Michaël Bruyneel

Composite structures optimization using sequential convex programming

The design of composite structures is considered here. The approximation concepts approach is used to solve the optimization problem. The convex approximations of the MMA family are briefly described. Several modifications of these approximations are presented. They are now based on gradient information at two successive iterations, avoiding the use of the expensive second-order derivatives. A two-point fitting scheme is also described, where the function value at the preceding design point is used to improve the approximation. Numerical examples compare these new purely non-monotonous schemes to the existing ones for the selection of optimal fibers orientations in laminates. It is shown how these two-point based approximations are well adapted to the problem and can improve the optimization task, leading to reasonable computational efforts. A procedure is also derived for considering simultaneously monotonous and nonmonotonous structural behaviors. The resulting generalized approximation scheme is well suited for the optimization of composite structures when both plies thickness and fibers orientations are considered as design variables. It is concluded that the newly developed approximation schemes of the MMA family are reliable for composite structures optimization. All the studied approximations are convex and separable: the optimization problem can then be solved using a dual approach.

Extensions of the Shape Functions with Penalization Parameterization for Composite-Ply Optimization

Nomenclature C = linear anisotropic material stiffness matrix of the ply l Ci = linear anisotropic material stiffness matrix of the candidate orientation i in the physical ply l n = number of candidate orientations in the ply l wi = weighting factor for the candidate orientation i in the ply l SFP = Shape Functions with Penalization R, S, T = design variables in the SFP material parameterization p = exponent used in the SFP parameterization

A bilevel integer programming method for blended composite structures

A new optimization algorithm is presented for manufacturable composite structures.The structure weight is optimized taking the stacking sequences as design variables.The constraints are the mechanical behavior of structure and the manufacturing rules.The manufacturing rules are taken into account using a backtracking procedure.A bilevel integer programming method is proposed to solve this problem. This paper proposes a new approach for the design of a composite structure. This approach is formulated as an optimization problem where the weight of the structure is minimized such that a reserve factor is higher than a threshold. The thickness of each region of the structure is optimized together with its stacking sequence and the ply drop-offs. The novelty of this approach is that, unlike in common practice, the optimization problem is not simplified and split into two steps, one for finding the thicknesses and one for the stacking sequence. The optimization problem is solved without any simplification assumption. It is formulated as a bilevel integer programming and it uses the backtracking procedure to satisfy the blending and the manufacturing rules. Some numerical experiments are performed to show the efficiency of the proposed optimization method over complex cases which cannot be solved with the existing methods.

Exploiting semi-analytical sensitivities from linear and non-linear finite element analyses for composite panel optimisation

This paper presents a solution procedure developed in the SAMCEF finite element code for the advanced optimal design of stiffened composite panels of an aircraft fuselage. The BOSS quattro, a task manager and optimization toolbox, is used for defining and running the optimization problem. The objective function to be minimized is the weight, and the restrictions depend on structural stability requirements, such as buckling and collapse. The design variables are the panel and stringer thicknesses of the conventional proportions (i.e. 0∘, 90∘ and ±45∘) in a homogenized laminate. Since a collapse analysis introduces geometric nonlinearities into the design process, the function evaluation can take a long time. In order to obtain a rapid optimal solution, a gradient-based method is used, and the first order derivatives need to be computed, in this case with an original semianalytical approach. The sensitivity analysis of buckling and collapse is reviewed. Numerical tests on an industrial case study demonstrate the possibility and the reliability of the approach. Solving such problems is clearly difficult and remains a challenge. Through the applications, this paper provides the opportunity to discuss convergence issues and the use of such advanced optimization techniques in the overall aircraft design process.

Strength analysis of CFRP composite material considering multiple fracture modes

The strength characteristic of CFRP composite materials often is dependent on the internal micro-structural fracture mode. Therefore, in order to precisely predict this strength, each fracture mode and its mutual influence must be taken into account in a simulation. In this paper, intra-ply fracture progression and load characteristics of a cyclic loading test were analyzed, utilizing a material model proposed by Ladeveze et al. The model can evaluate different fracture modes and the stiffness degradation resulting from them. The analyzed results were compared with actual test results to confirm the validity of the analysis. Another analysis was performed without considering the mutual influence of the different fracture modes, and the results were compared to discuss the necessity of the coupling.

Predictive Simulations of Damage Propagation in Laminated Composite Materials and Structures with LMS Samtech Samcef

In this paper, the advanced damage analysis of composite materials and structures made of continuous fibers embedded in a polymer matrix is addressed. The solution is based on the LMS Samtech Samcef finite element code, from Siemens PLM Software, which is now available in the Siemens NX CAE environment, with the specific focus of solving non-linear analysis problems for composites. Globally speaking, LMS Samtech Samcef is an implicit non-linear solver able to solve quasi-static and dynamic problems, with a comprehensive library of structural elements and kinematic joints. First, the sizing strategy based on the building block approach (pyramid of physical and virtual tests) is recalled. Applied for years in the aerospace industry, it is here extended to the automotive context. In this approach, the knowledge on the composite material and structure is built step by step from the coupon level up to the final full scale structure. In this paper, stages of the pyramid starting from the coupon level are considered, and the predictions obtained by numerical simulations are validated by test results. The non-linear analysis approach available in the LMS Samtech Samcef finite element code is then described. It is based on the continuum damage mechanics, and is used to study the progressive failure of composites in the plies and at their interface (delamination). The material models are described. The identification procedure for these damage models is also discussed: it is based on a very limited number of tests results at the coupon level. It is then shown how this information on the material behavior can be used at upper stages of the building block approach and so applied to larger scale structures and/or more complex load cases and different stacking sequences. The very good agreement obtained in this paper between simulation and test results on composite structures of increasing complexity tend to demonstrate that LMS Samtech Samcef can be used as a predictive numerical tool for the evaluation of the non-linear behavior of composites, including the progressive inter- and intra-laminar damage analysis.

Advanced Capabilities for the Simulation of Membrane and Inflatable Space Structures Using SAMCEF

SAMCEF Mecano is a general implicit non-linear software developed by Samtech. The paper describes several improvements that have been made in SAMCEF Mecano concerning the analysis of inflatable and membrane structures. Most of these developments have been carried out in the frame of an ESTEC contract (PASTISS project). Several examples illustrate the different developments.

Recent Progress In Preliminary Design Of Mechanical Components With Topology Optimization

Since 10 years topology optimization has been trying to bring an efficient answer to the automatic choice of the morphology of mechanical components, i.e. the number and the relative positions of the holes in the structural domains, the number and the nature of the structural members, their connectivity and the character of the connecting joints. This problem is one of the main questions to be addressed during the preliminary design phase of mechanical and structural components. Up to now, the selection of the mechanical morphology has been let to engineers’ experience or to their intuition (which is even worse sometimes). With topology optimization the choice of the morphology can now rely on rational arguments and can be driven with the help of mathematical tools. This has two advantages. At first topology optimization can facilitate the automation of the preliminary design, but it can also improve substantially the performance of new mechanical products, that is, topology optimization can propose original and innovative solutions to engineering problems.