Search results for "Finite element method"
showing 10 items of 746 documents
Functional A Posteriori Error Estimates for Time-Periodic Parabolic Optimal Control Problems
2015
This article is devoted to the a posteriori error analysis of multiharmonic finite element approximations to distributed optimal control problems with time-periodic state equations of parabolic type. We derive a posteriori estimates of the functional type, which are easily computable and provide guaranteed upper bounds for the state and co-state errors as well as for the cost functional. These theoretical results are confirmed by several numerical tests that show high efficiency of the a posteriori error bounds. peerReviewed
Shape optimization of elasto-plastic bodies under plane strains: Sensitivity analysis and numerical implementation
1992
Optimal shape design problems for an elastic body made from physically nonlinear material are presented. Sensitivity analysis is done by differentiating the discrete equations of equilibrium. Numerical examples are included.
Sensitivity analysis for discretized unilateral plane elasticity problem
1992
Abstract Numerical realization of optimal shape design problems requires gradient information which is used in minimization procedures. There are several possibilities for obtaining this information. Here we present a method, based on the use of the material derivative approach, applied to the finite element discretization of the problem. The advantage of this approach is that is gives the exact values of gradient and it can be very easily implemented on computers. We apply this method in the case of contact problems, where the situation is more involved compared with the case of elasticity problems with classical boundary conditions. We concentrate on a special choice of the cost functiona…
A New Numerical Method for Axisymmetrical Forming Processes
1987
Summary In this paper a numerical method for the analysis of axisymmetrical forming processes is proposed. This method represents the last development of a previous one which allows to solve forming problems in plane strain condition. The proposed model is baaed on the finite element discretization and on the linearization of the yield surface which leads to solve a LP problem. Two different examples of application, concerning the upsetting of a cylinder and of a hollow disk are reported.
A Comparative Analysis of Different Robust Design Approaches in Sheet Stamping Operations
2011
A crucial issue in sheet stamping optimization problems is related to the process robustness improvement: critical scattering in the investigated performances arises due to some noise variables influence, often evolving up design failure itself. In fact, strong variations in the final stamped part or fluctuations of strain distribution may lead to an uncontrolled process design. Such variability cannot be controlled but anyway it is possible to develop proper design tools able to identify robust process calibrations above which the noises variations effects are admissible. In this paper, a multi‐objective optimization problem was analyzed, with the aim to minimize both excessive thinning an…
Multi Stage Strategies for Single Point Incremental Forming of a Cup
2008
A five stage forming strategy for Single Point Incremental Forming of a circular cylindrical cup with a height/radius ratio of one is presented. Geometrical relations are discussed and theoretical strains are calculated. The influence of forming direction (upwards or downwards) is investigated for the second stage comparing explicit FE analysis with experiments. Good agreement is found between calculated and measured thickness distribution, overall geometry and strains. Using the proposed multi stage strategy it is shown possible to produce a cup with a height close to the radius and sides parallel to the symmetry axis in about half of the depth.
Monotonic solution of flow and transport problems in heterogeneous media using Delaunay unstructured triangular meshes
2013
Transport problems occurring in porous media and including convection, diffusion and chemical reactions, can be well represented by systems of Partial Differential Equations. In this paper, a numerical procedure is proposed for the fast and robust solution of flow and transport problems in 2D heterogeneous saturated media. The governing equations are spatially discretized with unstructured triangular meshes that must satisfy the Delaunay condition. The solution of the flow problem is split from the solution of the transport problem and it is obtained with an approach similar to the Mixed Hybrid Finite Elements method, that always guarantees the M-property of the resulting linear system. The…
Two-level Schwarz method for unilateral variational inequalities
1999
The numerical solution of variational inequalities of obstacle type associated with second-order elliptic operators is considered. Iterative methods based on the domain decomposition approach are proposed for discrete obstacle problems arising from the continuous, piecewise linear finite element approximation of the differential problem. A new variant of the Schwarz methodology, called the two-level Schwarz method, is developed offering the possibility of making use of fast linear solvers (e.g., linear multigrid and fictitious domain methods) for the genuinely nonlinear obstacle problems. Namely, by using particular monotonicity results, the computational domain can be partitioned into (mes…
Numerical Approximation of Elliptic Variational Problems
2003
This chapter is dedicated to the study of Elliptic Variational Inequalities (EVI). Different forms of such an EVI are considered. The Ritz—Galerkin discretization method is introduced, and methods to approximate the solution of an EVI are presented. The finite dimensional subspaces are built by use of the Finite Element Method. The discretized problems are solved using variants of the Successive OverRelaxation (SOR) method. The algorithms are tested on a typical example. The way to develop computer programs is carefully analysed.
Error Estimates and Automatic Adaptive Mesh Refinement for the Metal Forming FEM Analysis
1988
The Authors propose a new technique which enables a estimation of the error inherent with the FEM analysis of metal forming processes. The aim is to evaluate the zones where the error is higher in order to proceed to a refinement of the mesh in such zones, and to obtain a smaller value of the global error. Moreover, to simplify the analyst work in the progressive refinement of the mesh, it has been prepared a software able to read the drawing created by a CAD program and to generate, automatically, all the geometrical and topological data necessary to perform the analysis on Personal Computer. The automatic renumbering of the elements in the refined mesh has been performed with the aim to r…