摘要:

AbstractTwo variations of an iterative scheme are presented for the solution to algebraic eigensystems. These algorithms are used in conjunction with the method of reduced generalized co‐ordinates so thatnnumber of frequencies and mode shapes are obtained simultaneously. The bases of the scheme are the well‐known results of Stodola–Vianello and Gram–Schmidt. Advantages of the present schemes are realized both in computational effort and in computer storage. Examples are presented to illustrate the convergence characte

ISSN:0029-5981    

DOI:10.1002/nme.1620040202

出版商:John Wiley&Sons, Ltd    

年代:1972

数据来源: WILEY

摘要:

AbstractAn efficient digital computer method is presented for the determination of propagation of elastic stresses and deformations in certain geometrically non‐linear structures subjected to high impact loading. The finite element matrix displacement approach utilizing curved quadrilateral shell elements in conjunction with a nodewise predictor–corrector method employing Runge–Kutta extrapolation techniques has been adopted for the present solution.The related computer program written in FORTRAN V for the UNIVAC 1108 computer has proved to be effective for the solution of a range of practical problems including rectangular and cylindrical panels. Numerical results are presented for a relevant structure, the cell container and the negative electrode of an impact‐resistant battery subjected to high impact, simulating its free landing on a planetary

ISSN:0029-5981    

DOI:10.1002/nme.1620040203

出版商:John Wiley&Sons, Ltd    

年代:1972

数据来源: WILEY

摘要:

AbstractSources of data errors in the analysis of large frameworks are listed. Outputs of various forms for error detection are discussed; emphasis is given to the advantages of graphical output. For further error detection, a few procedures that can be included in computer programs are listed.

ISSN:0029-5981    

DOI:10.1002/nme.1620040204

出版商:John Wiley&Sons, Ltd    

年代:1972

数据来源: WILEY

摘要:

AbstractThe finite element method is applied to the free transverse vibration of circular and annular plates of varying thickness. An annular element is derived which incorporates the number of diametral modes in the deflection function. This results in an element having only four degrees of freedom, these being the deflection and slopes at the inner and outer radii of the element at an anti‐node of the particular vibration mode. Thickness variation in the radial direction is readily introduced, and stiffness and inertia matrices are presented for elements with linear and parabolic variations in thickness.The method is checked with several numerical examples. Calculations of free vibration of circular and annular plates of constant, linear and parabolic thickness variation are compared with available exact solution

ISSN:0029-5981    

DOI:10.1002/nme.1620040205

出版商:John Wiley&Sons, Ltd    

年代:1972

数据来源: WILEY

摘要:

AbstractFive previously employed numerical methods for the solution of Orr–Sommerfeld problems have been compared to each other and to a new method, the differential method ofnear‐orthonormalized integration. Brief summaries of each method are included. The comparison, based on seven factors, reflects the results of an implementation of a computer program for each method for the classic Orr–Sommerfeld problem of plane Poiseuille flow. This comparison shows that the new method and the algebraic finite difference method are currently the best available numerical solution methods for the problems in this class, with the new method being less problem depe

ISSN:0029-5981    

DOI:10.1002/nme.1620040206

出版商:John Wiley&Sons, Ltd    

年代:1972

数据来源: WILEY

摘要:

AbstractIn this paper, a method is described which allows a direct derivation of a set of first‐order finite difference equations to numerically compute the motion of any conservative or non‐conservative dynamic system with a finite number of degrees of freedom. The derivation of the method is based on an application of Lagrangian multipliers to a functional form of Hamilton's equations, and reduces the work required to obtain the most desirable form for numerical integration from the standpoint of computational efficiency and accuracy. For systems with many degrees of freedom, the required matrix inversions produce first derivatives of the co‐ordinates, instead of second derivatives, thus eliminating a potential source of error in numerical integration. Two examples are given to illustrate the m

ISSN:0029-5981    

DOI:10.1002/nme.1620040207

出版商:John Wiley&Sons, Ltd    

年代:1972

数据来源: WILEY

摘要:

AbstractThe convergence proof of plate eigenvalue solution from conforming displacement finite elements is presented. The analysis is based on converting a thick plate free vibration problem in to a corresponding isoperimetric variational problem. A conforming thick, plate element is used to illustrate the mathematical development. On the basis of the derived asymptotic rate of convergence of the approximate eigenvalues, the authors propose a practical method of improving the numerical solutions. Extension of the mathematical proof to cover classical thin plate finite elements is briefly discussed.

ISSN:0029-5981    

DOI:10.1002/nme.1620040208

出版商:John Wiley&Sons, Ltd    

年代:1972

数据来源: WILEY

摘要:

AbstractThis paper presents the derivation of the stiffness matrix for a lumped parameter hyperbolic paraboloid shell element. This element is used to obtain solutions to hyperbolic paraboloid shells with various edge conditions. Numerical example for three types of support conditions (a simple support, a clamped edge and a shell supported by concentric edge beams) are presented. To illustrate the applicability of the method, the results obtained by the lumped parameter element are compared with those obtained by well‐known methods of analysis such as the variational procedure, the finite difference and the finite element metho

ISSN:0029-5981    

DOI:10.1002/nme.1620040209

出版商:John Wiley&Sons, Ltd    

年代:1972

数据来源: WILEY

摘要:

AbstractTwo‐dimensional stagnation point flow of a viscous fluid is modified by the introduction of a thin plate placed symmetrically at the stagnation point. Separation of the boundary layer results in back flow near the plate even at small Reynolds numbers. The Navier–Stokes equations governing the flow are replaced by finite differences using unequal net spacing which is finer in the boundary layer. The choice of finite differences guarantees convergence of the iterative procedures used. Only those relaxation parameters, which are necessary to obtain convergence and also to make the method computationally efficient, have been used. Numerical results for Reynolds numbers 9, 100 and 400 are obtai

ISSN:0029-5981    

DOI:10.1002/nme.1620040210

出版商:John Wiley&Sons, Ltd    

年代:1972

数据来源: WILEY

摘要:

AbstractA mixed variational formulation is used as basis for developing a mixed finite element method for axisymmetric shell. The independent unknowns of the method are the axial and radial displacement components, the rotation of the normal to the middle surface and the meridional bending stress couple. The basic element is a frustrum of curved meridian. General advantages of the mixed method are presented, one of which is the possibility of using piece‐wise linear functions of the meridional arclength to represent the basic unknowns. Test results are presented for plate bending, transverse shear deformation, membrane behaviour, edge‐zone bending, bending near the junction of two shells, convergence of the method and accuracy of middle surface curvature interpolation. Shell geometries considered are cylindrical, conical, spherical and ellipsoidal. Good results are obtained which should increase interest in the relatively less known and less tested mixed method as compared to the stiffness met

ISSN:0029-5981    

DOI:10.1002/nme.1620040211

出版商:John Wiley&Sons, Ltd    

年代:1972

数据来源: WILEY