Orthotropic material orientation optimization method in composite laminates

This paper proposes a optimization method that is capable of simultaneous design of multiple layers in a composite laminate with respect to multiple objective functions. The optimization process obtains a continuous orientation of an orthotropic material for each layer of the laminate. Each layer by itself is a single design domain, which allows multiple domains to be stacked in various orientations. Multiple optimization objectives are considered resulting in layers that perform different functions. The layers are modeled within a three-dimensional structure and by discretizing the structure using three-dimensional elements, the interaction between individual layers can be modeled. This also allows the optimization method to obtain a three-dimensional orientation vector. In this study, the individual layers are assumed to be thin, limiting the orientation vector to the mid-plane of the layer. The optimization model is tested on a two-layer laminate in which one layer is optimized for thermal control by directing heat toward specified sections while shielding other sections and the second layer is optimized to reduce the total deformation of the laminate structure that results from the thermal load. The results of simultaneous optimization for both layers are shown for several different configurations of boundary conditions.     

A comparative study on the metaheuristic-based optimization of skew composite laminates

Engineering with Computers - Plate structures are the integral parts of any maritime engineering platform. With the recent focus on composite structures, the need for optimizing their design and...     

A first-ply failure analysis of composite laminates

A finite-element computational procedure is developed for the first-ply failure analysis of laminated composite plates. The procedure is based on the first-order shear deformation theory and a tensor polynomial failure criterion that contains the maximum stress, maximum strain, the Hill, Tsai-Wu and Hoffman failure criteria as special cases. By specifying the desired criterion, a first-ply failure analysis of composite laminates subjected to in-plane and/or bending loads can be achieved. A number of problems are presented to evaluate these failure criteria when applied to laminates subjected to in-plane and or bending loads.     

Stacking sequence optimization for constant stiffness laminates based on a continuous optimization approach

In this paper, an optimization procedure based on multi-phase topology optimization is developed to determine the optimal stacking sequence of laminates made up of conventional plies oriented at ?45°, 0°, 45 and 90°. The formulation relies on the SFP (Shape Functions with Penalization) parameterization, in which the discrete optimization problem is replaced by a continuous approach with a penalty to exclude intermediate values of the design variables. In this approach, the material stiffness of each physical ply is expressed as a weighted sum over the stiffness of the candidate plies corresponding to ?45°, 0°, 45 and 90° orientations. In SFP, two design variables are needed for each physical ply in the laminate to parameterize the problem with respect to the 4 candidate orientations. Even if only constant stiffness laminates of constant thickness are considered in this paper, specific design rules used in aeronautics for composite panels (i.e., no more than a maximum number of consecutive plies with the same orientation in the stacking sequence) are however formulated and taken into account in the optimization problem. The methodology is demonstrated on an application. It is discussed how the different design rules can affect the solution.     

A hybrid multilevel approach for aeroelastic optimization of composite wing-box

The quest for finding optimum solutions to engineering problems has been existing for a long time. In the last decade several optimization techniques have been applied to the structural design of composite wing structures. Generally many of these proposed procedures have dealt with different disciplines such as aerodynamics, structures, or dynamics separately. However an aeronautical design process is multidisciplinary since it involves strong couplings and interactions among, for instance, aerodynamics, dynamics, flight mechanics and structures. The main problem in a multidisciplinary aircraft design is usually the development of an efficient method to integrate structures or structural properties, which can be considered both as “global” and “local” design variables. This paper describes an integrated aerodynamic / dynamic / structural optimization procedure for a composite wing-box design. The procedure combines an aeroelastic optimization of a composite wing based on a general purpose optimizer such as the Sequential Quadratic Programming (SQP) and a composite optimization using Genetic Algorithm (GA). Both the optimizations are implemented through a hybrid multilevel decomposition technique.     

A unified approach to nonlinear buckling optimization of composite structures

A unified approach to nonlinear buckling fiber angle optimization of laminated composite shell structures is presented. The method includes loss of stability due to bifurcation and limiting behaviour. The optimization formulation is formulated as a mathematical programming problem and solved using gradient-based techniques. Buckling of a well-known cylindrical shell benchmark problem is studied and the solutions found in literature are proved to be incorrect. The nonlinear buckling optimization formulation is benchmarked against the traditional linear buckling optimization formulation through several numerical optimization cases of a composite cylindrical shell panel which clearly illustrates the advantage and potential of the presented approach.     

Impact damage in composite laminates

A low velocity impact damage model for the quasi-symmetric graphite fiber composite plates is presented. The distribution of damage in each layer of the plate was calculated by employing Di Sciuva's composite laminate theory together with Hashin's failure criterion for fiber-reinforced composites. The dynamic deformation of the target plate was represented by the lower vibrational modes of the plate. The principle of virtual work was applied in the formulation of the problem. In the analysis, the material was regarded as ‘damaged’ when its designed strength was reduced by the failure of its constituents. The constituent failures consisted of matrix crackings, fiber breakages, and delamination between layers. According to damage modes, the moduli of material in the damaged zone were reduced according to the failure criteria. The interaction between layers and its role in damage propagation were also studied.     

Special purpose symbolic computation software with application to the optimization of composite laminates

Symbolic computation software is developed in the C language for the transformation of coordinate axes, failure analysis and the calculation of design sensitivities. These computations arise in the design optimization studies of structures made of fibre composite materials. The symbolic computations are integrated into an optimization algorithm resulting in a combined symbolic and numerical approach to determine the optimal design. The results are illustrated by considering the minimum thickness design of a laminate under in-plane loads. For this problem, the special purpose symbolic computation software handles matrices whose entries are series of double trigonometric functions, and determines the component functions of the design objective.     

A unified approach to optimization of structural members under general constraints

A unified numerical approach, based on a control parameterization technique, for solving structural crosssectional optimization problems is presented. The key factor to the unified formulation lies in the framing of the objective functional and the constraints into the same unified canonical form. Consequently, the different types of objective functionals, geometrical and performance constraints can be treated in the same way, thus paving the path for the problems to be solved under a single approach using a general purpose software. To demonstrate this versatile approach, several illustrative examples of cross-sectional shape optimization of structural members under a variety of constraints were examined.     

An optimization approach for cloud composite services

Recently, a considerable literature has grown up around the theme of composite services verification. Namely, the verification of the non-functional aspect generally consisting of optimizing the quality of service (QoS) of the composite service. Great efforts have been devoted to the study of several optimization methods and their impact on the QoS of the composite service. Guaranteeing the service level agreements established with users remains one of the greatest challenges in this field. This essay explores a new composition approach based on a linear programming algorithm and compares the obtained results with existing works. Our approach aims to guarantee an efficient and optimal solution to the Cloud composite service problem. For evaluation, we have developed the CR-SIM simulator that selects and composes services in the Cloud context.

     

Multi-objective optimization of fiber reinforced composite laminates for strength,stiffness and minimal mass

We present a methodology for the multi-objective optimization of laminated composite materials that is based on an integer-coded genetic algorithm. The fiber orientations and fiber volume fractions of the laminae are chosen as the primary optimization variables. Simplified micromechanics equations are used to estimate the stiffnesses and strength of each lamina using the fiber volume fraction and material properties of the matrix and fibers. The lamina stresses for thin composite coupons subjected to force and/or moment resultants are determined using the classical lamination theory and the first-ply failure strength is computed using the Tsai–Wu failure criterion. A multi-objective genetic algorithm is used to obtain Pareto-optimal designs for two model problems having multiple, conflicting, objectives. The objectives of the first model problem are to maximize the load carrying capacity and minimize the mass of a graphite/epoxy laminate that is subjected to biaxial moments. In the second model problem, the objectives are to maximize the axial and hoop rigidities and minimize the mass of a graphite/epoxy cylindrical pressure vessel subject to the constraint that the failure pressure be greater than a prescribed value.     

Multicriterion optimization of composite laminates for maximum failure margins with an interactive descent algorithm

An interactive multicriterion optimization method for composite laminates subjected to multiple loading conditions is introduced. Laminate margins to initial failure (First Ply Failure, FPF) with respect of the applied loading conditions are treated as criteria. The original problem is reduced to a bicriterion problem by introducing parameters to combine linearly some criteria. The problem is solved by using an interactive descent algorithm. Both the conditions required for a discrete procedure to converge towards a Pareto optimum and numerical examples are given.     

Characterization of delamination effect on composite laminates using a new generalized layerwise approach

A dynamic analysis method has been developed to investigate and characterize the effect due to presence of discrete single and multiple embedded delaminations on the dynamic response of composite laminated structures with balanced/unbalanced and arbitrary stacking sequences in terms of number, placement, mode shapes and natural frequencies. A new generalized layerwise finite element model is developed to model the presence of multiple finite delamination in laminated composites. The new theory accurately predicts the interlaminar shear stresses while maintaining computational efficiency.     

Optimum stacking sequence design of composite laminates for maximum buckling load capacity using parameter-less optimization algorithms

This paper presents a comparative study of the application of parameter-less meta-heuristic algorithms in optimum stacking sequence design of com of composite laminates for maximum buckling load capacity. Here, JAYA algorithm, along with Salp Swarm Algorithm, Colliding Bodies Optimization, Grey Wolf Optimizer, and Genetic Algorithm with standard setting and self-adaptive version are implemented to the problem of composite laminates with 64 graphite/epoxy plies with conventional ply angles, under several bi-axial cases and panel aspect ratios. Optimization objective is to maximize the buckling load of symmetric and balanced laminated plate. Statistical analysis are performed for six cases and the results are compared in terms of mean, standard deviation, the coefficient of variation, best and worst solutions, accompanied by the percentage of the independent runs that found the global optimum \(\left( {{R_{{\text{op}}}}} \right)\) and near global optimum \(\left( {{R_{{\text{no}}}}} \right)\). The Kruskal–Wallis nonparametric test is also utilized to make further confidence in the examinations. Numerical results show the high capability of the JAYA algorithm for maximizing the buckling capacity of composite plates.

     

An investigation on design of signs in composite laminates to control bending-twisting coupling effects using sign optimization algorithm

Structural and Multidisciplinary Optimization - A sign optimization algorithm (SOA) is proposed to design the “±” signs in composite laminates to control the bending-twisting...     

A general approach to approximate solutions of nonlinear differential equations using particle swarm optimization

A general algorithm is presented to approximately solve a great variety of linear and nonlinear ordinary differential equations (ODEs) independent of their form, order, and given conditions. The ODEs are formulated as optimization problem. Some basic fundamentals from different areas of mathematics are coupled with each other to effectively cope with the propounded problem. The Fourier series expansion, calculus of variation, and particle swarm optimization (PSO) are employed in the formulation of the problem. Both boundary value problems (BVPs) and initial value problems (IVPs) are treated in the same way. Boundary and initial conditions are both modeled as constraints of the optimization problem. The constraints are imposed through the penalty function strategy. The penalty function in cooperation with weighted-residual functional constitutes fitness function which is central concept in evolutionary algorithms. The robust metaheuristic optimization technique of the PSO is employed to find the solution of the extended variational problem. Finally, illustrative examples demonstrate practicality and efficiency of the presented algorithm as well as its wide operational domain.     

A novel computational framework for structural optimization with patched laminates

Structural and Multidisciplinary Optimization - Fiber patch placement (FPP) is a manufacturing technique for discrete variable stiffness composites. In the FPP approach, a structural component is...