Buckling optimization of laminated composite plates using genetic algorithm and generalized pattern search algorithm

In this paper, genetic algorithm and generalized pattern search algorithm are used for optimal stacking sequence of a composite panel, which is simply supported on four sides and is subject to biaxial in-plane compressive loads. The problem has several global optimum configurations in the vicinity of local optima. The composite plate under consideration is 64-ply laminate made of graphite/epoxy. The laminate is taken to be symmetric and balanced, comprised of two-ply stacks with discrete fiber angles of 0₂, ± 45, 90₂ in the laminate sequence. The critical buckling loads are maximized for several combinations of load case and plate aspect ratio, and are compared with published results. Performance of both algorithms is compared in terms of capability of identifying global optima. It is found that genetic algorithm is efficient for problems with global optima.     

Sensor placement optimization applied to laminated composite plates under vibration

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.     

Topology optimization of piezoelectric macro-fiber composite patches on laminated plates for vibration suppression

Structural and Multidisciplinary Optimization - This work presents a new methodology for the topology optimization of piezoelectric actuators in laminated composite structures with the objective of...     

Hybrid-interface element for thick laminated composite plates

A novel 27-node three-dimensional hexahedral hybrid-interface finite element (FE) model has been presented to analyze laminated composite plates and sandwich plates using the minimum potential energy principle. Fundamental elasticity relationship between components of stress, strain and displacement fields are maintained throughout the elastic continuum as the transverse stress components have been invoked as nodal degrees of freedom. Continuity of the transverse stresses at lamina interface has been maintained. Each lamina is modeled by using hybrid-interface elements at the top and the bottom interfaces and conventional displacement based elements sandwiched between these interfaces. Results obtained from the present formulation have found to be in excellent agreement with the elasticity solutions for thin and thick composite cross-ply, angle-ply laminates, as well as sandwich plates. Additional results have also been presented on the variation of the transverse strains to highlight magnitude of discontinuity in these quantities due to difference in properties of face and core materials of sandwich plates. Present formulation can be used effectively to interface hybrid formulation that uses transverse stresses and displacements as degrees of freedom with conventional purely displacement based formulation for realistic estimates of the transverse stresses.     

Natural frequency and buckling optimization of laminated hybrid composite plates using genetic algorithm and simulated annealing

In this study, genetic algorithm and simulated annealing are used to maximize natural frequency and buckling loads of simply supported hybrid composite plates. The aim of the study is to use two different techniques of optimization on the frequency and buckling optimization of composite plates, and compare the techniques for their effectiveness. The composite plate is made of carbon/epoxy and glass/epoxy hybrid plies, and assumed to be symmetric and balanced. The effect of hybridization is investigated using both techniques. The buckling problem has many maxima in the vicinity of local maxima. The best configurations are identified for different plate aspect ratios. The performance of both techniques is compared in terms of number of function evaluations as well as the capability of finding best configurations.     

Optimal design of hybrid laminated composite plates with dynamic and static constraints

Optimization procedures are presented that consider the static and dynamic characteristic constraints for laminated composite plates and hybrid laminated composite plates subject to a concentrated load on the center of the plate. The design variables adopted are ply angle or ply thickness. Considered constraints are deflection, natural frequency and specific damping capacity. Using a recursive linear programming method, nonlinear optimization problems are solved, and by introducing the design scaling factor, the number of iterations is reduced significantly. Relating interactive optimization procedures with the finite element method analysis, various hybrid composite plates with arbitrary boundary conditions can be designed optimally. In the optimization procedure, verification of analysis and design of the laminated composite plates are compared with a previous paper. Various design results are presented on laminated composite plates and hybrid laminated composite plates.     

Region-by-region modeling of laminated composite plates

Several plate models have been proposed in the literature for the analysis of laminated plates. These are based either on an equivalent through-thickness formulation or a layerwise formulation. It is shown in the literature that while the equivalent models are economical, the layerwise models are expensive but are also more accurate, especially with respect to the transverse stresses. Generally, the same model is used throughout the domain. The current study addresses the issue of economical and accurate computation of local stresses, strains and displacements (as well as global quantities) using combinations of layerwise, equivalent or intermediate models in various regions of the domain. A region-by-region modeling strategy is presented for a chosen general family of equivalent, intermediate and layerwise models. The proposed strategy allows the user to put any model (of any order in the thickness direction) in any desired region of interest. The effectiveness of the strategy is demonstrated through numerical examples. It is shown that this approach can significantly reduce computational cost and can also lead to good resolution of the local stress and displacement fields for domains with unsymmetric laminae, cut-outs, local damage, corner edges, sudden transition of boundary conditions and material.     

Bifurcation and post-buckling analysis of laminated composite plates via reduced basis technique

A reduced basis technique and a problem-adaptive computational algorithm are presented for the bifurcation and post-buckling analysis of laminated anisotropic plates. The computational algorithm can be conveniently divided into three distinct stages. The first stage is that of determining the bifurcation point. The plate is discretized by using displacement finite element (or finite difference) models. The special symmetries exhibited by the response of the anisotropic plate are used to reduce the size of the analysis region. The vector of unknown nodal parameters is expressed as a linear combination of a small number of basis vectors, and a Rayleigh-Ritz technique is used to approximate the finite element equations by a small system of algebraic equations. The reduced equations are used to determine the bifurcation point and the associated eigen mode of the panel.In the second stage of the bifurcation buckling mode is used to obtain a nonlinear solution in the vicinity of the bifurcation point and new (updated) sets of basis vectors and reduced equations are generated. In the third stage the reduced equations are used to trace the post-buckling paths.The effectiveness of the proposed technique for predicting the bifurcation and post-buckling behavior of plates is demonstrated by means of numerical examples for plates loaded by means of prescribed edge displacements.     

Design of optimal constrained dynamic compensators for non-stationary linear stochastic systems

This paper deals with the design of fixed-order dynamic compensators for non-stationary linear stochastic systems with noisy observations, where the observation noise need not necessarily be white. An integral quadratic performance index defined over a finite time interval is employed and this yields a matrix variational problem in the compensator parameters. It is shown how the optimal, possibly time-varying, compensator parameters rnay be determined by direct solution of this variational problem using a conjugate-gradient technique. Consideration is also given to finding suboptimal compensators that are simpler to implement. In particular, an algorithm is proposed for designing compensators having gains that are constrained to be piecewise-constant functions of time, with provision for optimally choosing the instants at which gains changes occur. An illustrative numerical example is included.     

Hygrothermal bending of laminated composite plates with a cutout

Bending of laminated composite plates with a cutout subjected to moisture and temperature is investigated. An eight-noded isoparametric element, which takes transverse shear deformation into account, is used in the present analysis. Three types of cutouts are considered, namely, circular, rounded corner square, and square. The distribution of deflection and moment resultants are studied in anti-symmetric laminates for simply supported and clamped boundary conditions, subjected to uniform moisture and temperature.     

Finite element model updating of honeycomb sandwich plates using a response surface model and global optimization technique

Honeycomb sandwich plates are used widely in the aerospace industry. Building accurate finite element models of honeycomb sandwich plates is necessary for analyzing and optimizing the microvibration that occurs in spacecraft. This study investigated two types of finite element dynamic models of honeycomb plates: a sandwich shell model and a shell-volume-shell model. Two response surface model-based optimization methods and a particle swarm optimization method were compared for updating the finite element models. Finally, we validated the accuracy of the two optimized honeycomb sandwich plate finite element dynamic models by comparing the results obtained by the frequency response functions with experimental data.     

Free vibrations of laminated composite plates using second-order shear deformation theory

A complete set of linear equations of the second-order theory of laminated composite plates are obtained. A generalized Levy type solution in conjunction with the state space concept is used to analyze the free vibration behavior of cross-ply and antisymmetric angle-ply laminated plates. Exact fundamental frequencies of cross-ply plate strips are obtained for arbitrary boundary conditions. The exact analytical solutions are obtained for thick and moderately thick plates as well as for thin plates and plate strips. It is shown that the results of the second-order theory are very close to the results of the first-order and third-order theories reported in the literature, and different from those of the classical Kirchhoff’s theory for thick laminates.     

Free material optimization for laminated plates and shells

Free Material Optimization (FMO) is a powerful approach for conceptual optimal design of composite structures. The design variable in FMO is the entire elastic material tensor which is allowed to vary almost freely over the design domain. The imposed requirements on the tensor are that it is symmetric and positive semidefinite. Most of today’s studies on FMO focus on models for two- and three-dimensional structures. The objective of this article is to extend existing FMO models and methods to laminated plate and shell structures, which are used in many engineering applications. In FMO, the resulting optimization problem is generally a non convex semidefinite program with many matrix inequalities which requires special-purpose optimization methods. The FMO problems are efficiently solved by a primal-dual interior point method developed and implemented by the authors. The quality of the proposed FMO models and the method are supported by several large-scale numerical experiments.     

Dynamic stability of rectangular laminated composite plates

The dynamic stability of rectangular layered plates due to periodic in-plane load is studied in this paper. Using the finite strip method, the problem is reduced to that of one with finite degrees of freedom. Then following Bolotin's procedure, the regions of parametric instability have been determined. The influence of plate configuration, aspect ratio and static in-plane force have been studied.     

Optimum weight design of composite laminated plates

Optimum designs for the minimum weight of composite laminated plates subjected to size, displacement, buckling and natural frequency constraints are investigated by a technique of combining finite element method and mathematical programming, in which the structural analysis is based on the YNS theory. The recurrence relation based on the feasible direction method (FDM) and the scaling step is used to modify the design variables (ply-thicknesses and ply-orientations) during the iterative procedure. Grouping technique is engaged in the procedure in order that the number of design variables can be greatly reduced to make the problem more practical. Illustrative examples are given to show that the present technique is quite efficient and reliable.     

Adaptive memory programming for constrained global optimization

The problem of finding a global optimum of a constrained multimodal function has been the subject of intensive study in recent years. Several effective global optimization algorithms for constrained problems have been developed; among them, the multi-start procedures discussed in Ugray et al. [1] are the most effective. We present some new multi-start methods based on the framework of adaptive memory programming (AMP), which involve memory structures that are superimposed on a local optimizer. Computational comparisons involving widely used gradient-based local solvers, such as Conopt and OQNLP, are performed on a testbed of 41 problems that have been used to calibrate the performance of such methods. Our tests indicate that the new AMP procedures are competitive with the best performing existing ones.     

Elastic-plastic dynamic analysis of anisotropic laminated plates

This paper presents the application of a refined finite element model to the elastic and elastic-plastic dynamic analysis of anisotropic laminated plates. Dynamic analysis is based on Newmark's algorithm used in conjunction with the Hughes and Liu predictor-corrector scheme resulting in an ‘effective static problem’ which is solved using a Newton-Raphson-type process. Flow theory is used in the inelastic range and the Huber-Mises yielding surface extended by Hill for anisotropic materials is adopted. Numerical results obtained for two categories of anisotropic structures, namely cross-ply laminated plates and angle-ply laminated plates, are presented and the effects of anisotropy and bending/ stretching coupling on the dynamic elastic and elastic-plastic responses are discussed. The effects of lamina stack sequences and lamina angle sequences on the dynamic responses are also considered.     

A state space finite element for laminated composite plates

This paper presents a semi-analytical finite element solution for the stress analysis of cross-ply laminated composite plates. The method is based on a mixed variational principle that includes the variations of both displacements and stresses. Finite element approximation is introduced only for the in-plane variations of displacements and stresses, while the through-thickness distributions of them are obtained by using the method of state equation. Numerical tests show that the results obtained approach the analytical three-dimensional solutions. Moreover, the use of the recursive formulation of the state equation leads to the solution of an algebra equation system whose order does not depend on the number of material layers of the laminate. Compared with the traditional finite element method, the new solution always provides continuous distributions of both displacements and transverse stresses across material interfaces.     

Optimum design of laminated composite plates containing a quasi-square cutout

In this paper, an attempt has been made to calculate the optimal values of effective parameters on the stress distribution around a quasi-square cutout using different optimization algorithms such as Particle Swarm Optimization (PSO), Genetic Algorithm (GA) and Ant Colony Optimization (ACO). To achieve this goal, the analytical results of symmetric laminated composite plates containing a square cutout have been used. The analytical solution can be achieved with the development of the Lekhnitskii solution method. This method is based on using complex variable method in the analysis of two-dimensional problems. In order to use the method in stress analysis of laminates containing a square cutout, by using conformal mapping, the area outside the square cutout is mapped to the area outside of a unit circle. Effective parameters on stress distribution around the square cutout in symmetric laminated plates considered as design variables include: load angle, cutout orientation, bluntness and the stacking sequence of the laminate. Cost function in this problem is the maximum stress created around the cutout calculated by the analytical solution method. Another goal of this paper is to investigate the performance of aforementioned optimization algorithms. The results show that the PSO algorithm converges earlier than the other two methods and have the better cost function.