A. El Hami

Reliability analysis of the metal forming process

In this paper, we propose a reliability-mechanical study combination for treating the metal forming process. This combination is based on the augmented Lagrangian method for solving the deterministic case and the response surface method. Our goal is the computation of the failure probability of the frictionless contact problem. Normally, contact problems in mechanics are particularly complex and have to be solved numerically. There are several numerical techniques available for computing the solution. However, some design parameters are uncertain and the deterministic solutions could be unacceptable. Thus, a mechanical contact study is an important subject for reliability analysis: the augmented Lagrangian method coupled with the first order reliability method, and we use the Monte Carlo method to obtain the founding results. The metal forming process is treated numerically to validate the new approach.

Treatment of the composite fabric's shaping using a Lagrangian formulation

In this paper, we are interested in the simulation of prepreg composite deformation by deep-drawing and laying-up. It uses new bi-component finite elements made of woven material in which the nodal interior loads are deduced from fibre tensile strain energy and not polymerized resin membrane energy. Specific treatment is used to analyze the frictional-contact problem between the deformable prepreg composite and the steel rigid tools. The frictional-contact method is based on the Lagrangian formulation and the preconditioned conjugate gradient method. Some numerical tests are given to investigate the performance of the numerical strategies.

Comparison Study of Different Reliability-Based Design Optimization Approaches

In this paper, we present a new method based on Optimal Safety Factors (OSF) in the context of the Reliability-Based Design Optimization (RBDO) analysis of ultrasonic motors with traveling wave taking into account the contact between the different components (stator and rotor). We will underline also the different methods of the RBDO analysis and we highlight the advantage of our approach based on OSF. Numerical results are given to illustrate the proposed method.

Iterative projection on critical states for reliability-based design optimization

Reliability-Based Design Optimization (RBDO) has been developed to design structures that reach the best compromise between cost reduction and reliability by considering uncertainties. This is achieved by reformulating the initial optimization problem in order to introduce probabilistic constraints. Numerical evaluation of these constraints by direct approaches turns out to be difficult: estimation of probability of failure implies calculation of multidimensional integrals. The integrals often rely on complex models whose evaluation is time-consuming. In this article, the RBDO framework is used to propose a new approach. For this purpose, a method to project a deterministic optimal solution onto a reliable domain is provided. This is achieved by a two-step iterative scheme. A sensitivity analysis identifies a critical situation. The latter leads to an adapted reliable safety domain. This new area is used to define a reliable design through a Newton-like process. Corresponding safety margins can be easily interpreted as partial safety factors. Finally, numerical applications in engineering are discussed to show the efficiency and the interest of the proposed algorithm.

A New Hybrid Genetic Algorithm and Particle Swarm Optimization

In this paper, we present a new hybrid algorithm which is a combination of a hybrid genetic algorithm and particle swarm optimization. We focus in this research on a hybrid method combining two heuristic optimization techniques, genetic algorithms (GA) and particle swarm optimization (PSO) for the global optimization. Denoted as GA-PSO, this hybrid technique incorporates concepts from GA and PSO and creates individuals in a new generation not only by crossover and mutation operations as found in GA but also by mechanisms of PSO. The performance of the two algorithms has been evaluated using several experiments.

Reliability Analysis of Vibro-Acoustic Problem

The comprehension of the interactions between a fluid and an elastic solid has a capital importance in several industrial applications. When a structure vibrates in the presence of a fluid, there is interaction between the natural waves of each media: the fluid flow generates a structural deformation and/or the movement of a solid causes the displacement of the fluid. These applications require an effective coupling. In addition, the dynamic analysis of the industrial systems is often expensive from the numerical point of view. For the coupling fluid-structure finite elements models, the importance of the size reduction becomes obvious because the fluids freedom degrees will be added to those of the structure. A method of condensation will be used to reduce the matrixes size. One of the principal hypothesis in the use of component mode synthesis method is that the model is deterministic; it is to say that parameters used in the model have a defined and fixed values. Furthermore, the knowledge of variation response of a structure involving uncertain materials, geometrical parameters, boundary conditions, tolerances of manufactures and loading conditions is essential in global process of conception. In order to do that, the modal condensation method is extended to reliability analysis for the coupled fluid-structure finite elements models. A numerical vibratory study is leaded on a plate in the air and in immersion in water taking into account the acoustic aspect. The results of the reliability analysis tend to show the effectiveness of the proposed approach based on the condensation techniques.

Reliability-based design optimization analysis of tube hydroforming process

In this paper, we are interested particularly in the tube hydroforming process (THP). This process consists of applying an inner pressure combined with an axial displacement to manufacture the part. During the manufacturing phase, inappropriate choice of the load paths can lead to failure. Deterministic approaches are unable to optimize the process by taking into account the uncertainty. So we introduce the reliability-based design optimization (RBDO) to optimize the process under probabilistic constraints to ensure a high reliability level and stability during the manufacturing phase and avoid the occurrence of such plastic instability. Taking some uncertainties into account the process is very stable and associated with a low failure probability. The definition of the objective function and the probabilistic constraints take advantage of the forming limit diagram (FLD) and the forming limit stress diagram (FLSD) used as a failure criterion to detect the occurrence of wrinkling, severe thinning and necking. To validate the proposed approach, the THP is then introduced as an example. The numerical results show the robustness and efficiency of the RBDO to improve thickness distribution and minimize the risk of potential failure modes.

A NEW METHODOLOGY FOR AN OPTIMAL SHAPE DESIGN

The aim of this paper is to study the implementation of an efficient and reliable methodology for shape optimization problems where the objective function and constraints are not known explicitly and are dependent on the Finite Element Analysis (FEA). It is based on the Simultaneous Perturbation Stochastic Approximation (SPSA) method for solving unconstrained continuous optimization problems. We also propose Penalty SPSA (PSPSA) for solving constrained optimization problems, the constraints are handled using exterior point penalty functions within an algorithm that combines SPSA and exact penalty transformations. This paper presents a new structural optimization methodology that combines shape optimization, geometric modeling, FEA and PSPSA method to successfully optimize structural optimization problems. Several tests have been performed on some well known benchmark functions to demonstrate the robustness and high performance of the suggested methodology. In addition, an illustrative two-dimensional structural problem has been solved in a very efficient way. The numerical results demonstrate the robustness and high performance of the suggested methodology for structural optimization problems.

Optimization and Identification of the Characteristics of an Hydroformed Structures

In this study, we present an experimental/numerical methodology which aims to improve 3D thin sheet hydroforming. The experimental study is dedicated to the identification of stress-strain flow by using the Nelder-Mead simplex algorithm optimization from the global measure of displacement and force. Applications are made to the simulation of thin sheet hydroforming using different die geometry to show the efficiency of the proposed methodology to localize plastic instability, thinning of the blanks and damage initiation under different forming condition.

Structural Shape Optimization using an Adaptive Simulated Annealing

In structural design optimization, numerical techniques are increasingly used. In typical structural optimization problems there may be many locally minimum configurations. For that reason, the application of a global method, which may escape from the locally minimum points, remain essential. In this paper, a new hybrid simulated annealing algorithm for global optimization with constraints is proposed. We have developed a new algorithm called Adaptive Simulated Annealing algorithm (ASA); ASA is a series of modifications done to the Basic Simulated Annealing algorithm ( BSA) that gives the region containing the global solution of an objective function. In addition, the stochastic method Simultaneous Perturbation Stochastic Approximation (SPSA), for solving unconstrained optimization problems, is used to refine the solution. We also propose Penalty SPSA (PSPSA) for solving constrained optimization problems. The constraints are handled using exterior point penalty functions. The proposed method is applicable for any problem where the topology of the structure is not fixed, it is simple and capable of handling problems subject to any number of nonlinear constraints. Extensive tests on the ASA as a global optimization method are presented, its performance as a viable optimization method is demonstrated by applying it first to a series of benchmark functions with 2 - 30 dimensions and then it is used in structural design to demonstrate its applicability and efficiency. It is found that the best results are obtained by ASA compared to those provided by the commercial software ANSYS.