Hakim Naceur

Recent developments on the analysis and optimum design of sheet metal forming parts using a simplified inverse approach

Abstract A simplified efficient finite element method called the inverse approach (IA) has been developed to estimate the large elasto-plastic strains in thin metallic panels obtained by deep drawing. This paper deals with the main recent developments introduced by the authors on the IA to improve its efficiency in the analysis and optimum design of blank contours of complicated industrial parts. The IA mainly exploits the knowledge of the 3D shape of the final workpiece. An iterative scheme is used to find the original position of each material point in the initial flat blank after which it is possible to estimate the strains and stresses in the final workpiece. Important assumptions are adopted regarding the constitutive equations (the deformation theory of plasticity) and the action of the tools (the punch, die and blank holders). The IA implies only two degrees of freedom per node even if bending effects are considered. In this paper, we present several recent developments: (1) The bending effects are taken into account using a simple triangular shell element without increasing the number of dof per node. (2) Some analytical formulas are introduced to consider the restraining forces due to the drawbeads. (3) Some improvements of resolution algorithms such as the introduction of a relaxation coefficient, a damping factor and a good initial solution are realized. (4) Shape optimization of blank contours is performed using a numerical procedure based on the coupling of the IA and a sequential quadratic programming method (SQP). In this work, all sensitivities are computed analytically using the adjoint variable method. The numerical results of the IA on two benchmark tests are compared with experimental and other numerical results. The optimization procedure is applied to the blank optimum design of the Renault/Twingo dashpot cup where the objective function is defined to minimize the maximum of the thickness variations.

Optimization of drawbead restraining forces and drawbead design in sheet metal forming process

Abstract This paper presents an optimization procedure of drawbead restraining forces in order to improve the sheet metal formability in deep drawing process. A simplified finite element method called inverse approach (IA) has been developed for sheet forming analysis with the consideration of the drawbead restraining forces. This IA is combined with a mathematical programming algorithm to optimize the restraining forces and then to design the drawbeads. The obtained optimization procedure is very efficient due to the simplified assumptions of the IA and the analytical sensitivity analysis. The Square cup of Numisheet’93 and the Renault Twingo dashpot cup are presented to demonstrate the usefulness of the proposed optimization procedure for industrial applications. Verifications of the obtained results have been carried out using a precise incremental commercial code OPTRISTM based on explicit dynamic approach to show the effectiveness of our approach.

An efficient DKT rotation free shell element for springback simulation in sheet metal forming

This paper presents two simple and efficient DKT triangular shell elements for the springback simulation after the sheet forming process. The first is the DKT12 shell element resulting from the superposition of the CST membrane element and the DKT6 plate element. The second element is called DKTRF element (DKT rotation free element) involving its three neighboring elements and six corner nodes, with only three translations dof per node. The three rotations around the sides are expressed in terms of the 18 nodal translational dof. The present formulation is more general and accurate than existing rotation free elements, particularly in the case of deep shells. A static implicit algorithm using a simple updated Lagrangian formulation is adopted for the springback simulation. Some academic examples and benchmark tests show the accuracy and efficiency of these two shell elements.

Meshless method for shallow water equations with free surface flow

Solving problems with free surface often encounters numerical difficulties related to excessive mesh distortion as is the case of dambreak or breaking waves. In this paper the Natural element method (NEM) is used to simulate a 2D shallow water flows in the presence of theses strong gradients. This particle-based method used a fully Lagrangian formulation based on the notion of natural neighbors. In the present study we consider the full non-linear set of Shallow Water Equations, with a transient flow under the Coriolis effect. For the numerical treatment of the nonlinear terms we used a Lagrangian technique based on the method of characteristics. This will allow avoiding divergence of Newton-Raphson scheme, when dealing with the convective terms. We also define a thin area close to the boundaries and a computational domain dedicated for nodal enrichment at each time step. Two numerical test cases were performed to verify the well-founded hopes for the future of this method in real applications.

Response Surface Methodology for the Design of Sheet Metal Forming Parameters to Control Springback Effects using the Inverse Approach

This paper deals with the optimization of tools geometry in sheet metal forming in order to reduce the springback effects after forming. A Response Surface Method (RSM) based on Diffuse Approximation (DA) is used. A new modified version of the Inverse Approach (IA) used to analyze the stamping operation is presented. The bending/unbending moments and the final shape are used to calculate springback using an incremental approach based on the Updated Lagragian Formulation (ULF). The U‐bending benchmark of Numisheet’93 is used and good results of springback elimination have been obtained.

Rapid coupling optimization method for a tube hydroforming process

Abstract This paper deals with the optimization of tube hydroforming parameters in order to reduce defects that may occur at the end of the forming process such as necking and wrinkling. A specific methodology is proposed based on the coupling between an inverse finite element model for the rapid simulation of the tube hydroforming process, and a response surface method based on diffuse approximation. The response surfaces are built using moving least-squares approximations and constructed within a moving region of interest, which moves across a predefined discrete grid of authorized experimental designs. An application of hydroforming of a bulge from aluminium alloy 6061-T6 tubing has been utilized to validate the methodology. The final design is validated with ABAQUS Explicit Dynamic commercial code.

Assessment of ship manoeuvrability by using a coupling between a nonlinear transient manoeuvring model and mathematical programming techniques

In this paper, a numerical method based on a coupling between a mathematical model of nonlinear transient ship manoeuvring motion in the horizontal plane and Mathematical Programming (MP) techniques is proposed. The aim of the proposed procedure is an efficient estimation of optimal ship hydrodynamic parameters in a dynamic model at the early design stage. The proposed procedure has been validated through turning circle and zigzag manoeuvres based on experimental data of sea trials of the 190 000- dwt oil tanker. Comparisons between experimental and computed data show a good agreement of overall tendency in manoeuvring trajectories.

On the mechanical characterization and modeling of polymer gel brain substitute under dynamic rotational loading

The use of highly sensitive soft materials has become increasingly apparent in the last few years in numerous industrial fields, due to their viscous and damping nature. Unfortunately these materials remain difficult to characterize using conventional techniques, mainly because of the very low internal forces supported by these materials especially under high strain-rates of deformation. The aim of this work is to investigate the dynamic response of a polymer gel brain analog material under specific rotational-impact experiments. The selected polymer gel commercially known as Sylgard 527 has been studied using a specific procedure for its experimental characterization and numerical modeling. At first an indentation experiment was conducted at several loading rates to study the strain rate sensitivity of the Sylgard 527 gel. During the unloading several relaxation tests were performed after indentation, to assess the viscous behavior of the material. A specific numerical procedure based on moving least square approximation and response surface method was then performed to determine adequate robust material parameters of the Sylgard 527 gel. A sensitivity analysis was assessed to confirm the robustness of the obtained material parameters. For the validation of the obtained material model, a second experiment was conducted using a dynamic rotational loading apparatus. It consists of a metallic cylindrical cup filled with the polymer gel and subjected to an eccentric transient rotational impact. Complete kinematics of the cup and the large strains induced in the Sylgard 527 gel, have been recorded at several patterns by means of optical measurement. The whole apparatus was modeled by the Finite Element Method using explicit dynamic time integration available within Ls-dyna(®) software. Comparison between the physical and the numerical models of the Sylgard 527 gel behavior under rotational choc shows excellent agreements.

Geometrically nonlinear analysis of two-dimensional structures using an improved smoothed particle hydrodynamics method

Purpose – The purpose of this paper is to present an efficient smoothed particle hydrodynamics (SPH) method particularly adapted for the geometrically nonlinear analysis of structures. Design/methodology/approach – In order to resolve the inconsistency phenomenon which systematically occurs in the standard SPH method at the domain’s boundaries of the studied structure, the classical kernel function and its spatial derivatives were modified by the use of Taylor series expansion. The well-known tensile instabilities inherent to the Eulerian SPH formulation were attenuated by the use of the Total Lagrangian Formulation (TLF). Findings – In order to demonstrate the effectiveness of the present improved SPH method, several numerical applications involving geometrically nonlinear behaviors were carried out using the explicit dynamics scheme for the time integration of the PDEs. Comparisons of the obtained results using the present SPH model with analytical reference solutions and with those obtained using ABAQU...

Optimisation des forces de retenue pour le contrôle de la qualité des tôles minces embouties

ABSTRACT In the deep drawing process, drawbead restraining forces can control the material flow and thus the part quality in the sheet forming process. The Inverse Approach (I.A.) developed at UTC can be used for sheet forming simulation more efficiently than incremental methods. This I.A. is combined with a Sequential Quadratic Programming (SQP) algorithm to optimize the restraining forces in order to avoid necking and wrinkling. This optimization procedure seems to be very efficient due to the simplified assumptions of the I.A. and the analytical sensitivity analysis.