Post‐buckling analysis of imperfect laminates using finite strips based on a higher‐order plate theory

A finite strip procedure has been developed for the post‐buckling analysis of composite laminates when subjected to progressive end shortening. The finite strips are developed based on a higher‐order shear deformation plate theory and there are nine variables at each nodal line. Initial imperfection expressed in the form of suitable trigonometric function is allowed. Examples including isotropic plates and laminates with arbitrary lay‐up arrangement are presented. Numerical results for laminates with and without initial imperfection are used to illustrate the effect of imperfection. Copyright © 2003 John Wiley & Sons, Ltd.     

Experimental and Numerical Post‐buckling Analysis of Thin Aluminium Aeronautical Panels under Shear Load

In this work, a novel multi‐hinged test fixture, which can apply a pure shear load to thin panels, is presented. The new device has been used to perform several experimental tests on the shear behaviour of aluminium alloy panels. Four different test configurations have been considered: stiffened and not stiffened panels, with and without a central rectangular cut‐out. The specimens, made of Al 6082 T6, are tested under shear load boundary conditions up to buckling and post‐buckling occurrence. Furthermore, finite element analyses have been performed in order to simulate the four panel configurations tests. The new test fixture has shown the capability to buckle a panel attaining very large out‐of‐plane displacements, if compared to the outcomes of a traditional picture frame test fixture, under the same external load. Numerical and experimental results are finally compared, showing a satisfactory agreement.     

基于可靠性的复合材料结构稳定性约束优化设计

基于结构的可靠性, 研究了复合材料结构的稳定性约束优化设计方法。考虑材料及载荷的不确定性, 通过结构可靠性分析的响应面法和有限元法的结合, 对复合材料结构稳定性进行可靠性分析; 利用优化软件iSIGHT集成可靠性分析程序, 实现了以铺层层数及铺层角度为设计变量的复合材料结构稳定性约束问题的可靠性优化方法。对层合板及层合圆柱进行算例分析, 验证了本文中可靠性优化方法的有效性, 为工程实际中的复合材料结构稳定性约束优化设计问题提供借鉴。      

Design optimization of laminated composite structures using distributed grid resources

Parameter studies, genetic algorithms and Monte Carlo type calculations are examples of pleasantly parallel computational tasks. Pleasantly parallel computational tasks can be effectively calculated in computer clusters or grids. In this work, we consider a weight minimization problem of a laminated composite structure in the post-buckling region. The design variables are the number of layers and the layer orientations given in a discrete set of allowable angles for layer orientations. Optimization is carried out using a deterministic search process, where the lay-up configurations are generated iteratively in the design space from the selected design points of the population at the preceding cycle. Computation is performed using NorduGrid grid computing platform. In this work, we briefly go through some general grid concepts and the use of grid in optimization of laminated composite structures.     

A Koiter‐Newton approach for nonlinear structural analysis

A new approach termed the Koiter‐Newton is presented for the numerical solution of a class of elastic nonlinear structural response problems. It is a combination of a reduction method inspired by Koiter's post‐buckling analysis and Newton arc‐length method so that it is accurate over the entire equilibrium path and also computationally efficient in the presence of buckling. Finite element implementation based on element independent co‐rotational formulation is used. Various numerical examples of buckling sensitive structures are presented to evaluate the performance of the method. The examples demonstrate that the method is robust and completely automatic and that it outperforms traditional path‐following techniques. This improved efficiency will open the door for the direct use of detailed nonlinear finite element models in the design optimization of next generation flight and launch vehicles. Copyright © 2013 John Wiley & Sons, Ltd.     

An optimization of composite lattice cylinder using the approximate method

Recently, the approximate methods based on continuous models have been developed to perform structural analysis of composite lattice structures due to their relative simplicity and computational efficiency. This paper defines the modified effective stiffness considering the directionally dependent mechanical properties to an intersection of ribs and mode shape function of a composite lattice cylinder. It subsequently presents an approximate method based on the continuous model of conducting a buckling analysis of the composite lattice cylinder with various boundary conditions under uniform compression. This method considers the coupled buckling mode as well as the global and local buckling modes. The validity of the present method is verified by comparing the results of the finite element analysis. In addition, a parametric analysis is performed to investigate the effects of the design parameters on the critical load and buckling mode shape of the composite lattice cylinder based on the present method. Finally, we apply the present method to perform the optimization of a composite lattice cylinder for a high-speed vehicle to minimize the mass. Consequently, it is concluded that the present method is very suitable to optimization of composite lattice cylinders due to their relative simplicity and computational efficiency.     

Load increment procedure for post‐buckling analysis of laminated plates under in‐plane loads by finite strip method

A load increment procedure has been presented to integrate with the finite strip method for the post‐buckling analysis of laminated plates when subjected to uniform end shortening. In‐plane loads are introduced to reflect the end shortening effect. The Newton–Raphson procedure is implemented to attend a solution that satisfies the equilibrium condition and at the same time meets the loading requirements. Error associated with loading condition is minimised by adjusting the load factor to preserve the rate of convergence. The enhanced capability can be easily incorporated into the context of both classical and shear deformation plate theories. A range of application has been described. Convergence test and numerical results are presented for isotropic plate and laminates with general lay‐up arrangement. Copyright © 2000 John Wiley & Sons, Ltd.     

Level‐set topology optimization with many linear buckling constraints using an efficient and robust eigensolver

Linear buckling constraints are important in structural topology optimization for obtaining designs that can support the required loads without failure. During the optimization process, the critical buckling eigenmode can change; this poses a challenge to gradient‐based optimization and can require the computation of a large number of linear buckling eigenmodes. This is potentially both computationally difficult to achieve and prohibitively expensive. In this paper, we motivate the need for a large number of linear buckling modes and show how several features of the block Jacobi conjugate gradient (BJCG) eigenvalue method, including optimal shift estimates, the reuse of eigenvectors, adaptive eigenvector tolerances and multiple shifts, can be used to efficiently and robustly compute a large number of buckling eigenmodes. This paper also introduces linear buckling constraints for level‐set topology optimization. In our approach, the velocity function is defined as a weighted sum of the shape sensitivities for the objective and constraint functions. The weights are found by solving an optimization sub‐problem to reduce the mass while maintaining feasibility of the buckling constraints. The effectiveness of this approach in combination with the BJCG method is demonstrated using a 3D optimization problem. Copyright © 2016 John Wiley & Sons, Ltd.     

A fast method for binary programming using first‐order derivatives,with application to topology optimization with buckling constraints

We present a method for finding solutions of large‐scale binary programming problems where the calculation of derivatives is very expensive. We then apply this method to a topology optimization problem of weight minimization subject to compliance and buckling constraints. We derive an analytic expression for the derivative of the stress stiffness matrix with respect to the density of an element in the finite‐element setting. Results are presented for a number of two‐dimensional test problems.Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

Life‐cycle cost optimization of steel structures

This article addresses the life‐cycle cost optimization of steel structures. The main factors influencing the life‐cycle cost of a structure are delineated and their effects on various cost functions are discussed. A four‐criteria optimization model is presented for the life‐cycle cost optimization of steel structures. These criteria are (i) select discrete commercially available sections with the lowest cost, (ii) select commercially available sections with the lightest weight, (iii) select the minimum number of different types of commercially available sections, and (iv) select commercially available sections with the minimum total perimeter length. The last criterion models a representative type of cost incurred over the life of the structure, that is, preventative maintenance in the form of periodic painting of an exposed steel structure to avoid corrosion. The life‐cycle cost optimization model is based on fuzzy logic with the goal of formalizing the life‐cycle design process but with some input from the design engineer through introduction of weighting coefficients reflecting the relative importance of various criteria. The model is applied to a large steel structure with over 3300 members. Copyright © 2002 John Wiley & Sons, Ltd.     

Modelling the Effects of Geometric Imperfections on the Buckling and Initial Post‐buckling Behaviour of Flat Plates Under Compression Using Measured Data

Abstract: Recent developments in optical techniques have allowed accurate representations of the geometry of test specimens to be obtained. These enable the nature of geometric imperfections resulting from manufacture or set‐up to be captured in a form which allows them to be incorporated directly into models generated to predict the behaviour of the structure. This study examines the effect of such imperfections on the behaviour of a series of panels, simply supported along all four edges, and subject to uniaxial compressive in‐plane loading. In each case, digital image correlation is used to determine the initial profile and set‐up of the panel and to monitor its behaviour during test. The data are used to automatically generate a series of meshes representative of each of the specimens tested, suitable for finite element analysis. Comparison of the results obtained from these analyses with those found during the experiments modelled shows an improved correlation when compared with standard techniques for assessing imperfection sensitivity. Set‐up is straightforward, and models can be obtained quickly based on the data collected.     

Optimization of structures under buckling constraints using frame elements

Structural optimization is of increasing interest in a wide variety of application fields. In this article, structural optimization under stress and buckling constraints is investigated. A structure comprised of a set of frame elements is considered. The aim is to obtain the minimal mass structure, by optimizing the number of frame elements and their cross sectional dimensions. A formulation as a mixed-integer nonlinear optimization problem with a tailored objective function is introduced. This cost function is a combination of the structural mass and the sum of the second moments of inertia of each structural element. Moreover, a new algorithm, tailored to the considered problem, is proposed. Numerical results show that the proposed approach provides interesting structural mass savings.     

Optimal layout design of three‐dimensional geometrically non‐linear structures using the element connectivity parameterization method

The topology design optimization of ‘three‐dimensional geometrically‐non‐linear’ continuum structures is still difficult not only because of the size of the problem but also because of the unstable continuum finite elements that arise during the optimization. To overcome these difficulties, the element connectivity parameterization (ECP) method with two implementation formulations is proposed. In ECP, structural layouts are represented by inter‐element connectivity, which is controlled by the stiffness of element‐connecting zero‐length links. Depending on the link location, ECP may be classified as an external ECP (E‐ECP) or an internal ECP (I‐ECP). In this paper, I‐ECP is newly developed to substantially enhance computational efficiency. The main idea in I‐ECP is to reduce system matrix size by eliminating some internal degrees of freedom associated with the links at voxel level. As for ECP implementation with commercial software, E‐ECP, developed earlier for two‐dimensional problems, is easier to use even for three‐dimensional problems because it requires only numerical analysis results for design sensitivity calculation. The characteristics of the I‐ECP and E‐ECP methods are compared, and these methods are validated with numerical examples. Copyright © 2006 John Wiley & Sons, Ltd.     

双稳态复合材料层合结构的黏弹性模型

为探明双稳态复合材料层合结构在复杂环境条件下的应用,对双稳态复合材料层合结构的黏弹性行为进行了研究。首先,将纤维简化为弹性材料,考虑基底材料的黏弹性行为。然后,根据纤维和基底的材料属性,通过理论分析得到了双稳态复合材料层合结构的黏弹性材料属性;根据经典层合板理论、最小应变能原理和Maxwell黏弹性模型建立了双稳态复合材料层合结构的黏弹性模型,通过理论分析得到其第二稳态主曲率与扭曲率随加载时间和温度的变化关系。同时,利用有限元软件ABAQUS及其子程序UMAT建立了相应的有限元模型,研究了加载时间和温度对层合结构第二稳态性能的影响。理论与模拟结果均表明:层合结构第二稳态主曲率随加载时间的延长和温度的升高而增大;扭曲率随加载时间的延长而减小,一般情况下随温度的升高而增大,但在加载时间较长且温度较高时,可能会出现扭曲率随温度升高而减小的情况。理论计算结果与有限元模拟结果的比较显示两者吻合较好,可以通过有限元模拟对双稳态复合材料层合结构的黏弹性行为进行研究。      

Higher‐order multi‐resolution topology optimization using the finite cell method

This article presents a detailed study on the potential and limitations of performing higher‐order multi‐resolution topology optimization with the finite cell method. To circumvent stiffness overestimation in high‐contrast topologies, a length‐scale is applied on the solution using filter methods. The relations between stiffness overestimation, the analysis system, and the applied length‐scale are examined, while a high‐resolution topology is maintained. The computational cost associated with nested topology optimization is reduced significantly compared with the use of first‐order finite elements. This reduction is caused by exploiting the decoupling of density and analysis mesh, and by condensing the higher‐order modes out of the stiffness matrix. Copyright © 2016 John Wiley & Sons, Ltd.     

Optimization of composite structures under multiple load cases using a discrete approach based on lamination parameters

This paper presents a new optimization technique applicable to optimization of composite structures subjected to multiple objectives. The composite structures may be composed of an arbitrary number of laminates. The technique is especially suited for the case where the layers of the laminates may assume a discrete number of orientations. However, given the efficiency of the technique, it is readily extendable to situations where the ply orientations vary quasi‐continuously, for instance, by one degree in one degree. The high efficiency is obtained through application of lamination parameters, which, in the case of symmetric laminates, consist of only 10 parameters per laminate. Three traditional structures, a rectangular composite plate, a cantilever composite beam, and a stiffened composite panel, are optimized against buckling when subjected to multiple load cases. Copyright © 2015 John Wiley & Sons, Ltd.     

Optimization of passively damped composite structures

The paper considers a technique for the optimal design of structures made of viscoelastic materials with the purpose of reducing vibration amplitudes at dynamic loads. __________ Translated from Problemy Prochnosti, No. 5, pp. 128–134, September–October, 2006. Report on International Conference “Dynamics, Strength, and Life of Machines and Structures” (1–4 November 2006, Kiev, Ukraine).