Natural modes of vibration of variable stiffness composite laminates with curvilinear fibers

In this paper, natural frequencies and vibrational mode shapes of variable stiffness composite laminate (VSCL) plates with curvilinear fibers are studied. In each ply of this rectangular VSCL, the fiber-orientation angle changes linearly with respect to the horizontal coordinate. To define the modes of vibration of the laminates, a new p-version finite element, which follows third-order shear deformation theory (TSDT), is employed. The convergence properties of this new element are investigated. Taking manufacturing restrictions regarding the fiber curvatures into account, maps of natural frequencies as functions of tow-orientation angles are determined in demonstrative examples. It is verified that the use of curvilinear fibers instead of the traditional straight fibers introduces a greater degree of flexibility, which can be used to adjust frequencies and mode shapes.     

Vibration design of laminated fibrous composite plates with local anisotropy induced by short fibers and curvilinear fibers

The present paper studies an optimum design method for proposing new types of fiber reinforced composite plates with locally anisotropic structure. A finite element program is developed to analyze vibration of such locally anisotropic plates, and the fundamental frequency is taken as an object function to be maximized. First, for demonstrating the effectiveness of local anisotropy, the optimum distributions of short fibers are calculated without directional constraints using a simple genetic algorithm (GA), and the layerwise optimization (LO) concept is used to reduce the computation time in the finite element calculation. Secondly, optimum arrangements of continuous curvilinear fibers are obtained under the continuity constraints where fiber directions are considered as projections of contour lines of a cubic polynomial surface. Numerical results show that the local anisotropy successfully improves frequency property and the optimum directions of short fibers indicate physically reasonable orientations. Also, the plates with optimally shaped continuous fibers yield higher fundamental frequencies than the conventional plates with parallel fibers.     

Multi-physics design and optimization of flexible matrix composite driveshafts

Flexible matrix composites (FMCs) consist of low modulus elastomers such as polyurethanes which are reinforced with high-stiffness continuous fibers such as carbon. This fiber–resin system is more compliant compared to typical rigid matrix composites and hence allows for higher design flexibility. Continuous, single-piece FMC driveshafts can be used for helicopter applications. In the present investigation, an optimization tool using a genetic algorithm approach is developed to determine the best combination of stacking sequence, number of plies and number of in-span bearings for a minimum-weight, spinning, misaligned FMC helicopter driveshaft. In order to gain more insight into designing driveshafts, various loading scenarios are analyzed and the effect of misalignment of the shaft is investigated. This is the first time that a self-heating analysis of a driveshaft with frequency- and temperature-dependent material properties is incorporated within a design optimization model.     

Reliability of fiber-reinforced composite laminate plates

Many engineering structures ranging from aircrafts, spacecrafts and submarines to civil structures, automobiles, trucks and rail vehicles, require less weight and more stiff and strong materials. As a result of these requirements, the use of composite materials has increased during the past decades. In fact during the past five years, we have witnessed exponential growth in research and field demonstrations of fiber-reinforced composites in civil engineering. Manufacturers and designers have now access to a wide range of composite materials. However, they face great problems with forecasting the reliability of composites materials. Due to the differences among the properties of materials used for composites, manufacturing processes, load combinations, and types of environment, the prediction of reliability of composites is a very complex task. In this study, the reliability of fiber-reinforced composite laminate plates under random loads is investigated. The background of the problem is defined, the failure criterion chosen is presented, and the probability of failure is computed by Monte Carlo simulation.     

Optimum stacking sequence design of composite materials Part II: Variable stiffness design

A composite laminate may be designed as a permutation of several straight-fiber layers or as a matrix embracing fibers positioned in curvilinear paths. The former called a constant stiffness design and the latter known as variable stiffness design. The optimization algorithms used in constant stiffness design were studied in Part I of this review article. This paper completes the previous article by focusing on variable stiffness design of composite laminates. Different parameterization and optimization algorithms are briefly explained and compared and the advantages and shortcomings of each algorithm are discussed.     

Optimal curved fibre orientations of a composite panel with cutout for improved buckling load using the Efficient Global Optimization algorithm

Composite structures with cutouts (like panels with holes) are a challenge to design because discontinuities of this kind provoke stress concentrations and become critical regions. With curved fibres, the effect of these discontinuities can be decreased by choosing the fibre paths properly. In this article, fibre-path optimization to improve the buckling load of laminated composite panels with cutouts is studied. Two fibre path parameterizations are tested: the usual curvilinear Cartesian and the radial one, proposed in this article, in which the fibre orientations vary linearly with the Euclidean distance from the centre of the panel. To reduce the simulation costs associated with the optimization, the Efficient Global Optimization (EGO) algorithm is used. EGO is a technique based on a stochastic process approach (Kriging) that approximates expensive-to-evaluate functions and sequentially maximizes the expected improvement to update the surrogate at each iteration. A stiffened panel with a cutout subjected to compression and in-plane shearing loads is analysed. The results show that the buckling load when curved fibres are used is substantially higher than the buckling load for straight-fibre laminates. In addition, the optimization framework indicates a low final computational burden.     

A multi-objective optimization approach for design of blast-resistant composite laminates using carbon nanotubes

A reliable process for the design of blast-resistance composite laminates is needed. We consider here the use of carbon nanotubes (CNTs) to enhance the mechanical properties of composite interface layers. The use of CNTs not only enhances the strength of the interface but also significantly alters stress propagation in composite laminates. A simplified wave propagation simulation is developed and the optimal CNT content in the interface layer is determined using multi-objective optimization paradigms. The optimization process targets minimizing the ratio of the stress developed in the layers to the strength of that layer for all the composite laminate layers. Two optimization methods are employed to identify the optimal CNT content. A case study demonstrating the design of five-layer composite laminate subjected to a blast event is used to demonstrate the concept. It is shown that the addition of 2% and 4% CNTs by weight to the epoxy interfaces results in significant enhancement of the composite ability to resist blast.     

New ductile laminate structure of Ti-alloy/Ti-based metallic glass composite with high specific strength

Bulk laminate structure of Ti-alloy/Ti-based metallic glass composite(MGC) was prepared by melting a preform of alternate stack-up foils in the high vacuum atmosphere. The composite demonstrates a good combination of yield strength(~1618 MPa), plasticity(~4.3%) and specific fracture strength(384 × 10~3 Nmkg~(-1)) in compression. The maintained yield strength results from the unique microstructure composed of the Ti layer, the solution layer with gradient structure and the MGC layer. Such a multilayer structure effectively inhibits the propagation of shear band, leading to the enhanced plasticity. Those extraordinary properities suggest that combining ductile lamella with brittle metallic glass(MG) by such a lay-up method can be an effective way to improve mechanical properties of MG.     

Imaging microstructure and stress fields within a cross-ply composite laminate

Microfocus X-ray diffraction can be used in a scanning acquisition mode to image a fibre reinforced composite material in terms of a range of different parameters. This includes microstructural information, as well as detail of emerging stress fields around open hole geometries. In this study, the in situ deformation of a cross-ply laminate specimen is investigated. The results show a number of interesting phenomena related to stress transfer in such systems. This includes stress concentrations in fibres adjacent to the open hole and local shear forces acting upon fibres perpendicular to the deformation axis. In addition to imaging the sample, the technique also allows a number of mechanical parameters to be estimated. This includes transverse strain and longitudinal stiffness. Using isotropic elasticity theory, the stress concentration tangential to the open hole can be determined analytically.     

Effects of boundary conditions on buckling and postbuckling responses of composite laminate with various shaped cutouts

The objective of the present work is to study the effects of flexural boundary conditions on buckling and postbuckling behavior of axially compressed quasi-isotropic laminate, (+45/−45/0/90)_2s with various shaped cutouts (i.e., circular, square, diamond, elliptical–vertical and elliptical–horizontal) of various sizes using the finite element method. The FEM formulation is based on first order shear deformation theory and von Karman’s assumptions are used to incorporate geometric nonlinearity. The 3-D Tsai-Hill criterion is used to predict the failure of a lamina while the onset of delamination is predicted by the interlaminar failure criterion. It is observed that the laminates clamped and simply supported on all edges have the highest and lowest buckling and postbuckling strength, respectively, irrespective of cutouts shape and size. It is also noted that a fully clamped laminate with large size elliptical–vertical cutout can take higher compressive buckling load than the laminate without cutout for same boundary condition.     

Design of multifunctional structure with embedded electronic circuitry using composite laminate optimization techniques

This research investigates the optimization of a multifunctional structure with embedded electronic circuitry, following traditional composite laminate optimization methods. A heavily ‘de-featured’ finite element model provides thermal and mechanical analyses of the structure. The model places point heat sources at the surface component locations, and the optimization problem enforces strain constraints at these locations. A simple problem seeks the least-mass I-beam whose shear web contains a simple circuit, subject to strength and strain constraints. A second problem finds the lowest mass unmanned aerial vehicle (UAV) wing box configuration containing embedded circuitry subject to strength, deflection and strain constraints under two load cases. Sequential unconstrained minimization techniques and sequential quadratic programming perform the optimization; combinatorial methods are computationally impractical. Despite the model de-featuring and the use of calculus-based methods, the problem requires significant computational effort. The surface-component strain constraints result in structures with more mass than those without surface components.     

A [90/0]s composite laminate with part-through matrix cracks in adjacent plies

A [90/0]_s orthotropic composite laminate with part-through matrix cracks is considered. Stress intensity factors are determined for the cracks using a linear-elastic analysis. These matrix cracks run along the fiber direction of the individual plies. The crack-geometry considered here is one where the matrix cracks in adjacent plies form a cross-like pattern in the plan view of the laminate. The plies are assumed bonded by thin resin-rich adhesive layers. These adhesive layers are modeled as distributed shear springs. Each ply of the laminate is modeled as a thin elastic orthotropic layer under plane stress. The laminate is subject to both tensile and shear loading. The mathematical model for the stresses and displacements in the layers reduces to a pair of Fredholm integral equations which are solved numerically. The stress intensity factors show a strong dependence on crack-sizes and nature of loading. In particular, the magnitudes of the stress intensity factors for the matrix crack in the 0° layer are increased significantly by the crack in the adjacent 90° layer.     

Explicit solutions of magnetoelastic fields in a soft ferromagnetic solid with curvilinear cracks

The problem of curvilinear cracks lying on a soft ferromagnetic solid subjected to a remote uniform magnetic induction is considered. With the complex variable technique, the general solutions of both the magnetic field quantities and the magnetoelastic stresses can be obtained. In order to illustrate the effect of magnetic induction, the solutions for the problem with one arc crack and two arc cracks are presented in a closed form. The stress intensity factors in the vicinity of crack tip and the crack opening condition are also derived. Considering the magnetic stress induced by an oblique magnetic field on the crack surface, one can find that the stress intensity factors of mode-I and mode-II are related to the incident angle of magnetic induction, the crack half angle and the magnetic susceptibility as displayed with figures. It is noticed that the present work is available even for a ferromagnetic material with low susceptibility. For the limiting case of the crack half angle in the one arc crack problem approaching to zero, the stress intensity factors are also provided and analytically compared with the existing ones of the straight crack problem.     

Optimum stacking sequence design of laminated composite circular plates with curvilinear fibres by a layer-wise optimization method

The optimum stacking sequence design for the maximum fundamental frequency of symmetrically laminated composite circular plates with curvilinear fibres is investigated for the first time using a layer-wise optimization method. The design variables are two fibre orientation angles per layer. The fibre paths are constructed using the method of shifted paths. The first-order shear deformation plate theory and a curved square p-element are used to calculate the objective function. The blending function method is used to model accurately the geometry of the circular plate. The equations of motion are derived using Lagrange’s method. The numerical results are validated by means of a convergence test and comparison with published values for symmetrically laminated composite circular plates with rectilinear fibres. The material parameters, boundary conditions, number of layers and thickness are shown to influence the optimum solutions to different extents. The results should serve as a benchmark for optimum stacking sequences of symmetrically laminated composite circular plates with curvilinear fibres.     

Particle swarm optimization approach for multi-objective composite box-beam design

This paper presents a multi-agent search technique to design an optimal composite box-beam helicopter rotor blade. The search technique is called particle swarm optimization (‘inspired by the choreography of a bird flock’). The continuous geometry parameters (cross-sectional dimensions) and discrete ply angles of the box-beams are considered as design variables. The objective of the design problem is to achieve (a) specified stiffness value and (b) maximum elastic coupling. The presence of maximum elastic coupling in the composite box-beam increases the aero-elastic stability of the helicopter rotor blade. The multi-objective design problem is formulated as a combinatorial optimization problem and solved collectively using particle swarm optimization technique. The optimal geometry and ply angles are obtained for a composite box-beam design with ply angle discretizations of 10°, 15° and 45°. The performance and computational efficiency of the proposed particle swarm optimization approach is compared with various genetic algorithm based design approaches. The simulation results clearly show that the particle swarm optimization algorithm provides better solutions in terms of performance and computational time than the genetic algorithm based approaches.     

Multi-objective design optimization of variable stiffness composite cylinders

The bending-induced buckling improvement in a variable stiffness (VS) composite cylinder (made by fiber steering) is studied. For such a cylinder, the effect of the variation of the direction of the load on its buckling performance of the cylinder is also examined. Compromise programming, as a multi-objective optimization method, is used to design for buckling of the VS cylinder subjected to bending load in either of the two opposite directions. Different combinations of weight factors for the structural performance in the two opposite directions were also applied to obtain the Pareto frontier as the main decision making tool for the designers in a multi-objective design problem.     

含纤维波纹缺陷复合材料层合板的损伤分析

纤维波纹是复合材料层合板制备过程中的一种常见缺陷,会导致其刚度和强度显著下降,有效地预测含波纹缺陷复合材料层合板的失效强度具有显著的意义。基于此,本文采用解析的方式分别构造了纤维波纹呈正弦起伏与余弦起伏状的复合材料层合板模型。利用该模型,以Tsai-Wu准则作为失效判据,研究了一种含纤维波纹的碳纤维/环氧树脂复合材料层合板在受压情况下的损伤演化过程,得到了碳纤维/环氧树脂复合材料层合板的初始损伤强度。与有限元方法计算得到的损伤位置和损伤强度非常吻合,验证了本文算法的正确性。另外,相比于有限元方法,本文所述计算方法具有模型构造简单、计算效率高等优点,便于快速分析和确定含纤维波纹缺陷复合材料层合板的损伤位置与损伤强度。      

Higher-order theories for the free vibrations of doubly-curved laminated panels with curvilinear reinforcing fibers by means of a local version of the GDQ method

The aim of this paper is to investigate the dynamic behavior of singly and doubly-curved panels reinforced by curvilinear fibers. The Variable Angle Tow (VAT) technology allows the placement of fibers along curvilinear paths with the purpose of improving dynamic performance of plates and shells. The effect of the variation of constants which define analytically the fiber orientation is also investigated by several parametric studies. The Carrera Unified Formulation (CUF) with different thickness functions along the three orthogonal curvilinear directions is the basis of the present theoretical model. Various doubly-curved laminated panels reinforced by curvilinear fibers are analyzed using several structural theories. The Local Generalized Differential Quadrature (LGDQ) method is employed to solve numerically free vibration problems. Compared to the well-known GDQ method from which it descends, the LGDQ is characterized by banded matrices instead of full ones, since the current technique considers only few points of the whole domain. Therefore, the solution of the equation system needs a lower computational effort.     

A scatter search algorithm for stacking sequence optimisation of laminate composites

This paper explores the metaheuristic approach called scatter search for lay-up sequence optimisation of laminate composite panels. Scatter search is an evolutionary method that has recently been found to be promising for solving combinatorial optimisation problems. The scatter search framework is flexible and allows the development of alternative implementations with varying degree of sophistication. The main objective of this paper is to demonstrate the effectiveness of the proposed scatter search algorithm for the combinatorial problem like stacking sequence optimisation of laminate composite panels. Preliminary investigations have been carried out to compare the optimal stacking sequences obtained using scatter search algorithm for buckling load maximisation with the best known published results. Studies indicate that the optimal buckling load factors obtained using the proposed scatter search algorithm found to be either superior or comparable to the best known published results.

Later, two case studies have been considered in this paper. Thermal buckling optimisation of laminated composite plates subjected to temperature rise is considered as the first case study. The results obtained are compared with an exact enumerative study conducted on the problem to demonstrate the effectiveness and performance of the proposed scatter search algorithm. The second case study is optimisation of hybrid laminate composite panels for weight and cost with frequency and buckling constraints. The two objectives are considered individually and also collectively to solve as multi-objective optimisation problem. Finally the computational efficiency of the proposed scatter search algorithm has been investigated by comparing the results with various implementations of genetic algorithm customised for laminate composites. It was shown in this paper through numerical experiments that the scatter search is capable of finding practical solutions for optimal lay-up sequence optimisation of composite laminates and results are comparable and sometimes even superior to genetic algorithms.     

Parameter identification of autonomous vehicles using multi-objective optimization

In order to properly operate an autonomous vehicle navigation system, it is important that the vehicle and sensor models of the vehicle are defined by an accurate parameter set. This paper presents a technique for identifying parameters of an autonomous vehicle using multi-objective optimization, which enables the identification process without introducing additional parameters. A multi-objective optimization method has been further proposed to solve the optimization problem defined for the identification efficiently and promisingly. Results of numerical examples first show that the proposed optimization method can work well for various multi-objective optimization problems. Then, the proposed identification technique has been applied to the actual parameter identification of the autonomous vehicle developed by the authors, and an appropriate parameter set has been obtained.