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.     

嵌入多层黏弹性胶膜复合材料阻尼工字梁的多目标设计优化

针对嵌入多层黏弹性胶膜的复合材料阻尼工字梁,传统的混合单元法在进行结构动态分析与设计优化时存在很大困难的问题,采用基于离散层理论的多层梁单元建模分析复合材料阻尼工字梁.通过对正交各向异性铺层和腹板进行等效处理的方法,对工字梁凸缘嵌入单层阻尼层模型进行参数化分析;分别对嵌入多层或单层阻尼层的模型建立多目标优化模型,优化目标为模态损耗因子和固有频率最大化,设计变量为阻尼层层数（厚度）及其嵌入位置;应用多目标遗传算法进行优化求解.结果表明：基于离散层理论的阻尼梁单元计算精度好且易于优化,对于嵌入单层较厚阻尼和嵌入多层较薄阻尼的复合材料工字梁,获得的阻尼效果与动刚度损失基本相当,但对于高阻尼的方案,前者比后者的动刚度损失更大.     

A discrete layer beam finite element for the dynamic analysis of composite sandwich beams with integral damping layers

A discrete layer finite element is presented for the dynamic analysis of laminated beams. The element uses C⁰ continuous linear and quadratic polynominals to interpolate the in-plane and transverse displacement field, respectively, and is free from the effects of shear locking. Modal frequencies and damping are estimated using both the modal strain energy method and the complex modulus method. A forced response version of the model is also presented. The model predictions are compared with experimental data for composite sandwich beams with integral damping layers. Four damping configurations are considered, a constrained layer treatment, a segmented constrained layer treatment and two internal treatments.     

Optimal design of sandwich and laminated composite plates based on the planning of experiments

Optimal design problems of sandwich plates with soft core and laminated composite face layers, and multilayered composite plates are investigated. The optimal design problems are solved by using the method of the planning of experiments. The optimization procedure is divided into the following stages: choice of control parameters and establishment of the domain of search, elaboration of plans of experiment for the chosen number of reference points, execution of the experiment, determination of simple mathematical models from the experimental data, design of the structure on the basis of the mathematical models discovered, and finally verification experiments at the point of the optimal solution. Vibration and damping analysis is performed by using a sandwich plate finite elements based on a broken line model. Damping properties of the core and face layers of the plate are taken into account in the optimal design. Modal loss factors are computed using the method of complex eigenvalues or the energy method. Frequencies and modal loss factors of the plate are constraints in the optimal design problem. There are also constraints on geometrical parameters and the bending stiffness of the plate. The mass of the plate is the objective function. Design parameters are the thickness of the plate layers. In the points of experiments computer simulation using FEM is carried out. Using this information, simple mathematical models for frequencies and modal loss factors for the plate are determined. These simple mathematical functions are used as constraints in the nonlinear programming problem, which is solved by random search and the penalty function method. Numerical examples of the optimal design of clamped sandwich and simply supported laminated composite plates are presented. A significant improvement of damping properties of a sandwich plate is observed in comparison with a simple plate of equal natural frequencies.     

Damping of beams. Optimal distribution of cuts in the viscoelastic constrained layer

To damp the flexural vibrations of homogeneous beams or plates in a large frequency range, one of the most efficient methods is the use of constrained viscoelastic layers. Since most of the damping ability is due to shearing stresses in the viscoelastic layer, it is interesting to determine the most appropriate distribution of the shear in the layers. This paper presents the influence of a new parameter involved in this repartition, i.e. the distribution of cuts in the elastic constraining layer. It will be demonstrated that modal damping may be significantly modified in this way. The number and the locations of the cuts may vary and are determined to optimize the damping. The vibrating beam modal analysis is performed by a finite element analysis using special finite elements which have variable d.o.f. in order to take into account the lack of continuity of the viscoelastic constrained displacement field. Using a genetic algorithm, an optimal distribution of the cuts has been determined for a maximum damping of one or serval flexural modes.     

Vibration and damping analysis of composite plates using finite elements with layerwise in-plane displacements

Finite element analysis is performed to study the effects of layerwise in-plane displacements on fundamental frequencies and specific damping capacity for composite laminated plates. The cross-ply and angle-ply composite laminated plates with simply-supported boundary conditions are considered. The strain energies of each stress component are computed to quantify the amount of the transverse shear deformations for thin and thick plates. The results show that the length-to-thickness ratios, cross-ply ratios, and fiber orientations have a great influence on the in-plane displacement responses. It is also shown that the layerwise in-plane displacements should be taken into account for the dynamic analysis of thick composite plate.     

复合材料层合板低频声辐射优化

为使复合材料层合板低频声辐射性能最优,根据无限域声场的特点,介绍将有限元与无限元耦合进行声辐射性能分析的理论和方法,采用2个算例验证该方法的有效性.将有限元软件Abaqus与数值优化软件Isight相结合完成复合材料铺层角的优化,并提出逐层优化的思路.以含有8层单层板和1层阻尼芯层的复合材料层合板为研究对象,以铺层角为设计变量,采用逐层优化方法(layer-wise optimization method,LOM)优化层合板的声学性能,并分析阻尼芯层对层合板声辐射的影响.结果表明:合理的铺层角可以提高复合材料层合板的1阶固有频率,达到减少声辐射谱峰数量和降低辐射声功率的效果;增加阻尼芯层可以抑制声辐射谱峰,有利于提高层合板的低频声辐射性能.     

Three-dimensional finite-element analysis of laminated composites

A three-dimensional finite-element analysis treating the mechanical response of thick laminated composite plates in bending is presented. An isoparametric solid element with a cubic displacement expansion in planform and a linear variation through the thickness is used to model each layer of the laminate. The degrees-of-freedom of the element are retained at its boundaries so that interconnections between lamina with different fiber orientations can be made at their interfaces. An incore version of the conjugate gradient technique, which does not have bandwidth restrictions, is used to minimize the total potential energy of the system with the number of iterations to convergence being about one-fifth the total global degrees-of-freedom. Because a three-dimensional analysis is used, the effects of thickness-stretching, transverse shear, extension, and bending deformations are obtained. Comparisons with three-dimensional elasticity solutions are in excellent agreement and show the necessity of having individual elements for each layer when they have different fiber orientations and when the plates are thick.     

The genetic algorithm applied to stiffness maximization of laminated plates: review and comparison

The design of laminated structures is highly tailorable owing to the large number of available design variables, thereby requiring an optimization method for effective design. Furthermore, in practice, the design problem translates to a discrete global optimization problem which requires a robust optimization method such as the genetic algorithm. In this paper, the genetic algorithm, based on the real variable coding, is applied to the strain energy minimization of rectangular laminated composite plates. The results for both a point load and uniformly distributed load compare well with those achieved using trajectory methods for continuous global optimization.     

Maximization of buckling load of laminated composite plates with central circular holes using MFD method

This paper addresses optimal design of simply supported symmetrically laminated composite plates with central circular holes. The design objective is the maximization of the buckling load, and the design variable is considered as the fiber orientation. The first-order shear deformation theory is used for the finite element analysis. The study is complicated because the effects of bending–twisting coupling are also included for the buckling optimization. The modified feasible direction method is used to solve the optimization problems. Finally, the effect of different number of layers, boundary conditions, width-to-thickness ratio, plate aspect ratios, hole daimeter-to-width ratio, and load ratios on the results is investigated.     

Optimum design of composite laminates for minimum thickness

In this study, an optimization procedure is proposed to minimize thickness (or weight) of laminated composite plates subject to in-plane loading. Fiber orientation angles and layer thickness are chosen as design variables. Direct search simulated annealing (DSA), which is a reliable global search algorithm, is used to search the optimal design. Static failure criteria are used to determine whether load bearing capacity is exceeded for a configuration generated during the optimization process. In order to avoid spurious optimal designs, both the Tsai–Wu and the maximum stress criteria are employed to check static failure. Numerical results are obtained and presented for different loading cases.     

A numerical-experimental method for damage location based on rotation fields spatial differentiation

This paper presents a structural damage location method that decreases the number of spatial differentiations needed to compute modal curvature fields. The method is numerically and experimentally applied to isotropic and laminated rectangular plates, respectively. A speckle shear interferometer is used to measure the rotation fields of the laminated plate, while the isotropic plate is analysed by finite elements. It was found that the Gaussian differentiation is the most suited technique to compute the curvature fields. It is also demonstrated the superior performance of the curvature method using measured rotation fields instead of measured displacement fields.     

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.     

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.     

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.     

Application of the spline finite strip to the analysis of shear-deformable plates

A spline finite strip is proposed to analyse thick isotropic or laminated composite plates. The formulation is based upon the principle of virtual work and the third-order plate theory developed by Reddy. The variational functional requires the satisfaction of C₁,-continuity of the assumed vertical deflection variable which can be easily fulfilled by the present method. The proposed spline finite strip is a conforming element with a smaller number of unknowns at each node compared to other existing elements based on the third-order theory. For the analysis of thin isotropic or laminated plates, the present element shows no sign of shear locking. A number of computational examples are given to demonstrate the efficiency and the accuracy of the present method.     

基于等效模态阻尼的复合隔振系统振动计算方法

基于线性黏弹性假设,将应变能阻尼理论推广到复合隔振系统的等效模态阻尼计算中,运用Python和Abaqus编制相应的计算程序,该程序可考虑材料阻尼的频变特性。以多种材料组成的船舶双层复合隔振系统为算例,计算其等效模态阻尼和隔振器等效阻尼系数。分别采用直接积分法和模态叠加法计算系统振动响应,对比设备、筏架、船底壳的振动加速度响应,验证基于等效模态阻尼的模态叠加法的准确性。结果表明,该方法可以准确计算复杂组合模型的模态阻尼,算例的振动响应计算结果一致性较好,用模态叠加法可以大幅提高复合隔振系统稳态振动响应的计算效率。     

考虑强度和疲劳寿命影响的层合复合材料结构优化分析

工程应用中对复合材料轻量化的要求在不断提高,为了能够在满足工程应用对材料强度和疲劳寿命要求的同时,达到减轻结构质量的目的,研究了强度和疲劳寿命影响下的复合材料层合结构优化方法,并在此基础上提出了一种基于参数化有限元技术和改进遗传算法的复合材料层合结构优化方法。根据复合材料层合结构铺层参数属于离散型变量的特点,将遗传算法编码改为联合整数编码,并且为了能快速准确求出最优解,提出了精英保留策略、交叉和变异自适应度策略。最后,基于Visual Studio和ANSYS进行联合仿真,对所提出的方法进行验证,仿真结果表明,优化后的复合材料层合结构不仅能够满足强度和疲劳寿命的约束条件,并且其质量减少到初始质量的56.2%,优化效果明显,这表明所提出的基于参数化有限元技术和改进遗传算法的复合材料层合结构优化方法是可行的。     

A finite element formulation for composite laminates with smart constrained layer damping

A composite laminate with active constrained-layer damping treatment is studied. The interface element for viscoelastic damping layers has been developed based on the relative displacements between composite plates and piezoelectric constraining layers. As an example, the problem of forced oscillations of the laminated composite structure with a smart constrained damping treatment is solved and the vibration response of the composite plate with smart damping layers is calculated using the presently developed procedure.