Optimal Design for Non-Steady-State Metal Forming Processes—i. Shape Optimization Method

Fourment, Lionel; Chenot, Jean‐Loup

doi:10.1002/(sici)1097-0207(19960115)39:1<33::aid-nme844>3.0.co;2-z

Cited by 110 publications

(50 citation statements)

References 15 publications

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“…In section 4, we describe the adjoint equations technique [1][2]. The Lagrangien for problem is defined as follows:…”

Section: Abridged Version Of the Papermentioning

confidence: 99%

The Optimal Design of Extrusion Dies by the Finite Element Method

Azzabi

2003

Proc Appl Math and Mech

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In this work, a method for calculation of the optimal shapes of axisymmetrical converging dies by the finite element method is presented. The shape optimization problem considered in this paper is to find the best shape of the die such that the flow rate will be uniform at the die exit.The optimization problem is to minimize an objective function by varying a part of boundary (ie: the shape of die) subject to constraints imposed by the metal forming problem. In this method, the B-spline functions allow us to determine the shape of the die, using its control points as design variables. Abridged version of the paperIn the present work a sensitivity analysis for die extrusion problem with varying domain shape is considered: i.e., find a shape of the back wall of the die that meets some design objective. This paper is focused on the design of shaped dies by using sensitivities and optimization techniques. To reach this objective, the internal surface of the die is optimally designed in order to obtain a desired velocity at the exit of extrusion die. Changes in shape will be performed by variations in the contact boundary between the workpiece and the die through a finite number of control parameters (design variables). The optimum values of process parameters will be determined by various techniques of mathematical programming. This needs to construct and to minimize an objective function subject to constraints imposed by the metal forming problem. The optimization technique requires derivatives of the cost function with respect to the design variables. They can be carried out following two alternative approaches known as the direct differentiation and adjoint variable methods. Here, the adjoint approach is chosen to evaluate shape sensitivities and the B-spline functions is used here to represent the shapes of dies.In the extrusion process, the quality of the final products depends on being able to efficiently control the flow metal in the extrusion die. The contact condition between the workpiece and the die also induces non-uniform metal flow which causes local defect formation. In order to reduce the possibility of failure, but also to improve the quality of the extruded product, the prediction of the extrusion process in the given design parameters is required. The finite element method allows to provide the response of the process with fixed parameters.In section 2, we considered a steady-state analysis of forming processes at isothernal conditions. The workpiece is supposed isotropic, rigid-plastic, incompressible metallic body occupying the domain Ω(α) ∈ R 2 . Let the back wall of the die Γ α ⊂ ∂Ω(α):} is the shape which is to be determined, and α is a smooth function.The equilibrium equation to be solved reads in the weak form [3] [4]:whereε v is the volumetric strain rate, K is a large penalty constant for the incompressibility condition. v t and f t denote the velocity components in the tangential directions and friction force respectively. The relative sliding velocity frictional model, which c...

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“…In section 4, we describe the adjoint equations technique [1][2]. The Lagrangien for problem is defined as follows:…”

Section: Abridged Version Of the Papermentioning

confidence: 99%

The Optimal Design of Extrusion Dies by the Finite Element Method

Azzabi

2003

Proc Appl Math and Mech

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“…In the former, a computer aided design (CAD) geometry is given and its control points serve as design variables, as initially proposed by Braibant and Fleury [3]. For example, Fourment and Chenot [4] already proposed a parameter-based optimization approach for determining an optimal workpiece and die design in non-steady-state forming processes. Within parameter-free approaches, as considered in this contribution, the geometry is given in a discretized setting as a finite element (FE) model and its nodal positions serve as design variables.…”

Section: Introduction and Related Workmentioning

confidence: 99%

Case study on the influence of kinematic hardening within a parameter-free and non-invasive form finding approach

Landkammer

Steinmann

2016

MATEC Web Conf.

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Abstract. Inverse form finding -as a type of shape optimization -aims in determining the optimal preform design of a workpiece for a specific forming process, whereby the desired target geometry is known. Recently, a novel parameter-free and heuristic approach was developed to tackle this nonlinear optimization problem. Benchmark tests already delivered promising results. As a particular note-worthy feature of the approach, a coupling to an arbitrary finite element software is feasible in a non-invasive fashion. The aim of this contribution is to investigate the effect of kinematic hardening and cyclic loading on the convergence behavior of the algorithm.

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“…Accelerated algorithms for computing derivatives, like the direct differentiation or the adjoint state method, which in their simplest form linearize the discretized equilibrium equations, have been extensively described in literature, starting with [10,11], and developed to maturity by several groups of researchers, like [12][13][14]. A different version, which relies on first differentiating the continuum equilibrium equations, which are then discretized, has been put forward in [15].…”

Section: Introductionmentioning

confidence: 99%

On the impact of the time increment on sensitivity analysis during the elastic-to-viscoplastic transition in metals

Rauchs¹,

Ponthot

2010

Comput Mech

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In many constitutive models of elastoviscoplasticity, like for example overstress models, viscoplastic deformation takes place once the stress state lies outside the yield surface. In most computational implementations of such constitutive laws, the calculation of the viscoplastic deformation increment is performed in a one-step approach by applying the full nominal time increment to the rate-dependent deformation, even if during a part of the increment, purely elastic deformation takes place. This way, time increments affected by the transition from elastic to viscoplastic material behaviour are not properly accounted for, because such time increments exhibit both a purely elastic part and a elastoviscoplastic part. In fact, it has been reported in the literature that errors induced by the use of the conventional one-step approach are insignificant. In the present article, the impact of using the one-step approach, i.e. using the total time increment in case of the elastic-to-viscoplastic transition, on sensitivity analysis is investigated.

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Optimal Design for Non-Steady-State Metal Forming Processes—i. Shape Optimization Method

Cited by 110 publications

References 15 publications

The Optimal Design of Extrusion Dies by the Finite Element Method

The Optimal Design of Extrusion Dies by the Finite Element Method

Case study on the influence of kinematic hardening within a parameter-free and non-invasive form finding approach

On the impact of the time increment on sensitivity analysis during the elastic-to-viscoplastic transition in metals

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