石英纤维/环氧树脂复合材料结构静强度的可靠度计算及全局灵敏度分析

以石英纤维/环氧树脂复合材料结构为研究对象,考虑设计参数的随机性,采用全局灵敏度分析理论,研究了各输入随机因素对石英纤维/环氧树脂复合材料结构静强度响应的影响。首先利用MATLAB和NASTRAN的联合仿真得到各输入变量样本值对应的输出响应值,结合自适应Kriging模型构建极限状态函数的代理模型,在此基础上实现石英纤维/环氧树脂复合材料结构静强度可靠度及各输入变量的不确定性对输出响应及失效概率全局灵敏度的计算,得到输入变量的全局灵敏度排序结果,为工程实际中复合材料结构的优化设计提供一定指导。      

基于Morris方法的纤维复合材料结构件固化均匀性的全局灵敏度分析

纤维增强树脂基复合材料结构件的残余应力问题是制约其在航空航天、汽车和建筑领域大规模应用的关键问题。复合材料固化过程中温度场和固化度场的非均匀性是引起残余热应力和固化收缩应力的重要因素。为了探讨纤维复合材料结构件在固化成型过程中固化工艺温度、热传导系数、对流换热系数及结构件厚度对固化均匀性的敏感程度,采用数值模拟分析了这4个关键参数对温度场和固化度场均匀性的影响规律。模拟结果表明:升高固化工艺温度,复合材料温度场的非均匀性增大,固化度场的非均匀性减小;增大对流换热系数和热传导系数,复合材料温度场和固化度场的非均匀性减小;增加复合材料结构件的厚度,复合材料温度场和固化度场的非均匀性增大。在此基础上,应用Morris全局灵敏度分析方法对4个关键参数对复合材料固化均匀性的影响程度进行定量分析,得到固化均匀性的影响因素按灵敏程度由大到小的顺序为:结构件厚度、热传导系数、固化工艺温度、对流换热系数。     

基于失效概率偏导数的局部与全局混合灵敏度分析

基于失效概率偏导数的局部灵敏度与矩独立的全局灵敏度定义了一种新的混合灵敏度指标,该灵敏度指标不仅继承了传统的矩独立灵敏度的优点,而且反映了矩独立灵敏度和基于方差的灵敏度之间的内在联系。针对该矩独立的混合灵敏度指标计算量大的问题,该文首先将其转化为基于方差的混合灵敏度指标,然后利用能够高效计算条件矩的态相关参数(SDP)法进行求解。为了进一步提高计算效率,该文建立了基于重要抽样和截断重要抽样的SDP方法。算例结果验证了该文所提指标的合理性及所提方法的准确性。方法方法     

模糊分布参数的全局灵敏度分析新方法

为合理度量随机输入变量分布参数的模糊性对输出性能统计特征的影响,提出了模糊分布参数的全局灵敏度效应指标,并研究了指标的高效求解方法。首先,分析了不确定性从模糊分布参数至模型输出响应统计特征的传递机理,以输出性能期望响应为例,利用输出均值的无条件隶属函数与给定模糊分布参数取值条件下的隶属函数的平均差异来度量模糊分布参数的影响,建立了模糊分布参数的全局灵敏度效应指标。其次,为减少所提指标的计算成本、提高计算效率,采用了扩展蒙特卡罗模拟法(EMCS)来估算输入变量分布参数与模型输出响应统计特征的函数关系。最后通过对算例的计算,验证该文所提方法的准确性和高效性。     

基于MLS-SVM的结构整体可靠度与全局灵敏度分析

全局灵敏度分析,旨在考量结构系统中各输入随机变量对输出响应不确定性及风险水平影响的重要度。它能为后续的可靠度评估、故障诊断、系统设计、预测及优化等提供重要参考。尽管各类全局灵敏度分析方法不断涌现,但高维复杂结构(如风机叶片结构)灵敏度分析仍是目前的难题。该文针对空间分割全局灵敏度分析方法的三种可能计算形式及最优分割方案展开研究,通过标准算例分析和误差理论推导,提出能充分利用样本信息、有效减轻计算负担的求解形式及分割方案,并将其应用于风机叶片极限载荷工况下的全局灵敏度分析中,同时为未来设计更为高效、经济和可靠的风机结构提供参考。

     

基于灵敏度分析的复合材料层合板优化设计

工程结构中的复合材料层合板的几何参数往往具有随机性质.如何研究随机参数层合板的灵敏度,并对参数进行优化分析,这对正确估计结构设计的可靠性有着非常重要的意义.根据层合板的一阶剪切理论,采用样条有限元法,推导并建立了层合板的振动方程,刚度矩阵,质量矩阵,比例阻尼矩阵以及求解反对称层合板响应灵敏度的计算公式,在基于灵敏度分析的基础上,进行了复合材料层合板的基频分析和优化设计,并用网格法计算最佳铺层角.数值算例验证了算法的有效性.     

基于分层设计变量的复合材料层合板优化设计及灵敏度分析

在复合材料层合板的结构优化设计中,提出分层设计变量的优化方法以满足实际工程需要。在结构位移、自振频率和屈曲临界荷载灵敏度分析中,给出了刚度矩阵对分层厚度和分层角度设计变量的灵敏度计算公式,考虑了分层厚度变化引起层合板对称中心的改变,保证了计算准确性。数值算例验证了灵敏度算法的精度,应用实例显示了分层设计变量方法的实用性。     

不确定爆炸荷载作用下钢梁的可靠度分析

通过对已有爆炸荷载预测公式、计算图表和试验的海量数据的统计分析,建立了作用于建筑结构上爆炸荷载的统计模型;以典型钢梁为研究对象,考虑材料强度和构件尺寸的不确定性,基于单自由度体系理论和蒙特卡洛方法,建立了不确定爆炸荷载作用下钢梁失效概率的计算方法,并开发了实用计算程序;分析了炸药质量以及爆炸荷载和结构材料属性的不确定性等对钢梁失效概率的影响。研究表明：炸药质量和比例距离是影响爆炸荷载作用下钢梁失效概率的重要因素,在建筑结构抗爆分析中,必须考虑爆炸荷载的不确定性。     

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。     

复合材料结构敲击法无损检测的灵敏度研究

本文研究了应用敲击法(coin-tapmethod)对复合材料结构进行无损检测的基本原理,并建立了典型的损伤检测判据,同时对含不同大小损伤GFRP复合材料的最小可检测损伤进行了详细分析。     

Multiscale analytical sensitivity analysis for composite materials

We describe a methodology aimed at determining the sensitivity of the global structural behaviour, such deformation or vibration modes with respect to the local characteristics such as material constants of micro‐constituents. An analytical gradient computation, which involves the direct differentiation of the multiple scale strong forms with respect to the design parameters is developed. Comparison of the multiple scale sensitivity analysis (MASA) to the central finite difference (CFD) approximation in terms of accuracy and computation efficiency is carried out. We demonstrate the robustness of the MASA approach compared to the CFD approximation, which has been found to be highly sensitive to the choice of the step size, whose optimal value is problem dependent. Copyright © 2001 John Wiley & Sons, Ltd.     

Meshfree analysis and design sensitivity analysis for shell structures

A unified design sensitivity analysis method for a meshfree shell structure with respect to size, shape, and configuration design variables is presented in this paper. A shear deformable shell formulation is characterized by a CAD connection, thickness degeneration, meshfree discretization, and nodal integration. Because of a strong connection to the CAD tool, the design variable is selected from the CAD parameters, and a consistent design velocity field is then computed by perturbing the surface geometric matrix. The material derivative concept is utilized in order to obtain a design sensitivity equation in the parametric domain. Numerical examples show the accuracy and efficiency of the proposed design sensitivity analysis method compared to the analytical solution and the finite difference solution. Copyright © 2002 John Wiley & Sons, Ltd.     

Generalized Timoshenko modelling of composite beam structures: sensitivity analysis and optimal design

This article describes a new approach to design the cross-section layer orientations of composite laminated beam structures. The beams are modelled with realistic cross-sectional geometry and material properties instead of a simplified model. The VABS (the variational asymptotic beam section analysis) methodology is used to compute the cross-sectional model for a generalized Timoshenko model, which was embedded in the finite element solver FEAP. Optimal design is performed with respect to the layers’ orientation. The design sensitivity analysis is analytically formulated and implemented. The direct differentiation method is used to evaluate the response sensitivities with respect to the design variables. Thus, the design sensitivities of the Timoshenko stiffness computed by VABS methodology are imbedded into the modified VABS program and linked to the beam finite element solver. The modified method of feasible directions and sequential quadratic programming algorithms are used to seek the optimal continuous solution of a set of numerical examples. The buckling load associated with the twist–bend instability of cantilever composite beams, which may have several cross-section geometries, is improved in the optimization procedure.     

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.     

Discrete material optimization of general composite shell structures

A novel method for doing material optimization of general composite laminate shell structures is presented and its capabilities are illustrated with three examples. The method is labelled Discrete Material Optimization (DMO) but uses gradient information combined with mathematical programming to solve a discrete optimization problem. The method can be used to solve the orientation problem of orthotropic materials and the material selection problem as well as problems involving both. The method relies on ideas from multiphase topology optimization to achieve a parametrization which is very general and reduces the risk of obtaining a local optimum solution for the tested configurations. The applicability of the DMO method is demonstrated for fibre angle optimization of a cantilever beam and combined fibre angle and material selection optimization of a four‐point beam bending problem and a doubly curved laminated shell. Copyright © 2005 John Wiley & Sons, Ltd.     

Global design and analysis of deep sea FRP composite risers under combined environmental loads

The use of composite materials in offshore engineering for deep sea oil production riser systems has drawn considerable interest due to the potential weight savings and improvement in durability that can be achieved. The design of composite risers consists of two stages: (1) local design based on critical local load cases (LCs) to obtain the geometric configuration of the riser which will be analysed in the global design stage, and (2) global analysis of the full length composite riser under global loads including top tension force, platform motion, hydrostatic pressure, gravity, buoyancy, wave and current loads to determine and assess critical locations. This study describes the methodology, LCs, analysis procedure and results of the global design of the composite riser based on the geometries of the tubular optimised in the local design stage. The results show that a careful local design of the tubular using inclined reinforcements in addition to axial and hoop reinforcements can offer substantial weight savings and at the same time ensure that the structure is capable of withstanding the global loads applied on it.     

Integrated multi-objective robust optimization and sensitivity analysis with irreducible and reducible interval uncertainty

Uncertainty considered in robust optimization is usually treated as irreducible since it is not reduced during an optimization procedure. In contrast, uncertainty considered in sensitivity analysis is treated as partially or fully reducible in order to quantify the effect of input uncertainty on the outputs of the system. Considering this, and the usual existence of both reducible and irreducible uncertainty, an approach that can perform robust optimization and sensitivity analysis simultaneously is of much interest. This article presents such an integrated optimization model that can be used for both robust optimization and sensitivity analysis for problems that have irreducible and reducible interval uncertainty, multiple objective functions and mixed continuous-discrete design variables. The proposed model is demonstrated by two engineering examples with differing complexity to demonstrate its applicability.     

An efficient method for estimating global sensitivity indices

An efficient method is proposed to estimate the first‐order global sensitivity indices based on failure probability and variance by using maximum entropy theory and Nataf transformation. The computational cost of this proposed method is quite small, and the proposed method can efficiently overcome the ‘dimensional curse’ due to dimensional reduction technique. Ideas for the estimation of higher‐order sensitivity indices are discussed. Copyright © 2016 John Wiley & Sons, Ltd.     

Exact response bound analysis of truss structures via linear mixed 0‐1 programming and sensitivity bounding technique

In the present paper, finding the exact bound of structural response for truss structures is considered under bounded interval type uncertainty. This problem is challenging since seeking the exact bound corresponds to locating the global optima of a multivariate function (generally nonconvex). Traditional treatment of this problem involves the solution of a linear mixed 0‐1 programming problem, which is a highly computationally demanding task especially when large‐scale structures are taken into consideration. In order to alleviate the computational effort, a sensitivity bounding technique is developed in this work using the tools from convex analysis to disclose the monotonicity of concerned structural response function with respect to 0‐1 variables. It is shown that this technique can not only reduce the number of 0‐1 variables substantially but also change the computational complexity of the considered problem from nondeterministic polynomial–hard to nondeterministic polynomial–hard in some cases. The proposed approach provides the possibility of finding the exact bound of structural response for large‐scale truss structures within a reasonable time, and its effectiveness is demonstrated through several numerical examples.