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In practical engineering, the design scheme is generally a compromise solution that meets various requirements. In most cases, the traditional optimization method provides a single optimized solution, which may be prone to fail during the subsequent design stage because some unpredictable requirements may be not considered in the preliminary optimization process. For example, maximizing fundamental frequency is generally regarded as the optimization objective for aerospace structures under the vibration environment in the preliminary design stage. However, the optimized solution may fail for strength, buckling, or other requirements during the subsequent detailed design stage. Therefore, it is crucial to provide multiple alternative solutions for insurance. In this paper, a diverse discrete material optimization (DDMO) framework is proposed for multi-patch laminates. It can optimize the material topology layout and fiber orientations of composite structures simultaneously and provide multiple alternative solutions that have diversity in design space and different potential performance. In this paper, a diversity index for discrete variables is proposed and the discrete material optimization (DMO) method with the diversity index constraint is employed to perform the DDMO. Two illustrative examples are used to verify the effectiveness of the proposed optimization framework, including a simple example of a composite plate and a complex engineering example of an S-shaped curved shell. Results indicate that, the proposed method can provide multiple diverse alternative solutions with similar performance in the optimization objective, which are verified to have better potential performance than the single solution by the traditional single design method. Moreover, multiple design options by the diverse optimization method can contribute to reducing the probability of redesign and shortening the design cycle. [ABSTRACT FROM AUTHOR]

This paper presents a novel methodology to minimize the weight of a composite plate, taking into account both its structural integrity and its manufacturing constraints. This optimization problem has been abstracted, and reduced to, a graph problem where finding the optimum is equivalent to finding the shortest path in the graph. This graph is an implicit ternary decision tree and path finding is accomplished with a parallelized breadth-first search procedure. As a result of this search, the procedure is able to provide both a global optimum and a Pareto front. The implementation of an implicit decision tree as a way to optimize a laminate stacking sequence is a novel idea, in spite that both issues have been tackled in numerous publications separately. Its benefits are clearly stated in this work. [ABSTRACT FROM AUTHOR]

The location optimization of sensors is a essential problem in structural health monitoring systems. Taking the cost of sensors into account, it is uneconomical to install sensors on every part of a structure and moreover in aeronautical industry, the weight is a crucial factor. In this paper, a optimal placement optimization of sensor locations for structural health monitoring systems is studied. Several techniques of optimization of sensors are approached and applied in a shell structure. The structure, a laminate of carbon fiber, was modeled by the finite element method (FEM) and then subject to free vibration. Genetic algorithms (GAs) are then employed to locate the best sensor distribution to cover a specific number of low frequency modes. Numerical results have demonstrated the overall efficiency of sensor delivery methods. Specific problems occurred, especially regarding the method of effective independence, being less efficient and discrepant in relation to the other methods employed. In summary, the results obtained in this paper provide an optimal position for sensors in real SHM systems and experiments. [ABSTRACT FROM AUTHOR]

Variable stiffness (VS) composites made by fiber steering have received intensive attention due to the tailorability of the stiffness and strength properties. However, a significantly larger number of elements are required to converge for VS composites, which results in much longer runtime and makes the design and optimization more complicated. In this paper, an efficient design optimization method assisted by multi-fidelity surrogate models is presented for the buckling design of VS composites. To reduce the computational burden, a multi-fidelity surrogate model called hierarchical Kriging is constructed through a few expensive high-fidelity samples and many cheap low-fidelity samples. Fine and coarse finite element (FE) analysis is performed respectively to calculate the structural responses for corresponding datasets. The efficient global optimization based on a modified expected improvement criterion is employed and used to adaptively add new samples of variable-fidelity. Two case studies, a composite plate subjected to uniform uniaxial compression and a composite cylinder under pure bending, are investigated. The effects of different number of design variables and coarse FE model mesh density on the optimum configuration are studied to demonstrate the effectiveness and robustness of the method. The results indicate that the present method can remarkably reduce the number of high-fidelity FE evaluations and improve the optimization efficiency when compared with available methods in the literature. Additionally, the investigation in the mechanism of loading carrying capacity improvement shows that the increase is mainly due to the load redistribution. [ABSTRACT FROM AUTHOR]

A Lagrange parameterization of lamination parameters which are used for optimization of variable stiffness laminates is presented. The advantages of the approach are: a) the design variables become independent of the finite element mesh and, b) the smoothness of the solution is inherently guaranteed. Due to independency of design variables of the finite element mesh, the reduction in the number of design variables is drastic, once variable stiffness laminates usually demand a fine mesh. The lamination parameters formulation allows a more precise and concise approach to laminate design, removing difficulties related to fiber direction and stacking sequence, increasing the chances to find a global optimal solution. In this paper, the Lagrange parameterization is used for the maximization of the buckling load of a variable stiffness composite plate. [ABSTRACT FROM AUTHOR]

The lay-up optimization problems of composite plates against buckling are studied. The plate has symmetric lay-up and is loaded by an in-plane loading. The Classical Lamination Plate Theory is used. The necessary optimality conditions for the plate orthotropy/anisotropy optimization problems are considered, with special attention to bending-twisting coupling. The purpose of the optimization is to maximize the (lowest) buckling eigen value. The varied lay-up/layer orientation angles are considered both as smooth functions of the location coordinates and as having the same values at every point. It is shown that the twisting moment (calculated in the principal curvature axes) plays an important role in the conditions. Two example problems for a thin composite plate, loaded by shear, are considered. The first one corresponds to the case of one shear loading direction. The details of some known numerical solutions are studied. The obtained numerical results are in agreement with the theoretical results. The maximal lowest eigen values are 2-folded ones. A schematic model for treatment of the known optimal numerical solution (60° unidirectional lay-up for a long plate loaded by shear) is proposed. The second example problem corresponds to the case of shear loading acting in two opposite directions. The ways of equalizing the lowest buckling values corresponding to both loading directions are proposed. Numerical results for various aspect ratio and plate thickness values are presented. The potential of weight saving is demonstrated. [ABSTRACT FROM AUTHOR]

Grid structures are among the most lightweight elements for stiffening the plates and shells or as self-sufficient structures. There are different known grid patterns, which are composed of variable numbers of parallel ribs. Selecting an optimum pattern and geometries for a grid to achieve the minimum weight and maximum load-bearing capacity is a challenging procedure for designers. In the current study, a variable ribs model (VRM) is proposed to find the optimum architecture of a grid plate. Therefore, using a genetic algorithm process, a multi-objective optimization is implemented to maximize the axial or shear buckling loads at a minimum possible weight of a grid structure. Eleven geometrical parameters including thickness, width, and the number of ribs as well as the orientation of the grid plate are considered the design variables. The multi-objective optimization is carried out employing the ε-constraint method. The buckling loads are obtained based on the first-order shear deformation plate theory using the Ritz method. [ABSTRACT FROM AUTHOR]

This work deals with the layout optimization of piezoelectric fiber composite patches on a vibrating laminated composite plate and the discrete material design of the composite plate. The vibration of the composite plate is excited by an external mechanical loading, and a sinusoidal voltage with given amplitude and frequency is applied on the piezoelectric fiber composite patches. The analysis of the composite structure with piezoelectric fiber composite patches is performed via a finite element method in condensed form, where the piezoelectric effects are considered as induced force. As a view to minimize the dynamic response of the vibrating laminated composite structure, the Discrete Material Optimization method is employed to perform the design optimization of piezoelectric fiber composite patches and the stacking sequence, fiber angles, and selection of material for the composite structure. Numerical examples are presented to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

A sign optimization algorithm (SOA) is proposed to design the "±" signs in composite laminates to control the bending-twisting coupling effects. Owing to that the bending-twisting coupling stiffness are cubic on thickness, the innovation is to design the signs of ply orientations from the mid-plane to the outermost sequentially and iteratively. In this manner, the nondimensional anisotropic coefficients are controlled to the target values. Numerical examples are adopted to verify the effectiveness and efficiency of SOA. First, the signs of symmetric laminates [θ32]s are optimized with various boundaries, load ratios, and aspect ratios to show the bending-twisting coupling effects on bending, buckling, and vibration responses of composite plates. Second, the bending-twisting coupling effects are minimized since they may cause large errors in buckling load prediction when using closed-form solution after neglecting them. Third, the optimal sequences obtained from heuristic algorithms are employed for sign optimization. Results show that the bending-twisting coupling effects cannot be neglected; moreover, the buckling and vibration performances can be further improved by redesigning "±" signs in composite laminates. This research aims to provide a design technique to minimize the error induced by bending-twisting coupling and increase the probability to find the global optimum. [ABSTRACT FROM AUTHOR]

Optimization with Unified Particle Swarm Optimization (UPSO) method is performed for the enhancement of buckling load capacity of composite plates having damage under hygrothermal environment which has received little or no attention in the literature. Numerical results are presented for effect of damage in buckling behavior of laminated composite plates using an anisotropic damage model. Optimized critical buckling temperature of laminated plates with internal flaw is computed with the fiber orientation as the design variable by employing a UPSO algorithm and results are compared with undamaged case for various aspect ratios, ply orientations, and boundary conditions. FEM formulation and programming in the MATLAB environment have been performed. The results of this work will assist designers to address some key issues concerning composite structures. It is observed that the degradation of buckling strength of a structural element in hygrothermal environment as a result of internal flaws can be avoided to a large extent if we use these optimized ply orientations at design phase of the composite structure. This specific application proves the contribution of present work to be of realistic nature. [ABSTRACT FROM AUTHOR]

In this study, the structural optimization of notched composite laminates under in plane shear and normal tension loads were carried out. The objective function of the optimization problem was selected to be the maximum stiffness and the minimum strain respectively along with the orientation angles as the optimization variables. In order to determine the ultimate failure load, a previously developed progressive failure approach was adopted. Although numerous studies exist in the literature on this subject, within the scope of the present study, correlations with the experimental results were examined qualitatively by comparing predicted and experimentally determined damage states. Prior to obtaining the optimized results, a further investigation into the response of the structure under pure shear was studied by a parametric approach. A zeroth order optimization tool known as Nelder&Mead was utilized to obtain the optimized configurations. It was shown that the developed optimization scheme is suitable for an exact determination of maximum stiffness and the minimum strain for the given materials and geometry. The results were presented for various load configurations [ABSTRACT FROM AUTHOR]

A new two-stage stochastic partial differential equation (PDE)-constrained optimization methodology is developed for the active vibration control of structures in the presence of uncertainties in mechanical loads. The methodology relies on the two-stage stochastic optimization formulation with an embedded first-order black-box PDE-constrained optimization procedure. The PDE-constrained optimization procedure utilizes a first-order active-set algorithm with a conjugate gradient method. The objective function is determined through solution of the governing PDEs and its gradient is computed using automatic differentiation with hyper-dual numbers. The developed optimization methodology is applied to the problem of post-impact vibration control (via applied electromagnetic field) of an electrically conductive carbon fiber reinforced composite plate subjected to an uncertain, or stochastic, impact load. The corresponding governing PDEs consist of a nonlinear coupled system of equations of motion and Maxwell's equations. The conducted computational study shows that the obtained two-stage optimization solution allows for a significant suppression of vibrations caused by the randomized impact load in all impact load scenarios. Also, the effectiveness of the developed methodology is illustrated in the case of a deterministic impact load, where the two-stage strategy enables one to practically eliminate post-impact vibrations. [ABSTRACT FROM AUTHOR]