEY

摘要:

AbstractA minimum−time, thermal−to−thermal sailplane trajectory optimization problem is formulated as a non−linear optimal control problem. Numerical solutions are obtained using a gradiaent projection algorithm which incorporates conjugate directions of search. Further insight into the nature of the solutions and the computational process is ontained through an analysis of the linearized sailplane dynamics and the necessary conditions for optimality. Numerical results are presented for two sailplane types and various values of thermal strength and distance between thermals. An additional problem is formulated and solved for the case of bounded contr

ISSN:0029-5981    

DOI:10.1002/nme.1620121111

出版商:John Wiley&Sons, Ltd    

年代:1978

数据来源: WILEY