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.     

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.     

Optimal design of laminated composite beam structures

This work deals with design sensitivity analysis and optimal design of composite structures modelled as thin-walled beams. The structures are treated as a torsion-bending resistant beams. The analysis problem is discretized by a finite element technique. A two-node Hermitean beam element is used. The beam sections are made from an assembly of elements that correspond to flat layered laminated composite panels. Optimal design is performed with respect to the lamina orientations and thickness of the laminates. The structural weight is considered as the objective function. Constraints are imposed on stresses, displacements, critical load and natural frequencies. Two failure criteria are used to limit the structural strength: Tsai-Hill and maximum stress. The Tsai-Hill criterion is also adopted to predict the first-ply-failure loads. The design sensitivity analysis is analytically formulated and implemented. An adjoint variable method is used to derive the response sensitivities with respect to the design. A mathematical programming approach is used for the optimization process. Numerical examples are performed on three-dimensional structures.     

Optimal design of composite laminated plates with the discreteness in ply angles and uncertainty in material properties considered

An algorithm is developed for optimizing laminated plate stacking sequences and determining thicknesses, which incorporates discrete ply angles and considers the uncertainties of material properties in a two-step optimization process. The branch and bound method was modified to handle discrete variables; and convex modeling was used to allow the consideration of variable material properties. The numerical results obtained show that the optimal stacking sequences are determined with fewer evaluations of the objective function than might be expected from considerations of the size of the design space. Our results also show that the optimal thickness increases when elastic moduli uncertainties are considered, which indicates that such uncertainties should not be ignored at the design stage.     

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.     

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.     

Damping optimization of viscoelastic laminated sandwich composite structures

Recent developments on the optimization of passive damping for vibration reduction in sandwich structures are presented in this paper, showing the importance of appropriate finite element models associated with gradient based optimizers for computationally efficient damping maximization programs. A new finite element model for anisotropic laminated plate structures with viscoelastic core and laminated anisotropic face layers has been formulated, using a mixed layerwise approach. The complex modulus approach is used for the viscoelastic material behavior, and the dynamic problem is solved in the frequency domain. Constrained optimization is conducted for the maximization of modal loss factors, using gradient based optimization associated with the developed model, and single and multiobjective optimization based on genetic algorithms using an alternative ABAQUS finite element model. The model has been applied successfully and comparative optimal design applications in sandwich structures are presented and discussed.     

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.     

Minimum stress design of transversely isotropic sandwich plates based on higher-order theory

The minimum stress design of thick laminated sandwich plates is given based on a higher-order theory of plates which includes the effects of the normal and shear deformation. The surface layers are made of a transversely isotropic composite material and the results are given for isotropic and transversely isotropic core layers which can model a variety of materials including honcycomb. The theory is implemented using dedicated symbolic computation routines developed in the C programming language. The analysis is incorporated into an optimization algorithm to determine the optimal thicknesses of the surface layers for the minimum stress deisgn of three-layered sandwich plates. Numerical results are given for plates under sinusoidal loading and the effects of various input parameters are investigated. The stress behaviour which cannot be studied using a classical theory or a shear deformable theory only is indicated.     

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.     

Free vibration analysis of laminated composite plates based on FSDT using one-dimensional IRBFN method

This paper presents a new effective radial basis function (RBF) collocation technique for the free vibration analysis of laminated composite plates using the first order shear deformation theory (FSDT). The plates, which can be rectangular or non-rectangular, are simply discretised by means of Cartesian grids. Instead of using conventional differentiated RBF networks, one-dimensional integrated RBF networks (1D-IRBFN) are employed on grid lines to approximate the field variables. A number of examples concerning various thickness-to-span ratios, material properties and boundary conditions are considered. Results obtained are compared with the exact solutions and numerical results by other techniques in the literature to investigate the performance of the proposed method.     

Thermal stress analysis of laminated composite plates and shells

In this paper, Semiloof shell finite element formulation has been extended to thermal stress analysis of laminated plates and shells. The accuracy of the formulation has been verified using sample problems available in the literature. Thermal stresses in cross-ply and angle-ply laminated plates and shells subjected to thermal gradients across the thickness are presented for different boundary conditions, taking into account the temperature dependence of the material properties. The behaviour of laminates under thermal load is found to be different from that under mechanical loads in certain respects.     

复合材料悬臂外伸板的非线性动力学建模及数值研究

研究了横向气动载荷和参数激励联合作用下复合材料悬臂外伸矩形板在伸出过程中的非线性动力学问题.根据Reddy的高阶剪切层合板理论,应用Hamilton原理建立了外伸板在横向气动力和参数激励作用下的非线性动力学方程,其中横向气动力采用一阶活塞气动力.然后应用Galerkin方法对系统偏微分形式的非线性方程进行离散,得到了一组时变系数的非线性动力学方程.在此方程的基础上,对复合材料悬臂外伸板进行了数值模拟分析,讨论了外伸速度对悬臂外伸板非线性动力学特性的影响.     

Optimization of nonhomogeneous facesheets in composite sandwich plates

The optimal design of composite sandwich plates in which the facesheets are composed of a carbon fiber/epoxy net is considered. The objective of the work is to obtain minimum mass designs while maintaining constraints on the first natural frequency and selected facesheet stress components. The facesheets are assumed to be composed of an orthotropic net of unidirectional composite fiber strips and the optimal design (the least mass design) is achieved by changing the strip widths and the spacings between them. It is demonstrated that varying the spatial fiber strip distribution can lead to significant structural advantages; in the example presented, a 32% facesheet mass reduction is achieved.     

复合材料层合板非线性热振动分析

采用有限元方法研究复合材料层合板结构在线性温度场作用下非线性热振动特性．采用特征值屈曲分析方法,判断了结构在线性温度场作用下的临界屈曲分歧点,计算了结构的一阶弯曲固有频率,分析了铺层角度及铺层层数对结构临界屈曲温度分布和结构固有频率的影响,总结了其对复合材料层合板结构热振动特性影响的一般规律．这些结论对复合材料结构设计、抗热设计有一定的指导意义．     

Biaxial buckling and post-buckling of composite laminated plates on two-parameter elastic foundations

A post-buckling analysis is presented for a simply supported, composite laminated rectangular plate under biaxial compressive loading and resting on a two-parameter (Pasternak-type) elastic foundation. The analysis uses a perturbation technique to determine the interactive buckling loads and post-buckling equilibrium paths. The initial geometrical imperfection of the plates is taken into account. Numerical examples are presented that relate to the performances of perfect and imperfect, antisymmetrically angle-ply and symmetrically cross-ply laminated rectangular plates. Typical results are presented in dimensionless graphical form.     

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.     

Response of hybrid laminated composite plates under low-velocity impact

The response of hybrid laminated composite plates subjected to low velocity impact was investigated using shear deformation theory. As a result, the fractional energy loss of two hybrid composite plates with the same component ratio has different values according to the stacking sequence. A Graphite-Kevlar-Graphite plate has low energy loss and a Kevlar-Graphite-Kevlar plate much higher energy loss. Contact forces between the impactor and plates, center deflections of the plates and velocity changes of the impactor to time have different values according to the material properties of the impacted surface. Various composite plates with the same material in the impacted surface behaved with a similar response.     

Reliability based design with a degradation model of laminated composite structures

Uncertainties in deviations of physical properties lead to a probabilistic failure analysis of the composite materials. The proposed optimization model for laminate composites is based on reliability analysis considering the ultimate failure state. To avoid difficulties associated with the complete analysis of the failure modes, bounds are established for the failure probability of the structural system. These bounds are related with theintact and degraded configurations of the structure. Using thefirst ply failure and thelast ply failure theories and a degradation model for the mechanical properties with load sharing rules we obtain the failure probabilities corresponding to the two above configurations. The failure probability of each configuration is obtained using level 2 reliability analysis and the Lind-Hasofer method.The optimization algorithm is developed based on the problem decomposition into three subproblems having as objectives the maximization of the structural efficiency atintact and degraded configurations of the structure and weight minimization subjected to allowable values for the structural reliability. Additionally, the search for the initial design is performed introducing a weight minimization level. It is expected to explore the remaining load capacity of the structures afterfirst ply failure as a function of the anisotropic properties of the composites. The design variables are the ply angles and the thicknesses of the laminates. The structural analysis for the model developed is performed through the finite element method mainly using the isoparametric degenerated shell finite element. The sensitivities are obtained using the discrete approach through the adjoint variable method. In order to show the performance of the analysis two examples are presented.     

From periodic to chaotic oscillations in composite laminated plates

The geometrically non-linear, linear elastic, oscillations of composite laminated plates are studied in the time domain by direct numeric integration of the equations of motion. A p-version finite element, where first-order shear deformation is followed and that was recently proposed for moderately thick plates, is employed to define the mathematical model. By applying transverse harmonic forces, the variation of the oscillations with the angle of the fibres is investigated. With this kind of excitation, only periodic motions with a period equal to the one of the excitation are found. However, introducing in-plane forces, m-periodic or quasi-periodic oscillations, as well as chaotic oscillations are computed. The existence of chaos is confirmed by calculating the largest Lyapunov exponent.