ISSN:0029-5981    

DOI:10.1002/nme.1620120402

出版商:John Wiley&Sons, Ltd    

年代:1978

数据来源: WILEY

摘要:

AbstractWe consider finite elements that have internal degrees‐of‐freedom. These d.o.f. are condensed before elements are assembled into the structure, and must be recovered later for use in element stress computation. References 1 and 2 describe two different ways to do the calculations. This paper compares the computational costs of the two methods. Test runs were made to assess costs. Relative costs depend on several factors. The factors are discussed, and suggestions are made as to the better method in various circumstan

ISSN:0029-5981    

DOI:10.1002/nme.1620120403

出版商:John Wiley&Sons, Ltd    

年代:1978

数据来源: WILEY

ISSN:0029-5981    

DOI:10.1002/nme.1620120404

出版商:John Wiley&Sons, Ltd    

年代:1978

数据来源: WILEY

摘要:

AbstractA general‐purpose technique has been developed for solving non‐linear partial differential equations. A set of approximating functions with undetermined parameters is used to evaluate the differential equation and boundary conditions at discrete points, forming a set of residuals to be minimized. The parameters which minimize the sum of squared residuals are determined by a non‐linear least‐squares minimization technique. Initial value problems are solved by integrating the equations with respect to time at the fitting points by a predictor‐corrector algorithm. The resulting formulation is independent of the form of the problem and the approximating functions, so that a broad class of problems may be solved with a single computer program. The technique is applied to several boundary and initial value problems in one and two spatial dimensions. The tecnique is applied to several boundary and initial value problems in one and two spatial d

ISSN:0029-5981    

DOI:10.1002/nme.1620120405

出版商:John Wiley&Sons, Ltd    

年代:1978

数据来源: WILEY

摘要:

AbstractThe general inverse problem is one for which measurements are made on some of the state variables and it is desired to find the forcing functions. This problem is a natural one for the method of dynamic programming. The formulation and solution of the problem are presented in matrix form, together with two illustrative examples of an inverse heat conduction problem and an inverse structural dynamics problem.

ISSN:0029-5981    

DOI:10.1002/nme.1620120406

出版商:John Wiley&Sons, Ltd    

年代:1978

数据来源: WILEY

摘要:

AbstractIn a previous paper1a method was described for computing the current distribution and inductance of systems of infinitely‐long, perfectly‐conducting, straight conductors. The method relied on the solution of a Fredholm Integal equation of the first kind, and in the present paper the method is extended to equations of the second kind in order to study the inductance and a.c. resistance factor of resistive for which approximate formulas and experimental results exist, with which the method is in good agreement over a range of grequencies of particular practical practical interest. Results have also been obtained for rectangular conductors connected in paral

ISSN:0029-5981    

DOI:10.1002/nme.1620120407

出版商:John Wiley&Sons, Ltd    

年代:1978

数据来源: WILEY

摘要:

AbstractA correlation is geven between two notations currently used in the formulation of geometrically non‐linear analysis in a Lagrangian co‐ordinate system. The first referred to as the B‐notation results in the linear elastic, initial displacement and initial stress matrices, whilst the second, here called the N‐notation features matrices that repeat in the total potential energy, equilibrium and incremental equilibrium equations. An explicit example of the correlation is presented for a pin‐jointed ba

ISSN:0029-5981    

DOI:10.1002/nme.1620120408

出版商:John Wiley&Sons, Ltd    

年代:1978

数据来源: WILEY

摘要:

AbstractA long established approximation, normally invoked in the development of classical rolling theory, is that the work roll‐strip interface assumes a circular profile. Although valid for a wide range of practical rolling conditions, the approximation is definitely suspect for instance in the last and penultimate stand of a thin sheet tandem mill, and algorithms based on classical theory may fail to converge. This paper computing solutions. In deriving the algorithm it is convenient to employ the formalism of functional One notable feature is that the gradients have to be carefully defined with respect to the correct ‘space’, in order that physically inadmissible discontinuties are not introduced during the hill‐climbing. Computed roll gap solutions sometimes display elastic deformation regions embedded within the normal plastic deformation zone. It is thought that this is the first time this possibility has been allowed for in the formulation, or solutions obtained exhibiting this

ISSN:0029-5981    

DOI:10.1002/nme.1620120409

出版商:John Wiley&Sons, Ltd    

年代:1978

数据来源: WILEY

摘要:

AbstractA Reissner type variational principle is utilized to formulate a mixed finite element model for a finite‐strain analysis of Mooney‐Rivlin rubber‐like materials. An incremental and stationary Lagrangian formulation is adopted. The functional consists of incremental displacements and incremental hydrostatic and distortional stresses as variables. In the finite element formulation the displacements are interpolated in terms of nodal displacements while the two different strss components are approximated independently. The stress parameters for the distortional stresses are eliminated at the element level and the resulting matrix equations for each incremental solution involve the incremental nodal displacements and the average hydrostatic pressure in each element as unknowns. Four‐node quadrilateral plane stain elements were used to analyze the inflation of an infinitely long thick‐walled cylinder subjected to internal pressure. Both resulting displacements and stresses are found to converge to exact values as the magnitude of the loading increments is d

ISSN:0029-5981    

DOI:10.1002/nme.1620120410

出版商:John Wiley&Sons, Ltd    

年代:1978

数据来源: WILEY

摘要:

AbstractAn adaptive procedure for selecting the step size when incremental or continuation methods are used to solve sets of non‐linear equations is presented. The increment size is limited by requiring the corrective iteration procedure employed to reduce the drifting error to be within a contractive boundary at each level. The usefulness of the procedure is extended by the development of a set of conditions for detecting impending divergence of the corrective iteration process. These conditions, used in conjunction with the step size selection procedure permit the continuation of the solution through highly non‐linear regions and also provide a simple means of isolating a limit point, if one exists. Two additional benefits of the procedure are an effective convergence criterion for terminating the iteration process and a simple means for switching between the Newton‐Rephson and modified Newton‐Raphson iteration procedures. The paper concludes with a number of example problems, three are hyperelastic bodies at finite strain and the final example is the large displacement analysis of an elastic beam. The results illustrate that the procedure is computationally inexpensive, using only information normally obtained in a non‐linear analysis, flexible in the sense that a dense or sparse distribution of points along the total solution curve may be obtained, and effective, normally requiring less total computational effort than a constant step size

ISSN:0029-5981    

DOI:10.1002/nme.1620120411

出版商:John Wiley&Sons, Ltd    

年代:1978

数据来源: WILEY