R. Le Riche

Improved genetic algorithm for minimum thickness composite laminate design

Abstract The use of a genetic algorithm for the minimum thickness design of composite laminated plates is explored. A previously developed genetic algorithm for laminate design is thoroughly revised and improved, by incorporating knowledge of the physics of the problem into the genetic algorithm. Constraints are accounted for by combining fixed and progressive penalty functions. Improved selection, mutation, and permutation operators are proposed. The use of an operator called scaling mutation that projects designs toward the feasible domain is investigated. The improvements in the genetic algorithm are shown to reduce the average price of a genetic search by more than 50%.

Coupled compression RTM and composite layup optimization

A methodology for studying the implications of taking into account manufacturing at early design stages is presented. It is applied to a rectangular laminate made by RTM and compression (RTCM). The plate is designed for injection time, maximum mold pressure, stiffness and buckling. Semi-analytical, numerically inexpensive models of the processes and structure enable a thorough investigation of the couplings between process and structure by comparing four design formulations: in decoupled problems, either the process or the structure is optimized; then, the process is optimized with targetted low or high structural performance. A globalized Nelder-Mead optimization algorithm is used. The rigour of the method and the relative simplicity of the application case provide a clear description of how maximum mold pressures, injection times and final structures properties are traded-off.

Bayesian Identification of Elastic Constants in Multi-Directional Laminate from Moiré Interferometry Displacement Fields

The ply elastic constants needed for classical lamination theory analysis of multi-directional laminates may differ from those obtained from unidirectional laminates because of three dimensional effects. In addition, the unidirectional laminates may not be available for testing. In such cases, full-field displacement measurements offer the potential of identifying several material properties simultaneously. For that, it is desirable to create complex displacement fields that are strongly influenced by all the elastic constants. In this work, we explore the potential of using a laminated plate with an open-hole under traction loading to achieve that and identify all four ply elastic constants (E1, E2, ν12, G12) at once. However, the accuracy of the identified properties may not be as good as properties measured from individual tests due to the complexity of the experiment, the relative insensitivity of the measured quantities to some of the properties and the various possible sources of uncertainty. It is thus important to quantify the uncertainty (or confidence) with which these properties are identified. Here, Bayesian identification is used for this purpose, because it can readily model all the uncertainties in the analysis and measurements, and because it provides the full coupled probability distribution of the identified material properties. In addition, it offers the potential to combine properties identified based on substantially different experiments. The full-field measurement is obtained by moiré interferometry. For computational efficiency the Bayesian approach was applied to a proper orthogonal decomposition (POD) of the displacement fields. The analysis showed that the four orthotropic elastic constants are determined with quite different confidence levels as well as with significant correlation. Comparison with manufacturing specifications showed substantial difference in one constant, and this conclusion agreed with earlier measurement of that constant by a traditional four-point bending test. It is possible that the POD approach did not take full advantage of the copious data provided by the full field measurements, and for that reason that data is provided for others to use (as on line material attached to the article).

An object-oriented simulation-optimization interface

Progress in the field of structural optimization naturally leads to an increasing number of structural models and optimization algorithms that need to be considered for design. Software architecture is of central importance in the ability to account for the complex links tying new structural models and optimizers. An object-oriented programming pattern for interfacing simulation and optimization codes is described in this article. The concepts of optimization variable, criteria, optimizers and simulation environment are the building blocks of the pattern. The resulting interface is logical, flexible and extensive. It encompasses constrained single or multiple objective formulations with continuous, discrete or mixed design variables. Applications are given for composite laminate design.

Comparison between the basic least squares and the Bayesian approach for elastic constants identification

The basic formulation of the least squares method, based on the L2 norm of the misfit, is still widely used today for identifying elastic material properties from experimental data. An alternative statistical approach is the Bayesian method. We seek here situations with significant difference between the material properties found by the two methods. For a simple three bar truss example we illustrate three such situations in which the Bayesian approach leads to more accurate results: different magnitude of the measurements, different uncertainty in the measurements and correlation among measurements. When all three effects add up, the Bayesian approach can have a large advantage. We then compared the two methods for identification of elastic constants from plate vibration natural frequencies.

Identification of the in vivo elastic properties of common carotid arteries from MRI: a study on subjects with and without atherosclerosis.

The stiffness of the arterial wall, which is modified by many cardiovascular diseases such as atherosclerosis, is known to be an indicator of vulnerability. This work focuses on the in vivo quantification of the stiffness of the common carotid artery (CCA) by applying the Magnitude Based Finite Element Model Updating (MB-FEMU) method to 13 healthy and diseased volunteers aged from 24 to 76 years old. The MB-FEMU method is based on the minimisation of the deviation between the image of a deformed artery and a registered image of this artery deformed by means of a finite elements analysis. Cross sections of the neck of each subject at different times of the cardiac cycle are recorded using a Phase Contrast cine-MRI. Applanation tonometry is then performed to obtain the blood pressure variations in the CCA throughout a heart beat. First, a time averaged elastic modulus of each CCA between diastole and systole is identified and a stiffening of the artery with age and disease is observed. Second, four elastic moduli are identified during a single heart beat for each artery, highlighting the nonlinear mechanical behaviour of the artery. A stiffening of the artery is observed and quantified at systole in comparison to diastole.

A mixed evolutionary/heuristic approach to shape optimization

The problcm of finding the optimal shape of a continuous structure is ~ using, altematively, hcuristic, cvolutionary and mixcd cvolutionary and hewistic optimization stratcgies. Boundaries arc represcntcd by B-splines. Two hcuristics for minimizing the wcight of a structure subjcct to limits on von Mises stresses and geometrical constraints arc implementcd: gcncralizcd biological growth and pcnalizcd biological growth. Penalized biological growth adds to gcneralizcd biological growth a control for shape changes. This control il bascd on the overallstatc of constraints satisfaction in the structure. The two bcuristics arc vcry efficient at improving the designs. but they do not yield gJoba11y optjma1 Sbapcs. Thereforc, thcy arc intcrfaccd with an cvolutionary optimizer. Differcnt strategies for mixing cvolutionary scarch and biological growth are comparcd. Resuits arc obtained for fan disk shape problcms. They show that mixing evolutionary scarch with biological growth improves the efficiency of the optimization. The method off ers to the designer ncw paths for a bettcr component detennination. C 1998 John Wilcy & Sons, Ltd.