Thermal buckling optimisation of composite plates using firefly algorithm

Abstract

Composite plates play a very important role in engineering applications, especially in aerospace industry. Thermal buckling of such components is of great importance and must be known to achieve an appropriate design. This paper deals with stacking sequence optimisation of laminated composite plates for maximising the critical buckling temperature using a powerful meta-heuristic algorithm called firefly algorithm (FA) which is based on the flashing behaviour of fireflies. The main objective of present work was to show the ability of FA in optimisation of composite structures. The performance of FA is compared with the results reported in the previous published works using other algorithms which shows the efficiency of FA in stacking sequence optimisation of laminated composite structures.     

Mixed least-squares finite element model for the static analysis of laminated composite plates

This paper presents a mixed finite element model for the static analysis of laminated composite plates. The formulation is based on the least-squares variational principle, which is an alternative approach to the mixed weak form finite element models. The mixed least-squares finite element model considers the first-order shear deformation theory with generalized displacements and stress resultants as independent variables. Specifically, the mixed model is developed using equal-order C⁰ Lagrange interpolation functions of high p-levels along with full integration. This mixed least-squares-based discrete model yields a symmetric and positive-definite system of algebraic equations. The predictive capability of the proposed model is demonstrated by numerical examples of the static analysis of four laminated composite plates, with different boundary conditions and various side-to-thickness ratios. Particularly, the mixed least-squares model with high-order interpolation functions is shown to be insensitive to shear-locking.     

Effects of random system properties on the thermal buckling analysis of laminated composite plates

This paper examines the effect of random system properties on thermal buckling load of laminated composite plates under uniform temperature rise having temperature dependent properties using HSDT. The system properties such as material properties, thermal expansion coefficients and thickness of the laminate are modeled as independent random variables. A C⁰ finite element is used for deriving the eigenvalue problem. A Taylor series based first-order perturbation technique is used to handle the randomness in the system properties. Second-order statistics of the thermal buckling load are obtained. The results are validated with those available in the literature and Monte Carlo simulation.     

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.     

Shape optimization of stiffeners in stiffened composite plates with thermal residual stresses

The finite element analysis method is used to examine the influence of manufacturing-induced thermal residual stresses on the optimal shape of stiffeners in stiffened, symmetrically laminated plates. Three stiffener arrangements are studied via an optimization process in which the objective is to maximize the first natural frequency of the stiffened plate. The optimization problem is solved using the method of moving asymptotes (MMA). The numerical simulations indicate that thermal residual stresses can either cause a dispersion of stiffeners along the perimeter or a concentration around the centre. Further, the optimum fundamental frequency tends to increase with increasing temperature difference.     

Optimization of the buckling load for composite structures taking thermal effects into account

This paper deals with optimization of the buckling load for laminated composite structures. A new methodology has been developed where thermal residual stresses introduced in the manufacturing process are included in the buckling analysis. The thermal effects are also included in the calculation of the buckling load sensitivities, and it is therefore possible to “tailor” the thermal residual stresses in order to increase the buckling load. Rectangular plates and circular cylindrical shells subjected to axial compression are considered. The structures are optimized twice; the first time the thermal residual stresses are ignored in the optimization, and the second time the thermal residual stresses are included in the optimization. These two sets of optimizations give two important results. Firstly, it is possible to increase the buckling load for the structures significantly when the thermal residual stresses are taken into account. Secondly, structures which have been optimized ignoring the effects of thermal residual stresses, may have a buckling load which is much less than expected when the effects of the thermal residual stresses are included. Received November 7, 1999     

Application of differential quadrature method to the delamination buckling of composite plates

The delamination buckling response of a composite panel containing through-the-width delamination is numerically modeled using a solution that is based on the differential quadrature method (DQM). The composite is modeled as a general one-dimensional beam–plate having a through-the -width delamination that can be at any arbitrary location through its thickness; hence, dividing the domain into four regions. The DQM is applied to each region and with the imposition of appropriate boundary conditions, the problem is transformed into a standard eigenvalue problem. Numerical results are presented, illustrating the stability and validity of the method. The results also demonstrate the efficiency of the method in treating this class of engineering problem.     

A mortar spectral method for the analysis and optimization of L-shaped laminated plates

We present a new mortar approach in the spectral context for the analysis and optimization of L-shaped thin composite laminates. Its roots may be found in the (very few) existing mortar approaches for the bi-Laplacian that are herein extended to handle the fourth-order elliptic operator governing thin anisotropic laminates. For the computation of the structural matrices, exact symbolic integration is used rather than more classical Gauss–Lobatto quadrature schemes. Thanks to the underlying spectral approach, considerable CPU times savings are obtained compared with finite-element approaches when the optimal design of the laminates is pursued. A few numerical studies that are concerned with the analysis and the optimization of L-shaped single-layered plates are described in detail.     

Maximization of buckling loads of composite panels using flexural lamination parameters

Unstiffened composite panels are optimized by using flexural lamination parameters as continuous design variables for the case in which the amounts of 0°, ±45°, and 90° plies are given. It is shown that for this case, the lamination parameters are located in a hexagonal domain. Continuous optimization is compared with genetic optimization for the stacking sequence that accounts for the discreteness of the design space and constraints on the number of contiguous plies of the same orientation. It is shown that only for very thin panels with low aspect ratios is there a significant difference between the continuous and discrete solutions.     

Buckling analysis of laminated composite plates with an elliptical/circular cutout using FEM

In this study, a buckling analysis was carried out of a woven–glass–polyester laminated composite plate with an circular/elliptical hole, numerically. In the analysis, finite element method (FEM) was applied to perform parametric studies on various plates based on the shape and position of the elliptical hole. This study addressed the effects of an elliptical/circular cutout on the buckling load of square composite plates. The laminated composite plates were arranged as symmetric cross-ply [(0°/90°)₂]_s and angle-ply [(15°/−75°)₂]_s, [(30°/−60°)₂]_s, [(45°/−45°)₂]_s. The results show that buckling loads are decreased by increasing both c/a and b/a ratios. The increasing of hole positioned angle cause to decrease of buckling loads. Additionally, the cross-ply composite plate is stronger than all other analyzed angle-ply laminated plates.     

Optimization of the reinforcement of a 3D medium with thin composite plates

The reinforcement with a thin composite plate of a 3D linear elastic medium on its external boundary or inside is considered. A linear analysis of the 3D problem leads to a variational formulation in which the reinforcement is modelled by a Kirchhoff–Love plate. Considering the sum of the compliance and a cost as the design objective, a numerical example of the optimization of this reinforcement is performed taking into account the in-plane membrane rigidity only (i.e. the bending aspects are not treated numerically).     

In-plane and shear buckling analysis of FG-CNTRC annular sector plates based on the third-order shear deformation theory using a numerical approach

The buckling analysis of thick composite annular sector plates reinforced with functionally graded carbon-nanotubes (CNTs) is presented under in-plane and shear loadings based on the higher-order shear deformation theory. It is considered that the plate is resting on the Pasternak-type elastic foundation. The overall material properties of functionally graded carbon nanotube-reinforced composites (FG-CNTRCs) are estimated through the micromechanical model. The governing equations are derived on the basis of the higher-order shear deformation plate theory, and the quadratic form of the energy functional of the system is presented. An efficient numerical method is presented in the context of variational formulation to obtain the discretized version of stability equations. The validation of the present study is demonstrated through comparisons with the results available in the literature and then comprehensive numerical results are given to investigate the impacts of model parameters on the stability of CNT-reinforced composite annular sector plates.     

Computation of elastic buckling loads of rectangular thin plates using the extended Kantorovich method

In this paper, the extended Kantorovich method proposed by Kerr is further extended to the eigenvalue problem of elastic stability of various rectangular thin plates. By taking advantage of the availability and reliability of state-of-the-art ordinary differential equation solvers, multi-term trial functions have been employed, which is a significant extension to Kerr’s single term approach. As a result, the accuracy is greatly improved and some special problems that a single-term trial function fails to solve are now accommodated. A large number of numerical experiments have been carried out and the computed buckling loads are either exact or more accurate than the best known results in the literature.     

Optimal design of a high-speed slotless permanent magnet synchronous generator with soft magnetic composite stator yoke and rectifier load

This paper presents a specific design methodology of a DC generation system using a high-speed slotless generator with surface-mounted magnets and soft magnetic composite (SMC) stator yoke connected to a rectifier. The method is based on an analytical design model of the machine, an electrical model of the machine-rectifier system and a non-linear optimization procedure. The coupling between both models is achieved by a specific correction mechanism during the iterative process that performs an efficient convergence of the optimization procedure. The machine design model is derived from an analytical computation of the two-dimensional magnetic field distribution created by the magnets, the armature currents and the stator eddy currents that circulate in the SMC material. It has been cross-validated by 2D finite element analysis. The design approach is applied to the specifications of a 1.5 MW, 18,000 rpm slotless permanent magnet generator with a rated DC output voltage of 1500 V.