摘要:

AbstractA finite element formulation which includes the piezoelectric or electroelastic effect is given. A strong analogy is exhibited between electric and elastic variables, and a ‘stiffness’ finite element method is deduced. The dynamical matrix equation of electroelasticity is formulated and found to be reducible in form to the well‐known equation of structural dynamics, A tetrahedral finite element is presented, implementing the theorem for application to problems of three‐dimensional electroela

ISSN:0029-5981    

DOI:10.1002/nme.1620020202

出版商:John Wiley&Sons, Ltd    

年代:1970

数据来源: WILEY

摘要:

AbstractThis paper is concerned with the development of general discrete models for the analysis of boundary‐value problems in the first strain–gradient theory of elasticity. Extensions of the finite element method are constructed for this purpose, and general equations of motion are derived for finite elements of a class of micro‐polar materials which are characterized by strain energy functions involving strains and second gradients of strains or displacements. The notion of generalized nodal doublets is introduced. The problem of a composite consisting of a strain–gradient sensitive microlayer embedded between semi‐infinite bodies is examined as an example problem. Some of the results are compared with available exact

ISSN:0029-5981    

DOI:10.1002/nme.1620020203

出版商:John Wiley&Sons, Ltd    

年代:1970

数据来源: WILEY

摘要:

AbstractA numerical method is presented for the solution of the radially symmetric heat conduction problem in a melting sphere. The method employs the embedding technique; this permits the solution to be written in the form of an ordinary integro‐differential equation which is readily solved numerically by means of a forward integration scheme. The accuracy of the method is briefly discussed and numerical results for both constant and variable heat inputs are presente

ISSN:0029-5981    

DOI:10.1002/nme.1620020204

出版商:John Wiley&Sons, Ltd    

年代:1970

数据来源: WILEY

摘要:

AbstractMethods for the analysis of complex, highly redundant structures subjected to intermittent loads causing biaxial membrane stress and stress reversal into the plastic range are presented. The Bauschinger effect in multi‐axial stress is taken into account by the use of Ziegler's modification of Pragers kinematic hardening theory. The implementation of this plasticity theory in the discrete element methods involves the application of the loading in small increments. A linear relationship between increments of plastic strain and of stress, arising out of the theory, is used in conjunction with a linear matrix equation that governs the elastic behaviour of the structure. In the latter equation, plastic strains are interpreted as initial strains. A solution to the linear matrix equation, expressed in terms either of stress or of total strain, may be obtained by utilizing one of two alternative procedures. The methods are capable of treating materials which exhibit elastic–plastic behaviour involving ideal plasticity, linear or non‐linear strain hardening, or limited strain hardening. Application is made to several representative structures. Comparison of some of the results with existing test data for both monotonic and reversed loading shows good correl

ISSN:0029-5981    

DOI:10.1002/nme.1620020205

出版商:John Wiley&Sons, Ltd    

年代:1970

数据来源: WILEY

摘要:

AbstractA newly developed numerical Laplace transform inversion technique is described. A derivation of the method, termed the ‘multidata method’, is presented along with a description of a similar collocation method. Similarities and differences between the two numerical methods are described and discussed. Results of parameter studies of both methods are presented which demonstrate the sensitivity to error displayed by the collocation method and the magnitude of the improvement in accuracy obtainable with the multidata method as compared with the collocation method, especially when errors exist in the function to be inver

ISSN:0029-5981    

DOI:10.1002/nme.1620020206

出版商:John Wiley&Sons, Ltd    

年代:1970

数据来源: WILEY

摘要:

AbstractA general digital computer method based on a Sturm sequence procedure is described for determining the natural frequencies and associated modes of undamped free vibration of frames and other structures whose stiffness and mass matrices are of band form. A program which uses the method for the analysis of plane multi‐storey building frames is outlined, and numerical results are presented for a simple test case and for a 19‐storey fr

ISSN:0029-5981    

DOI:10.1002/nme.1620020207

出版商:John Wiley&Sons, Ltd    

年代:1970

数据来源: WILEY

摘要:

AbstractIn this study, finite element solution procedures are developed for an elastica problem of inextensible beams. The element stiffness matrices are obtained by using Galerkin's method. Results of a numerical example compare reasonably well with those obtained by using the elliptical integral.Extensions of this research are currently being made to include membrane effects of beams and to develop plate element stiffness matrices for elastica problems of plate structures.

ISSN:0029-5981    

DOI:10.1002/nme.1620020208

出版商:John Wiley&Sons, Ltd    

年代:1970

数据来源: WILEY

摘要:

AbstractThis report summarizes an experimental application of the finite element approach to two‐dimensional inviscid fluid flow.The method results in a matrix equation relating the vector of velocities at the nodal points with the vector of singularities. The singularities, which are concentrated at the nodes, consist of a source and a vortex.On solution of this equation (defining the flow in the region), boundary conditions must te stipulated. This usually involves setting the internal singularities to zero and making certain modifications ro those lying on the boundary of the region.Some results of the application to a particular problem are included in the pape

ISSN:0029-5981    

DOI:10.1002/nme.1620020209

出版商:John Wiley&Sons, Ltd    

年代:1970

数据来源: WILEY

摘要:

AbstractSome typical results of an extensive series of evaluations of parallelogram‐shaped plate bending elements with increasing levels of sophistication are presented. It is shown that, contrary to experience in other fields of stress analysis, this sophistication does not lead to striking improvements in accuracy in the solution of simple rectangular and skew plate problems. A computational procedure is described whereby stiffness matrices may be automatically generated from the minimum of input data specifying the displacement modes prescribed for the elemen

ISSN:0029-5981    

DOI:10.1002/nme.1620020210

出版商:John Wiley&Sons, Ltd    

年代:1970

数据来源: WILEY

摘要:

AbstractA conforming plate bending solution using simple polynomial deflection functions of third‐degree inside each triangular element is presented. In order to avoid normal slope discontinuities along the sides of the elements, the plate displacement parameters are subjected to ‘slope continuity conditions’ acting as constraints to the minimum potential energy problem. This is then solved by the classical method of Lagrange introducing multipliers as new auxiliary variables. If a special variational formulation of the problem is used, it can be shown that the Lagrangean multipliers are generalized stress parameters. The suggested solution is therefore basically a ‘mixed’ solution, the unknown variables of the problem being both displacement and stress parameters. Several numerical results are

ISSN:0029-5981    

DOI:10.1002/nme.1620020211

出版商:John Wiley&Sons, Ltd    

年代:1970

数据来源: WILEY