摘要:

AbstractA state‐space model for representing the non‐linear material deformation and an optimal control scheme for obtaining desired process conditions in the deforming material are presented in this paper. The formulation is general for various metal‐forming processes including forging and extrusion operations. The state variables selected in the formulation are the die/billet contact nodal velocities and the nodal velocities of the critical finite elements of the billet. The control input is the ram velocity, which is determined by using the linear quadratic regulator (LQR) theory to maintain desired strain rates within the selected finite elements. The influence of an optimally designed ram velocity on the deforming material is studied using performance measures. This paper includes the development of the state‐space model from non‐linear finite element formulation, optimal control strategy and numerical example cases with di

ISSN:0029-5981    

DOI:10.1002/nme.1620361202

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

摘要:

AbstractThis paper presents and discusses a Lanczos‐based eigensolution technique for evaluating the natural frequencies and modes from frequency‐dependent eigenproblems in structural dynamics. The new solution technique is used in conjunction with a mixed finite element modelling procedure which utilizes both the polynomial and frequency‐dependent displacement fields in formulating the system matrices. The method is well suited to the solution of large‐scale problems.The new solution methodology presented here is based on the ability to evaluate a specific set of parameterized non‐linear eigenvalue curves at given values of the parameter through an implicitly restarted Lanczos technique. Numerical examples illustrate that the implicitly restarted Lanczos method with secant interpolation accurately evaluates the exact natural frequencies and modes of the non‐linear eigenproblem and verifies that the new eigensolution technique coupled with the mixed finite element modelling procedure is more accurate than the conventional finite element models. In addition, the eigenvalue technique presented here is shown to be far more computationally efficient on large‐scale problems than the determinant search techniques traditionally employed for solving exact vibra

ISSN:0029-5981    

DOI:10.1002/nme.1620361203

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

摘要:

AbstractThe Navier‐Stokes incompressible model is used to describe two‐dimensional metal casting flow. Such flows involve moving free boundaries. A new numerical algorithm has been developed using the Lagrangian finite‐element method. It allows treatment of flows with moderate Reynolds numbers. The main feature is to avoid the calculation of the convective term, together with an automatic remeshing technique, to cure the mesh distortions. The problem of the free oscillation of a liquid is treated to verify the formulation. An application of this method to the computation of an industrial metal casting flow situation is pres

ISSN:0029-5981    

DOI:10.1002/nme.1620361204

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

摘要:

AbstractA new approach to solve problems in the optimal shape design of eigenvalues is presented. The idea behind the approach is based on a combination of the known material derivative method4,7and a specially adapted Green's functions formulation.14In the current study, numerical testing has been limited to two‐dimensional shape optimization. The two test cases involve the first eigenvalues of boundary value problems which model (i) free vibrations of a fixed membrane and (ii) natural frequencies of clamped thin plates. The basic algorithm can easily be adapted to serve other types of boundary value problems dealing with the highest eigenvalues that occur in applied mechanics. Computational aspects of the proposed approach, such as accuracy of the obtained sensitivities, cost of computation and so on are discussed in References 16 (in preparation

ISSN:0029-5981    

DOI:10.1002/nme.1620361205

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

摘要:

AbstractA finite element procedure, which utilizes Fourier series, is developed to compute the large deformations and deflections in axisymmetric elastomeric solids subjected to non‐axisymmetric loading. Nearly incompressible and incompressible, isotropic strain energy density functions describe the elastic properties. The nearly incompressible functions become compatible with an analytical integration scheme by using a novel variable to approximate the dilatation. A large spherical elastomeric bearing is analysed with this procedur

ISSN:0029-5981    

DOI:10.1002/nme.1620361206

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

摘要:

AbstractA bending theory for thin shells undergoing finite rotations is presented, and its associated finite element model is described. The kinematic assumption is based on a shear elastic Reissner‐Mindlin theory. The starting point for the derivation of the strain measures are the resultant equilibrium equations and the associated principle of virtual work. Within this formulation the polar decomposition of the shell material deformation gradient leads to symmetric strain measures. The associated work‐conjugate stress resultants and stress couples are integrals of the Biot stress tensor. This tensor is invariant with respect to rigid body motions and, therefore, appropriate for the formulation of constitutive equations. Finite rotations are introduced via Eulerian angles. The finite element discretization of arbitrary shells is based on the isoparametric concept formulated with respect to a plane reference configuration. The numerical model is applied to different non‐linear plate and shell problems and compared with existing formulations. Due to a consistent linearization, the step size of a load increment is only limited by the local convergence behaviour of Newton's m

ISSN:0029-5981    

DOI:10.1002/nme.1620361207

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

摘要:

AbstractThis paper presents an application of the dual reciprocity boundary element method to non‐linear magnetic field analysis. Advanced techniques employed in the procedure include discontinuous elements, quasi‐singular and hyper‐singular integration schemes and the Galerkin formulation. Numerical results are included to show the performance of the proposed app

ISSN:0029-5981    

DOI:10.1002/nme.1620361208

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

摘要:

AbstractIt is proposed to capture localized plastic deformation via the inclusion of regularized displacement discontinuities at element boundaries (interfaces) of the finite element subdivision. The regularization is based on a kinematic assumption for an interface that resembles that which is pertinent to the classical shear band concept. As a by‐product of the regularization, an intrinsic band width is introduced as a ‘constitutive’ property rather than a geometric feature of the finite element mesh. In this way the spurious mesh sensitivity, which is obtained when the displacement approximation is continuous, can be avoided. Another consequence is that the interfacial relation between the elements is derived directly from the conventional constitutive properties of the continuously deforming material. An interesting feature is that the acoustic tensor will not only play a role for diagnosing discontinuous bifurcation but will also serve as the tangent stiffness tensor of the interface (up to within a scalar factor). An analytical investigation of the behaviour of the interface is carried out and it is shown that dilatation may indeed accompany slip within a ‘shear’ band for a general plasticity model. The significance of proper mesh alignment is demonstrated for a simple problem in plane strain and plane stress. It is shown that a unique structural post‐peak response (in accordance with non‐linear fracture mechanics) can be achieved when the plastic softening modulus is properly related to the bandwidth. The paper concludes with a numerical simulation of the gradual development of a shear band in

ISSN:0029-5981    

DOI:10.1002/nme.1620361209

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

摘要:

AbstractThis paper describes a new class of algorithms for integrating linear second‐order equations and those containing smooth non‐linearities. The algorithms are based on a combination of ideas from standard Newmark integration methods and extrapolation techniques. For the algorithm to work, the underlying Newmark method must be stable, second‐order accurate, and produce asymptotic error expansions for response quantities containing only even‐ordered terms. It is proved that setting the Newmark parameter γ equal to 1/2 gives a desirable asymptotic expansion, irrespective of the setting for β. Numerical experiments are conducted for one linear and two non‐linear a

ISSN:0029-5981    

DOI:10.1002/nme.1620361210

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

摘要:

AbstractThis paper addresses the formulation and discrete approximation of dynamic contact/impact initial‐value problems. The continuous problem is presented in the context of non‐linear kinematics. Standard semi‐discrete time integrators are introduced and are shown to be unsuccessful in modelling the kinematic constraints imposed on the interacting bodies during persistent contact. A procedure that bypasses the aforementioned difficulty is proposed by means of a novel variational formulation. Numerical simulations are conducted and the results are reported and disc

ISSN:0029-5981    

DOI:10.1002/nme.1620361211

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY