Multilevel optimization including progressive failure analysis and robust design optimization for composite stiffened panels, in which the ultimate load that a post-buckled panel can bear is maximized for a chosen weight, is presented for the first time. This method is a novel robust multiobjective approach for structural sizing of composite stiffened panels at different design stages. The approach is integrated at two design stages labelled as preliminary design and detailed design. The robust multilevel design methodology integrates the structural sizing to minimize the variance of the structural response. This method improves the product quality by minimizing variability of the output performance function. This innovative approach simulates the sequence of actions taken during design and structural sizing in industry where the manufacture of the final product uses an industrial organization that goes from the material characterization up to trade constraints, through preliminary analysis and detailed design. The developed methodology is validated with an example in which the initial architecture is conceived at the preliminary design stage by generating a Pareto front for competing objectives that is used to choose a design with a required weight. Then a robust solution is sought in the neighbourhood of this solution to finally find the layup for the panel capable of bearing the highest load for the given geometry and boundary conditions.

Advanced composites are increasingly being used as a structural material because of their balanced properties, higher impact resistance, and easier handling and fabrication compared with unidirectional composites. However, complex architecture of these composites leads to difficulties in predicting the mechanical response necessary for product design. Different methods for micromechanical analysis for the evaluation of effective mechanical properties of advanced composites are compared. Difficulties in modeling are highlighted and recommendations are given for micromechanical analysis using the finite element method.

This paper focuses on Deterministic and Reliability Based Design Optimization (DO and RBDO) of composite stiffened panels considering post-buckling regime and progressive failure analysis. The ultimate load that a post-buckled panel can hold is to be maximised by changing the stacking sequence of both skin and stringers composite layups. The RBDO problem looks for a design that collapses beyond the shortening of failure obtained in the DO phase with a target reliability while considering uncertainty in the elastic properties of the composite material. The RBDO algorithm proposed is decoupled and hence separates the Reliability Analysis (RA) from the deterministic optimization. The main code to drive both the DO and RBDO approaches is written in MATLAB and employs Genetic Algorithms (GA) to solve the DO loops because discrete design variables and highly nonlinear response functions are expected. The code is linked with Abaqus to perform parallel explicit nonlinear finite element analyses in order to obtain the structural responses at each generation. The RA is solved through an inverse Most Probable failure Point (MPP) search algorithm that benefits from a Poly-

A numerical model capable of dealing with progressive degradation of plain woven composites in a computationally efficient manner is presented in this article. A semi-analytical homogenization method is used to derive effective properties of the composite from the material properties of the constituents. The progressive failure is described using nonlocal continuum damage mechanics where the driving internal variable for the damage is the nonlocal strain. The model was implemented into Abaqus/Explicit, where the failure of a longitudinal tension and an open hole tension specimens were simulated in a multi-scale manner and verified experimentally.

A new multi-fidelity modelling-based probabilistic optimisation framework for composite structures is presented in this paper. The multi-fidelity formulation developed herein significantly reduces the required computational time, allowing for more design variables to be considered early in the design stage. Multi-fidelity models are created by the use of finite element models, surrogate models and response correction surfaces. The accuracy and computational efficiency of the proposed optimisation methodology are demonstrated in two engineering examples of composite structures: a reliability analysis, and a reliability-based design optimisation. In these two benchmark examples, each random design variable is assigned an expected level of uncertainty. Monte Carlo Simulation (MCS), the First-Order Reliability Method (FORM) and the Second-Order Reliability Method (SORM) are used within the multi-fidelity framework to calculate the probability of failure. The reliability optimisation is a multi-objective problem that finds the optimal front, which provides both the maximum linear buckling load and minimum mass. The results show that multi-fidelity models provide high levels of accuracy while reducing computation time drastically.

In this paper, a multi-objective probabilistic design optimisation approach is presented for reliability and robustness analysis of composite structures and demonstrated on a mono-omega-stringer stiffened panel. The proposed approach utilises a global surrogate model of the composite structure while accounting for uncertainties in material properties as well as geometry. Unlike the multi-level optimisation approach which freezes some parameters at each level, the proposed approach allows for all parameters to change at the same time and hence ensures global optimum solutions in the given parameter design space (for both probabilistic and deterministic optimisations) within a certain degree of accuracy. The proposed approach is used in this study to conduct extensive multi-objective probabilistic and deterministic optimisations (without considering safety factors) on a mono-stringer stiffened panel. In particular, a global surrogate model is developed utilising the computational power of a highperformance computing facility. The inputs of the surrogate model are the omega-stringer geometry and the mechanical properties of the composite material, while the outputs are the fundamental linear buckling load (LBL) and the nonlinear postbuckling strength (NPS). LBL and NPS are obtained via detailed parametric finite element models of the mono-stringer stiffened panel; in the nonlinear model, the interface between the skin and the omega-stringer is modelled via cohesive elements to allow for debonding in the post-buckled regime. Extensive multi-objective optimisations are conducted on the surrogate model using deterministic and probabilistic approaches to examine the omega-stringer geometric parameters mostly affecting the system robustness and reliability. The differences between deterministic and probabilistic designs are highlighted as well.

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The propagation characteristic of Lamb waves activated by Piezoelectric actuators and collected by sensors in a stiffened panel has been investigated. A network of actuators is used to scan the structure before and after the presence of damage. A diagnostic imaging algorithm has been developed based on the probability of damage at each point of the structure measured by the signal reading of sensors in the baseline and damaged structure. A damage localization image is then reconstructed by superimposing the image obtained from each sensor-actuator path. Three-dimensional finite element model with a transducer network is modelled. Damage is introduced as a small softening area in the panel. Applying the imaging algorithm, the damage location was predicted with good accuracy. The validity of the algorithm was tested for multiple damages.