Thermal Aspects in Deep Hole Drilling of Aluminium Cast Alloy Using Twist Drills and MQL

AbstractThe deep hole drilling process with solid carbide twist drills is an efficient alternative to the classic single-lip deep hole drilling, due to the generally higher feed rates possible and the consequently higher productivity. Furthermore the minimum quantity lubrication (MQL) can be applied, in order to reduce the production costs and implement an environmentally friendly process. Because of the significantly reduced cooling performance when using MQL, a higher heat loading results for the tool and the workpiece. This paper presents the investigations of the temperature distribution in the workpiece and the heat balance of the deep hole drilling process

Adaptive finite element approximation of problems in elasto-plasticity theory

SIGLEAvailable from TIB Hannover: RR 1606(97-11) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

A Cascadic Multigrid Algorithm for Variational Inequalities

When classical multigrid methods are applied to discretizations of variational inequalities, several complications are frequently encountered mainly due to the lack of simple feasible restriction operators. These diculties vanish in the application of the cascadic version of the multigrid method which in this sense yields greater advantages than in the linear case. Furthermore, a cg-method is proposed as smoother and as solver on coarse meshes. The eciency of the new algorithm is elucidated by test calculations for an obstacle problem and for a Signorini problem

On FE-discretisations with least-squares stabilisation: a posteriori error control for the membrane-problem

Mixed finite element schemes for solving problems in continuum mechanics are often used to obtain higher-order approximation for the stresses. However, it is viewed as a drawback of these methods that one has to construct suitable non-standard finite element spaces to obtain stable discretisations. An alternative approach is to augment the original mixed formulation by least-squares-like terms, allowing the use of standard finite element spaces for the approximation. For this scheme weighted a posteriori error estimates can be derived by duality arguments. The underlying dual problems have to be chosen according to the mesh-dependent stabilisation parameters in order to guarantee optimal-order estimation of the least-squares terms. The construction of a stabilised finite element scheme and the appropriate adaptive algorithm is developed for a model example in elasticity theory. Numerical tests show that only the mesh-dependent duality argument results in asymptotically correct error bounds. (orig.)SIGLEAvailable from TIB Hannover: RR 1606(98-29) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

An adaptive displacement/pressure finite element scheme for treating incompressibility effects in elasto-plastic materials

In this note a mixed finite element formulation is described for coping with (nearly) incompressible behaviour in elasto-plastic problems. In addition to the displacements an auxiliary variable, playing the role of a pressure, is introduced resulting in Stokes-like problems. The discretisation is done by a stabilised conforming Q1/Q1-element and the corresponding algebraic systems are solved by an adaptive multigrid scheme using a smoother of block Gauss-Seidel type. The adaptive algorithm is based on the general concept of using duality arguments to obtain weighted a posteriori error bounds. This procedure is carred out here for the described discretisation of elasto-plastic problems. Efficiency and reliability of the proposed adaptive method is demonstrated at (plane strain) model problems. (orig.)Available from TIB Hannover: RR 1606(98-33) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

A posteriori error control and mesh adaptation in elasticity and elasto-plasticity

A new technique for a posteriori error control and adaptive mesh design is presented for finite element models in elasticity and elasto-plasticity. It is based on weighted a posteriori error estimates for general error functionals which are derived by duality arguments. This approach was originally proposed in [6] as a natural extension of the ideas developed by C. Johnson, et al., [11] and [13], for adaptive finite element methods. The conventional strategies for mesh refinement in finite element methods are mostly based on a posteriori error estimates for the global energy norm in terms of local residuals of the computed solution. These estimates reflect the approximation properties of the trial functions by local interpolation constants while the stability property of the continuous model enters through a global coercivity constant. However, meshes generated on the basis of such global error estimates may not be appropriate in computing local quantities like point values or contour integrals and in the case of very heterogeneous or nonlinear material behavior. More accurate and efficient error estimation can be achieved by using suitable weighting factors which can be obtained numerically in the course of a feed-back process from the solutions of discretised dual problems. This general approach is discussed here for finite element models in linear elasticity and perfect plasticity. (orig.)SIGLEAvailable from TIB Hannover: RR 1606(97-36) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

A posteriori error estimation and mesh adaptation for finite element models in elasto-plasticity

A new approach to a posteriori error estimation and adaptive mesh design based on techniques from optimal control is presented for primal-mixed finite element models in elasto-plasticity. This method uses global duality arguments for deriving weighted a posteriori error bound for arbitrary functionals of the error representing physical quantities of interest. In these estimates local residuals of the computed solution are multiplied by certain weights which are obtained by solving a linearized global dual problem numerically. The resulting local error indicators are used in a feed-back process for generating economical meshes. This approach is developed here for the Hencky and Prandtl-Reuss models in linear-elastic perfect plasticity. Its performance is demonstrated for a plane-strian benchmark problem. (orig.)SIGLEAvailable from TIB Hannover: RR 1606(98-32) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

A posteriori error control in finite element methods via duality techniques: application to perfect plasticity

In this paper a new technique for a posteriori error control and adaptive mesh design is presented for finite element models in perfect plasticity. The approach is based on weighted a posteriori error estimates derived by duality arguments as proposed in [4] and [18] for linear problems. The conventional strategies for mesh refinement in finite element methods are mostly based on a posteriori error estimates for the global energy norm in terms of local residuals of the computed solution. These estimates reflect the approximation properties of the trial functions by local interpolation constants while the stability property of the continuous model enters through a global coercivity constant. However, meshes generated on the basis of such global error estimates are not appropriate in computing local quantities as point values or contour integrals and in the case of nonlinear material behavior. More accurate and efficient error estimation can be achieved by using suitable weights which can be obtained numerically in the course of the refinement process from the solutions of linearized dual problems. This feed-back approach is developed here for primal-mixed finite element models in linear-elastic perfect plasticity. (orig.)SIGLEAvailable from TIB Hannover: RR 1606(97-16) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

A posteriori error estimates for nonconforming finite element schemes

We derive a posteriori error estimates for nonconforming discretizations of Poisson's and Stokes' equations. The estimates are residual based and make use of weight factors obtained by a duality argument. Crouzeix-Raviart elements on triangles and rotated bilinear elements are considered. The quadrilateral case involves the introduction of additional local trial functions. We show that their influence is of higher order and that they can be neglected. The validity of the estimate is demonstrated by computations for the Laplacian and for Stokes' equations. (orig.)Available from TIB Hannover: RR 1606(98-56) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Error estimation and adaptive mesh design for FE models in elasto-plasticity

Also published in: Stein, E. (ed.): Error-Controlled Adaptive FEMs in Solid Mechanics. John Wiley and Sons Ltd., 2000SIGLEAvailable from TIB Hannover: RR 1606(2000,24) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman