A hybrid force/stiffness matrix method for the analysis of thin-walled composite frames

A novel method for the analysis of frames constructed of thin-walled members of anisotropic composite materials is presented in this paper. The method accounts for non-isotropic coupling effects that exist in composite material beams due to the anisotropy of the composite material laminates that form the thin-walled cross section. The method also accounts for warping effects known to be significant in thin-walled members. The analysis is performed by the direct stiffness matrix method utilizing a new approach that divides each thin-walled member of the frame into one-dimensional warping-beam superelements and non-warping conventional beam elements. The element stiffness matrices for these two one-dimensional beam elements are obtained by a numerical procedure that is based on the classical force method analysis. The stiffness matrices of both beam elements are 12 × 12 matrices corresponding to the six degrees of freedom per node required for conventional space frame analysis. The remarkable feature of this representation is that warping is accounted for without introducing additional degrees of freedom to account for the bimoment and warping twist in the members. This is accomplished by use of the warping-beam superelement that linearizes the regions of non-uniform torsion in the thin-walled beam. Examples of space frame structures constructed of thin-walled composite material I-beams are presented to demonstrate the method. Results of analyses using the proposed method are compared with those obtained from two-dimensional finite element models.     

旋转几何非线性复合材料薄壁梁的自由振动分析

研究具有几何非线性的旋转复合材料薄壁梁的自由振动。梁的变形引入了Von Kármán几何非线性, 基于Hamilton原理和变分渐进法 (Variational-Asymptotical Method -VMA),导出旋转复合材料薄壁梁的非线性振动偏微分方程组。采用Galerkin法将振动方程离散化为常微分方程组。借助于谐波平衡法 (Harmonic Balance Method -HBM) 建立自由振动的振幅-非线性固有频率关系方程。将上述方程化为非线性特征值问题,采用迭代算法进行求解。将所建立的旋转复合材料薄壁梁非线性自由振动分析模型和计算方法,应用于周向均匀刚度配置(Circumferentially Uniform Stiffness –CUS) 构型复合材料薄壁梁,通过数值计算揭示了纤维铺层角、旋转速度对非线性振动固有频率-振幅关系的影响。     

Sensitivity analysis of frequency response functions of composite sandwich plates containing viscoelastic layers

In the scope of structural dynamics, sensitivity analysis is a very useful tool in a number of numerical procedures such as parameter identification, model updating, optimal design and uncertainty propagation. In this paper the formulation of first-order sensitivity analysis of complex frequency response functions (FRFs) is developed for composite sandwich plates composed by a combination of fiber-reinforced and elastomeric viscoelastic layers, in arrangements that are frequently used for the purpose of noise and vibration attenuation. Although sensitivity analysis is a well known numerical technique, the main contribution intended for this study is its extension to viscoelastic structures, which are characterized by frequency- and temperature-dependent material properties and, thus, require particularly adapted analytical and numerical procedures. Due to the fact that finite element discretization has become the most used method for dynamic analysis of complex structures, the sensitivity analysis addressed herein is based on such models, being computed from the analytical derivatives of the FRFs with respect to a set of design parameters, such as fiber orientations and layer thicknesses. Also, a procedure for evaluating the sensitivity of the FRFs with respect to temperature of the viscoelastic material is suggested. After discussion of various theoretical aspects, including a parameterization scheme of the structural matrices with respect to the design variables, first-order response derivatives are calculated for a composite plate with inherent structural damping, and for a composite sandwich plate with a viscoelastic core. The results are compared to those obtained from first-order finite-difference approximations.     

A sequential linear least square algorithm for tracking dynamic shapes of smart structures

This paper presents a sequential linear least square algorithm for tracking dynamic shapes of piezoelectric smart structures. The dynamic shape discussed in this paper is defined as a host structural shape varying with time, and the tracking technique is to find an electric voltage history for each piezoelectric device over a time period so that the desired structural movements can be achieved. In the theoretical formulation, dynamic equations of piezoelectric smart structures are introduced by finite element analysis, and then a solution procedure for a set of time‐dependent electric voltages is derived by combining the linear least square method and the Houbolt numerical integration scheme. The formulation indicates that this algorithm can be used to find the time‐dependent voltages for tracking structural movements of piezoelectric smart structures. The present novel formulation is then demonstrated through numerical examples for tracking dynamic shapes of piezoelectric smart beams and plates. The numerical results for the smart beam are compared with the experimental ones. It is shown that the present sequential linear least square algorithm is capable of efficiently simulating dynamic shape tracking for smart structures. Copyright © 2006 John Wiley & Sons, Ltd.     

Geometrically nonlinear composite beam structures: design sensitivity analysis

The purpose of this paper is to develop a finite element model for optimal design of composite laminated thin-walled beam structures, with geometrically nonlinear behavior, including post-critical behavior. A continuation paper will be presented with design optimization applications of this model. The structural deformation is described by an updated Lagrangean formulation. The structural response is determined by a displacement controlled continuation method. A two-node Hermitean beam element is used. The beams are made from an assembly of flat-layered laminated composite panels. Beam cross-section mass and stiffness property matrices are presented.

Design sensitivities are imbedded into the finite element modeling and assembled in order to perform the structural design sensitivity analysis. The adjoint structure method is used. The lamina orientation and the laminate thickness are selected as the design variables. Displacement, failure index, critical load and natural frequency are considered as performance measures. The critical load constraint calculated as the limit point of the nonlinear response is also considered, but a new method is proposed, replacing it by a displacement constraint.     

考虑剪力滞效应的层合箱梁矩阵分析方法

给出了考虑剪力滞后及剪切变形效应条件下,复合材料薄壁层合箱梁静力行为控制微分方程组的初参数解。以此为基础,推导出了层合箱梁单元的刚度矩阵和等效结点荷载列阵,从而使薄壁层合箱梁的剪力滞、剪切变形效应分析方便地纳入了工程中广泛应用的矩阵位移法程序系统,为复合材料连续层合箱梁等复杂结构的强度及刚度分析提供了有效的计算手段。      

Finite element response sensitivity analysis using three‐field mixed formulation: general theory and application to frame structures

This paper presents a method to compute response sensitivities of finite element models of structures based on a three‐field mixed formulation. The methodology is based on the direct differentiation method (DDM), and produces the response sensitivities consistent with the numerical finite element response. The general formulation is specialized to frame finite elements and details related to a newly developed steel–concrete composite frame element are provided. DDM sensitivity results are validated through the forward finite difference method (FDM) using a finite element model of a realistic steel–concrete composite frame subjected to quasi‐static and dynamic loading. The finite element model of the structure considered is constructed using both monolithic frame elements and composite frame elements with deformable shear connection based on the three‐field mixed formulation. The addition of the analytical sensitivity computation algorithm presented in this paper extends the use of finite elements based on a three‐field mixed formulation to applications that require finite element response sensitivities. Such applications include structural reliability analysis, structural optimization, structural identification, and finite element model updating. Copyright © 2006 John Wiley & Sons, Ltd.     

FINITE ELEMENT ALGORITHMS FOR DYNAMIC SIMULATIONS OF VISCOELASTIC COMPOSITE SHELL STRUCTURES USING CONJUGATED GRADIENT METHOD ON COARSE GRAINED AND MASSIVELY PARALLEL MACHINES

Recently much attention has been paid to high-performance computing and the development of parallel computational strategies and numerical algorithms for large-scale problems. In this present study, a finite element procedure for the dynamic analyses of anisotropic viscoelastic composite shell structures by using degenerated 3-D elements has been studied on vector and coarse grained and massively parallel machines. CRAY hardware performance monitors such as Flowtrace and Perftrace tools are used to obtain performance data for subroutine program modules and specified code segments. The performances of conjugated gradient method, the Cray sparse matrix solver and the Feable solver are evaluated. SIMD and MIMD parallel implementation of the finite element algorithm for dynamic simulation of viscoelastic composite structures on the CM-5 is also presented. The performance studies have been conducted in order to evaluate efficiency of the numerical algorithm on this architecture versus vector processing CRAY systems. Parametric studies on the CM-5 as well as the CRAY system and benchmarks for various problem sizes are shown. The second study is to evaluate how effectively the finite element procedures for viscoelastic composite structures can be solved in the Single Instruction Multiple Data (SIMD) parallel environment. CM-FORTRAN is used. A conjugate gradient method is employed for the solution of systems. In the third study, we propose to implement the finite element algorithm in a scalable distributed parallel environment using a generic message passing library such as PVM. The code is portable to a range of current and future parallel machines. We also introduced the domain decomposition scheme to reduce the communication time. The parallel scalability of the dynamic viscoelastic finite element algorithm in data parallel and scalable distributed parallel environments is also discussed. © 1997 by John Wiley & Sons, Ltd.     

Identification of damages in composite multilayered cylindrical panels with delaminations

In this study, effective theoretical and computational (the finite element method) procedures are introduced and used to characterize the dynamic behavior of beams and of cylindrical panels with circular cross-section; both structures have the single delamination between laminate layers. Based on the computed results it is possible to determine the effect of delamination on the overall structural dynamic behavior. Those results are used to quantify the difference between the results of the relevant parameters in the cases of perfect and defected structures. Usually, the wave propagation can be observed with the use of piezoelectric sensors. Therefore, in the next step of our analysis we modeled delaminated structures with a finite number of PZT sensors to consider also their influence on the structural dynamic response. The numerical analysis have been conducted with the use of 3D finite elements. It deals with the analysis of a cylindrical shell with an axisymmetric delamination and of a cylindrical panel having a square local delamination. A lot of numerical results allow us to understand better the influence of various parameters on the form of wave propagation in cylindrical multilayered shells. The numerical results are also validated by an experimental analysis for cylindrical panels.     

Finite element formulation for anisotropic coupled piezoelectro‐hygro‐thermo‐viscoelasto‐dynamic problems

A finite element algorithm has been developed for the efficient analysis of smart composite structures with piezoelectric polymer sensors or/and actuators based on piezoelectro‐hygro‐thermo‐viscoelasticity. Variational principles for anisotropic coupled piezoelectro‐hygro‐thermo‐viscoelasto‐dynamic problems have also been proposed in this study. As illustrative studies, dynamic responses in laminated composite beams and plates with PVDF sensors and actuators are obtained as functions of time using the present finite element procedures. The voltage feedback control scheme is utilized. The proposed numerical method can be used for analysing problems in the design of smart structures as well as smart sensors and actuators. Copyright © 1999 John Wiley & Sons, Ltd.     

考虑墙体作用的低层冷弯薄壁型钢轻型房屋住宅体系弹塑性动力分析

低层冷弯薄壁型钢结构住宅体系的抗震性能是进行该类结构推广应用的关键。该文基于ANSYS软件建立了该类结构体系的数值模型,在考虑冷弯薄型钢构件及门窗洞口加强与否、考虑组合墙体作用与否等情况下,分别进行了设防烈度为7度时常遇地震下的静力分析和弹性时程分析和设防烈度分别为7度、8度和9度时罕遇地震下的弹塑性时程分析。结果表明:常遇地震作用时结构弹性层间位移由风荷载控制,罕遇地震作用下结构弹塑性层间侧移则由地震作用控制;是否考虑组合墙体及墙面板材料特性对结构承载力、变形及抗震性能影响显著。在设防烈度分别为7度、8度和9度时的罕遇地震作用下,考虑组合墙体时结构最大弹塑性层间位移角可满足现行抗震规范(GB50011-2010)要求,双面OSB墙面板且角柱进行加强时抗震性能最好。该文结果可为进一步进行此类结构体系的抗震性能研究及应用提供参考。     

子结构物理参数识别与输入地震动的复合反演研究

利用结构的动力响应同时识别结构物理参数并反演输入过程的工作称为复合反演.本文研究一类基于子结构分析的地震动复合反演问题.通过结构动力矩阵的分解并结合作者提出的一种在输入信息未知的条件下识别结构物理参数的方法,提出了一类复合反演算法.算例分析表明了算法的实用性.     

Post-yield behavior of fixed steel beams encased in concrete with plastic rotation capability under monotonic loads

Flexural strength calculated based on only curvature at sections shows some inconsistencies at large strains compared with nonlinear finite element analyses which considered damaged concrete plasticity. The prediction of the post-yield behavior of steel–concrete composite structures has been a complex issue, rendering analytically inaccurate prediction of the post-yield deflection of composite beams when plastic flows were not considered. The accurate prediction of the post-yield deformation of composite steel beams encased in structural concrete should account for the strain based on plastic rotation. The plastic rotation is influenced by the inelastic energy dissipation. The post-yield behavior of steel–concrete composite structures is affected by the inclination of diagonal cracks of concrete, and the stiffening effect of concrete tension between cracks. Plastic strain occurring in the steel section also contributes to in-elastic behavior of composite structures. The aim of this study was to idealize plastic flow of steel beams encased in structural concrete at fixed foundation. Plastic flows were calculated by non-linear finite element analysis including the consideration of concrete plasticity. The post-yield deflection was, then, predicted in a manner reflecting plastic deformation. The proposed idealization agreed well with numerical data obtained by means of nonlinear finite element analysis, providing a simplified but reliable procedure for practicing engineers designing composite structures in the inelastic region.     

Delamination detection in laminated composite beams using hybrid elements

This investigation pursues two goals. One of them is developing a three-dimensional finite element with an embedded interface for analyzing the laminated composite structure. The composite element efficiency is numerically proven. Delaminatoin is an important failure mechanism in certain types of composite structures. Detecting this type of damage is currently a problem of interest to the structural health monitoring community. The second goal of the paper is presenting a novel and well-organized procedure for the identification of delaminatoin in laminated composite beams. The damage identification scheme is formulated by an inverse problem, where analysis data from related finite element modeling, are used to quantify the magnitude and local of delaminatoin. The inverse problem is then transformed to an optimization statement, and the optimum delaminatoin parameters are found by minimizing the objective function. In this study, a genetic algorithm is used for the optimization process. Several numerical examples are analyzed for the accuracy test, and a few of them are presented here.     

变截面复合材料薄壁转轴在不同约束下的振动与稳定性

该文针对复合材料变截面薄壁旋转轴在不同约束下的振动与稳定性问题,提出了一个动力学模型。基于变分渐进法和拉格朗日方程,推导了复合材料变截面薄壁转轴的自由振动方程。在转轴的结构模型中,综合考虑了扭转、拉伸和弯曲引起的截面翘曲的影响。采用伽辽金法,分析了截面按线性或者抛物线变化的变截面旋转轴的固有频率和临界转速,其中还考虑了一端固定一端自由和一端固定一端铰支两种边界条件以及复合材料铺层角的影响。此外,通过对比分析模型的计算结果与商用有限元软件ANSYS的结果,该文所提出的分析模型的有效性在一定程度上得到了验证。     

Prediction of impact damage on sandwich composite panels

Sandwich structures are extensively employed in the aerospace and automobile industries. The understanding of their behaviour under impact conditions is extremely important for the design and manufacturing of these engineering structures since impact problems are directly related to structural integrity and safety requirements. This paper investigates the damage behaviour of composite sandwich panels with aramid paper honeycomb (NOMEX) and polyetherimide (PEI) foam cores under transverse impacts at high velocities. A numerical model was developed using the dynamic explicit finite element (FE) structure analysis program PAM-CRASH. For both sandwich structures numerical analysis reproduces physical behaviour observed experimentally in high velocity impact tests.     

复合材料空间薄壁梁的有限元分析模型

在剪切梁理论的基础上, 采用9 节点平面单元模拟梁任意截面形状; 采用27 节点体单元, 模拟截面出平面外的二次翘曲位移, 从而建立了空间复合材料任意截面薄壁梁考虑二次翘曲的有限元分析模型。根据本文中导出的复合材料有限元模型编制了相应的分析计算程序。算例表明: 本文中建立的复合材料薄壁梁模型正确, 可以用于考虑多种耦合影响因素作用下复杂结构空间薄壁复合材料梁的有限元分析计算。      

A Rate Dependent Constitutive Model for Glass-Fibre / Epoxy-Matrix Woven Fabrics

This paper deals with the modelling until rupture of composite structures made of glass-fibre / epoxy-resin woven fabrics submitted to dynamic loadings. The model is built at the mesoscale of the elementary ply. It takes into account the slightly nonlinear brittle behaviour of the fibres under tensile sollicitations, their nonlinear behaviour in compression as well as the strongly non linear and irreversible behaviour of the ply in shear. Strain rate effects are also introduced and special attention is paid to the objectivity of the model in the context of finite element calculation. Therefore the choice of a delayed damage mesomodel coupled with viscoplasticity is made. In order to identify the values of the parameters of the model, an optimization procedure based on a gradient-free direct search method has been developed. As a logical proceeding to this study, the model ability to avoid strain localization and mesh dependence is then checked on simple uniaxial examples. The last part of this paper is devoted to structural calculation. The results of the simulations of both the impact on composite plate and the crushing of thin-walled tube demonstrate the capability of the model to reproduce observed physical phenomena.     

大变形薄壁复合材料旋转梁静动态特性分析

该文研究了大变形薄壁复合材料旋转梁的静、动态特性以及复合材料旋转梁不同铺层角、转速对固有频率的影响变化规律。在梁截面上设立翘曲节点引入翘曲变形,假设应变沿薄壁厚度呈二次曲线形式变化;由Hamilton原理,推导了复合材料梁的大变形公式;建立了考虑剪切、翘曲薄壁复合材料大变形梁静、动态分析的有限元模型,并编写了相应的计算程序。分析了复合材料薄壁梁大变形状态下的静态变形行为;在旋转状态下,考虑哥氏力影响,不同转速、不同铺层角对复合材料梁动态特性的影响。计算结果表明:能够用该文建立的模型计算复合材料梁的静动态特性,与相关文献计算结果进行比较,说明了模型的优越性。     

复合材料层合板屈曲稳定性优化设计及其灵敏度计算方法

笔者在有限元分析基础上研究了以屈曲稳定性作为约束条件或优化目标的复合材料层合板结构优化设计及其灵敏度分析方法,重点讨论了屈曲临界荷载灵敏度对内力场和载荷的依赖关系及其在铺层优化、尺寸优化和形状优化问题中的不同计算方法,并在JIFEX软件中实现了复杂结构复合材料层合板优化设计方法。数值算例验证了本文算法和程序的有效性。