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.     

新一代火箭卫星整流罩的模态特性分析、试验与模型修正

针对全透波段非金属夹层结构的新一代运载火箭卫星整流罩,建立有限元模型,计算了半罩在不同边界条件下的模态特性.地面模态试验中,采用垂直悬挂和置于海绵垫上多种方式模拟自由边界条件,基于频响函数和特征值、特征向量辨识半罩模态,基于试验结果采用模型缩聚迭代算法对仿真计算模型进行模型修正,得到高精度的可供全箭动力学分析和整流罩分离分析使用的有限元模型.     

非线性动态突变系统的多模型自适应执行器故障补偿设计

本文针对因多重不确定执行器故障而引起系统动态突变的非线性系统,设计了一种基于多模型切换的自适应执行器故障补偿控制策略,以提高系统应对动态突变的能力,同时实现不确定执行器故障的快速精确补偿.针对执行器故障模式的不确定性问题,采用基于多模型的参数估计方法,设计了自适应控制器组;基于最优性能指标函数,提出了一种控制切换机制,...     

Use of a rate-dependent continuum damage model to describe strain-softening in laminated composites

A continuum damage model developed to describe the rate-dependent dynamic response of laminated polymer composites is investigated for its behavior during strain-softening. The formulation is shown to lead to mathematically well-posed wave propagation problems as well as to unique and stable solutions. Numerical simulations of unidimensional wave-propagation in the through-thickness direction of a transversely isotropic laminate are performed. For a realistic range of damage propagation time constants the results are shown to be mesh insensitive and convergence to a finite amount of dissipated energy is obtained; two issues of concern in modeling dynamically strain-softening solids. Thus the model is validated with respect to strain-softening regimes.     

A class of C finite elements for the static and dynamic analysis of laminated plates

A general higher-order deformation theory is developed to analyse the behaviour of an arbitrary laminated fibre-reinforced composite plate. Three-dimensional effects such as the warping of sections and the presence of interlaminar stress field components are taken into account assuming a power series expansion of displacements along the thickness. A class of C⁰ finite element models based on this theory is then developed for mono- and bi-dimensional elements. Applications of the models to bending and vibration of laminated plates are then discussed. The present solutions are compared with those obtained using the three-dimensional elasticity theory, classical laminate theory and other higher-order theories.     

Nonlinear transient responses of initially stressed composite plates

The nonlinear transient response of initially stressed composite plates is investigated using the finite element method. A nine-node isoparametric quadrilateral element is developed to model laminated plates under initial deformation and initial stress according to the Mindlin plate theory and von Karman large deflection assumptions. In the time integration, the Newmark constant acceleration method in conjunction with an efficient and accurate iteration scheme is used. Numerical results for deflections and bending moments for isotropic and laminated plates are obtained.     

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.     

Coupling of a nonlinear finite element structural method with a Navier-Stokes solver

A new three-dimensional viscous aeroelastic solver is developed in the present work. A well validated full Navier-Stokes code is coupled with a nonlinear finite element plate model. Implicit coupling between the computational fluid dynamics and structural solvers is achieved using a subiteration approach. Computations of several benchmark static and dynamic plate problems are used to validate the finite element portion of the code. This coupled aeroelastic scheme is then applied to the problem of three-dimensional panel flutter. Inviscid and viscous supersonic results match previous computations using the same aerodynamic method coupled with a finite difference structural solver. For the case of subsonic flow, multiple solutions consisting of static, upward and downward deflections of the panel are discussed. The particular solution obtained is shown to be sensitive to the cavity pressure specified underneath the panel.     

Distributed finite‐time tracking of multiple Euler–Lagrange systems without velocity measurements

This paper investigates the distributed finite‐time tracking problem of networked agents with multiple Euler–Lagrange dynamics. To achieve finite‐time tracking, a distributed finite‐time protocol is first proposed on the basis of both relative position and relative velocity measurements. By using tools from homogeneous theory, it is theoretically shown that the proposed protocol can guarantee finite‐time tracking in the presence of control input constraints. On the basis of the state feedback analysis and with the aid of second‐order sliding‐mode observer approach, a new class of finite‐time tracking protocols based only on the relative position measurements is developed and employed. It is proved that the multiple agents equipped with the designed protocols can track the target location in finite time. Furthermore, a decentralized finite‐time protocol based on a distributed estimator is proposed to solve the finite‐time tracking problems with a dynamic leader. The effectiveness of the theoretical results is finally illustrated by numerical simulations. Copyright © 2014 John Wiley & Sons, Ltd.     

A three-dimensional hybrid stress isoparametric element for the analysis of laminated composite plates

In view of the increasing interest in using composite materials for aerospace structures, the analysis of laminated composite plates becomes essential. A three-dimensional eight-node hybrid stress finite element method is developed for the analysis of laminated plates. The hybrid stress model is based on the modified complementary energy principle and takes into account the transverse shear deformation effects. The displacement field is interpolated through shape functions and nodal displacements. All three displacement components are assumed to vary linearly through the thickness of each lamina. The stress field is interpolated through assumed stress polynomials with 55 stress parameters for each lamina. All six stresses are included and satisfy the homogeneous equilibrium equations. The validity of the hybrid stress finite element model is determined by comparing the predicted numerical results with the existing three-dimensional elasticity solutions. Excellent accuracy and fast convergence are observed in the numerical results.     

Dynamic finite element analysis of laminated beams with delamination cracks using contact-impact conditions

A new finite element modeling technique is presented to investigate the static and dynamic behavior of laminated composite beams with partial delamination. In this study, a recently developed rectangular beam element is used. The element has lateral and axial displacements as degrees of freedom, but not rotation. For simplicity, linear shape functions are used for the beam element. As a result, the element has six degrees of freedom, four of which are the axial nodal displacements at the corner points and the other two are the lateral displacments at the ends. In addition, contact-impact conditions are applied to the finite element modeling to avoid overlapping of the upper and lower portions of a delaminated section. The numerical study shows that, depending on existence of an embedded delamination crack and its size, the response is different for a beam with a crack and subjected to a short impulse load. Hence, the present modeling technique may be used for detection of an embedded delamination crack.     

Design of laminated composite plates for optimal dynamic characteristics using a constrained global optimization technique

The lamination arrangements of moderately thick laminated composite plates for optimal dynamic characteristics are studied via a constrained multi-start global optimization technique. In the optimization process, the dynamical analysis of laminated composite plates is accomplished by utilizing a shear deformable laminated composite finite element, in which the exact expressions for determining shear correction factors were adopted and the modal damping model constructed based on an energy concept. The optimal layups of laminated composite plates with maximum fundamental frequency or modal damping are then designed by maximizing the frequency or modal damping capacity of the plate via the multi-start global optimization technique. The effects of length-to-thickness ratio, aspect ratio and number of layer groups upon the optimum fiber orientations or layer group thicknesses are investigated by means of a number of examples of the design of symmetrically laminated composite plates.     

An error analysis approach for laminated composite plate finite element models

Errors in laminated composite plate finite element models occur at both the individual element level and at the discretization level. This paper shows that parasitic shear causes individual element errors and that its sources must be eliminated if numerically and physically correct results are to be provided by the finite element analysis. In addition, discretization errors occur when the behavior of the continuum is represented by a finite number of degrees of freedom. A procedure to estimate discretization errors in laminated composite plate finite element models and guide refinement, in order to achieve an acceptable level of accuracy, is developed. The error estimator built is based on the energy norm of the error in stress resultants.     

Dynamics of a large scale rigid–flexible multibody system composed of composite laminated plates

A novel computational approach for the dynamic analysis of a large scale rigid–flexible multibody system composed of composite laminated plates is proposed. The rigid parts in the system are described through the Natural Coordinate Formulation (NCF) and the flexible bodies in the system are modeled via the finite elements of Absolute Nodal Coordinate Formulation (ANCF), which can lead to a constant mass matrix for the derived system equation of motion. For modeling composite laminated plates accurately, a new composite laminated plate element of ANCF is proposed and the corresponding efficient formulations for evaluating both the elastic force and its Jacobian of the element are derived from the first Piola–Kirchhoff stress tensor. To improve computational efficiency, the sparse matrix technology and graph theory are used to solve the huge set of linear algebraic equations in the process of integrating the equations of motion by using the generalized-a method, and an OpenMP based parallel scheme is also introduced. Finally, the effectiveness of the proposed approach is validated through two numerical examples. One is the static simulation of a single composite laminated plate under gravity and the other is the dynamic simulations of unfolding process of a satellite system with a pair of complicated antennas.     

A three-dimensional state space finite element solution for laminated composite cylindrical shells

On the basis of the theory of three-dimensional elasticity, this paper presents a state space finite element solution for stress analysis of cross-ply laminated composite shells. This is a continuation of the authors’ previously published work on laminated plates [Compos. Struct. 57 (1–4) (2002) 117; Comput. Methods Appl. Mech. Engrg. 191 (37–38) (2002) 4259]. Once again a state space formulation is introduced to solve for through-thickness stress distributions, while the traditional finite elements are used to approximate the in-surface variations of state variables. A three-dimensional laminated shell element is established in an arbitrary orthogonal curvilinear coordinate system, while the application of the element is shown by calculating stresses in laminated cylindrical shells. Compared with the traditional finite element method, the new solution provides accurate continuous through-thickness distributions of both displacements and transverse stresses.     

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.     

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.     

Buckling and postbuckling of circular plates containing concentric penny-shaped delaminations

Buckling and postbuckling analyses of circular laminated composite plates with delaminations are presented. An axisymmetric finite element model based on a layer-wise laminated composite plate theory is developed to formulate the problem. Geometric nonlinearity in the sense of von Kármán and imperfections in the form of initial global deflection and initial delamination openings are included. A simple contact algorithm which precludes the physically inadmissible overlapping between delaminated surfaces is proposed and incorporated into the analysis.

Numerical results are obtained addressing the effects of the initial imperfections, the number of delaminations and their sizes on the critical buckling load and buckling mode shapes as well as postbuckling responses.     

A new finite element for free edge effect analysis in laminated composites

This paper presents a finite element model based on the Multiparticle Model of Multilayered Materials (M4) developed in Institut Navier-LAMI during the last years. The laminated plate is considered as a superposition of Reissner plates coupled by interfacial stresses. An eight-node multiparticle element is developed here. This element has 5n degrees of freedom per node (n is the layer’s number of the laminate). A finite element program called MPFEAP has been developed for the implementation of the multiparticle element. The proposed finite element model is capable of computing interlaminar stresses and other localized effect which is impossible with classical 2D finite element model. Some examples of free edge problem are provided to illustrate the accuracy of the present element in predicting interlaminar stresses.     

Sensitivity analysis and optimization of thin laminated structures with a nonsmooth eigenvalue based criterion

This paper presents a discrete model for the design sensitivity analysis of thin laminated angle-ply composite structures using a plate shell element based on a Kirchhoff discrete theory for the bending effects. To overcome the nondifferentiability of multiple eigenvalues, which may occur during a structural optimization involving free vibrations or buckling design situations, a nonsmooth eigenvalue based criterion is implemented. Angle-ply design variables and vectorial distances from the laminated midle surface to the upper surface of each layer are considered as design variables. The design sensitivities and the directional derivatives are evaluated analytically. The efficiency and accuracy of the model developed is discussed with two illustrative cases which show the need to compute sensitivities of multiple eigenvalues as directional derivatives for laminated composite structures.