摘要:

AbstractThe numerical integration of the rate equation of an elastic–plastic material is considered. Special attention is focused on the discretization via the fully implicit backward Euler method in the small strain case with linear elasticity and the yield function a general quadratic in stress space. Here the calculation of the plastic (Lagrange) multiplier reduces to the computation of the smallest positive root of a polynomial in one variable. Explicit formulae are given for some special case

ISSN:0029-5981    

DOI:10.1002/nme.1620280103

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractIn this work, a modal solution method for transient heat conduction utilizing a co‐ordinate transformation matrix generated by the Lanczos algorithm is presented. The special characteristics of this co‐ordinate transformation are also discussed. The comparisons made in the NASA Insulation Test problem analysis shown that this approach is more cost‐effective than direct solutions, without loss of acc

ISSN:0029-5981    

DOI:10.1002/nme.1620280104

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractOwing to the failure of the finite element analyst to employ a properly refined computational model, the accuracy of preliminary finite element computations is often low. Thus, it is useful to introduce a computational procedure for improving the results obtained from a preliminary finite element solution. Such a procedure is presented in this paper. In this procedure the solution error components are decomposed into two parts. One of the error components is assumed to have a long period variation. The other component is assumed to have a short period variation. Multiplicative and additive correction procedures are introduced to iteratively eliminate the two error components. The multiplicative and additive correction procedures are implemented using multi‐level solution technique

ISSN:0029-5981    

DOI:10.1002/nme.1620280105

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractThis paper presents a geometrically non‐linear formulation (GNL) for the three dimensional curved beam elements using the total Lagrangian approach. The element geometry is constructed using co‐ordinates of the nodes on the centroidal or reference axis and the orthogonal nodal vectors representing the principal bending directions. The element displacement field is described using three translations at the element nodes and three rotations about the local axesThe element displacement field has also been described in the literature using Euler parameters, Milenkovic parameters, or Rodriges parameters representing the effects of large rotations.. The GNL three dimensional beam element formulations based on these element approximations are restricted to small nodal rotations between two successive load increments. The element formulation presented here removes such restrictions. This is accomplished by retaining non‐linear nodal terms in the definition of the element displacement field, and the consistent derivation of the element properties. The formulation presented here is very general and yet can be made specific by selecting proper non‐linear functions representing the effects of nodal rotations. The details of the element properties are presented and discussed. Numerical examples are also presented to demonstrate the behaviour and the accuracy of the elements. A comparison of the results obtained from the present formulation with those available in the literature using a linearized element approximation clearly demonstrate the superiority of the formulation in terms of large load steps, large rotations between two load steps and extremely good convergence characteristics during equilibrium iterations. The displacement approximation of these elements is fully compatible with the isoparametric curved shell elements (with large rotations), and since the elements possess offset capability, these elements can also serve as stiffeners for the curved

ISSN:0029-5981    

DOI:10.1002/nme.1620280106

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractThe alternative to quadrature, as a procedure for dealing with the integrations required in the direct boundary element method (DBEM), is to carry out the integration analytically and code the results directly. The potential benefits are efficient computer programs; the avoidance of numerical instability; and generally, better accuracy. The technique is developed in this paper.Serious problems arise when Gauss quadrature is employed for the integration of functions which contain, or are close to singularities. A numerical integration approach may fail at the first stage of the analysis, that is, during the assembly of the discrete equations; or it may fail at the subsequent stage of computing domain points near the boundary. The severity of the problem is dependent both on the strength of the singularity, and on geometry. These points are illustrated with examples.

ISSN:0029-5981    

DOI:10.1002/nme.1620280107

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractAn efficient method is developed for sensitivity analysis in shape optimization of axisymmetric structures. The technique of isoparametric mapping is used to generate the finite element mesh from a small set of master elements and master nodes. Co‐ordinates of selected master nodes are used as design variables. Shape function values of master elements at derived finite element nodes obtained during the isoparametric mapping process are utilized to calculate the gradients of weight and response of the structures with respect to the design variables. Analytic formulations of the gradients are developed for sensitivity analysis of axisymmetric structures. An optimization procedure using a sequential linear programming method is applied to effectively utilize the calculated gradients. Numerical examples of optimum design of disks subject to thermo‐mechanical loadings are presen

ISSN:0029-5981    

DOI:10.1002/nme.1620280108

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractThis paper presents the development of a straightforward displacement type triangular finite element for bending of a flat plate with the inclusion of transverse (or lateral) shear effects. The element has twenty two degrees of freedom consisting of ten for the lateral displacement of the midplane and six for rotations of the normal to the undeformed midplane of the plate. The latter are taken as independent of the slopes of the deformed midplane in order to include deformation due to transverse shear. The element is fully conforming and may be orthotropic. At interelement boundaries, the element matches adjacent elements both with respect to lateral displacement of the midplane and the rotations of the normal. The result is an efficient ‘linear moment’ triangular element but with transverse shear deformation included. Numerical computations for a number of examples are presented. The results show the element to be more flexible than most other finite element models and agree closely with those from a numerical solution of the three dimensional elasticity equations. The results also converge to those from thin plate theory when the thickness to length ratio becomes small or when the transverse shear moduli are artificially increa

ISSN:0029-5981    

DOI:10.1002/nme.1620280109

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractThe successive quadratic programming (SQP) method is used with the finite element method (FEM) to solve frictionless geometrically non‐linear contact problems involving large deformations of the elastica in the presence of flat rigid walls. To formulate the SQP problems, the potential energy (PE) is expanded in a Taylor series of second order in displacement increments about a configuration near a contact solution. The SQP problems consist of minimizing the Taylor expansion of the PE subject to the inequality constraints which represent contact. The quadratic programming (QP) method is made part of a Newton–Raphson (NR) search in which the QP corrections are made when a NR step does not satisfy the constraints. A revised simplex method developed by Rusin is used to solve the QP problems. The elastica is modelled with a total Lagrangian FEM developed by Fried. Solutions are obtained for the end loaded buckled elastica in point contact with a rigid wall and for a uniformly loaded elastica in regional contact with a rigid wall. The problems are also solved using a penalty method. The results obtained for the point contact problem are compared to an analytical solution. Calculations were made to obtain numerical information on maximum load step size and the number of inverse operations required for each load step. Cases in which the elastica stiffened substantially as a result of the initiation of contact are also discus

ISSN:0029-5981    

DOI:10.1002/nme.1620280110

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractBased on purely kinematical considerations the possibility of inextensional bending is introduced to isoparametric curvedC° elements, which, otherwise, are plagued by severe membrane (and shear) locking. The analysis is restricted to arches and axisymmetric deformations of shells, i.e. kinematically two‐dimensional problems. The results show exceptionally good accuracy. High reliability of the approach is guaranteed by absence of spurious kinematic modes on the element level, which complements its ability to bend inextensionally (in the case of arche

ISSN:0029-5981    

DOI:10.1002/nme.1620280111

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractThe paper addresses the question of the accuracy and reliability of the computational analysis of the rhombic plate problem. The Kirchhoff model has a large error (measured in the energy norm) in comparison with the three dimensional solution with a soft simple support; also for very thin plates (t= 1/100a) and all angles (up to α = 90°). The Reissner–Mindlin model gives results 3–5 times better and is less sensitive to the change of the plate angle. The Kirchhoff model is a relatively good approximation of three dimensional setting for a hard simple support. The paradoxical (polygon) behaviour of the simply supported Kirchhoff plate extends to the Reissner–Mindlin model with a hard support. The finite element solution of the Kirchhoff model is addressed in detail. It is shown that higher degree methods are clearly preferable and that the skewness of the elements does not influence essentially the accuracy of the method; the singularity of the solution, which strongly depends on the skewness of the plate, is the primary cause of the deterioration of the performance of

ISSN:0029-5981    

DOI:10.1002/nme.1620280112

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY