Post‐buckling optimization of composite structures using Koiter's method

Thin‐walled structures, when compressed, are prone to buckling. To fully utilize the capabilities of such structures, the post‐buckling response should be considered and optimized in the design process. This work presents a novel method for gradient‐based design optimization of the post‐buckling performance of structures. The post‐buckling analysis is based on Koiter's asymptotic method. To perform gradient‐based optimization, the design sensitivities of the Koiter factors are derived, and new design optimization formulations based on the Koiter factors are presented. The proposed optimization formulations are demonstrated on a composite square plate and a curved panel where the post‐buckling stability is optimized. Copyright © 2016 John Wiley & Sons, Ltd.     

Detailed design of a lattice composite fuselage structure by a mixed optimization method

In this article, a procedure for designing a lattice fuselage barrel is developed. It comprises three stages: first, topology optimization of an aircraft fuselage barrel is performed with respect to weight and structural performance to obtain the conceptual design. The interpretation of the optimal result is given to demonstrate the development of this new lattice airframe concept for the fuselage barrel. Subsequently, parametric optimization of the lattice aircraft fuselage barrel is carried out using genetic algorithms on metamodels generated with genetic programming from a 101-point optimal Latin hypercube design of experiments. The optimal design is achieved in terms of weight savings subject to stability, global stiffness and strain requirements, and then verified by the fine mesh finite element simulation of the lattice fuselage barrel. Finally, a practical design of the composite skin complying with the aircraft industry lay-up rules is presented. It is concluded that the mixed optimization method, combining topology optimization with the global metamodel-based approach, allows the problem to be solved with sufficient accuracy and provides the designers with a wealth of information on the structural behaviour of the novel anisogrid composite fuselage design.     

Min–max dynamic response optimization of mechanical systems using approximate augmented Lagrangian

A globally convergent and efficient algorithm for min–max dynamic response optimization using the ALM method is presented. This algorithm employs an approximate augmented Lagrangian for line searches, and an exact augmented Lagrangian for finding search directions. This approximate augmented Lagrangian is composed of the linearized cost and constraint functions projected on the search direction. It is noted that an approximate penalty term has the same approximate Hessian as that of the Gauss–Newton method. This makes the approximate augmented Lagrangian to have almost second-order accuracy near the optimum. In the unconstrained optimization process of the proposed method, some modifications are also suggested to remove the possible distortion of optimization trajectory when the side constraints on design variables are separately handled. Also, the efficiencies of two treatments for handling a max-value cost function are discussed in the context of the proposed method. The numerical performance of the proposed method is investigated by solving three min–max dynamic response optimization problems and comparing the results with those in the literature. This comparison shows that the suggested algorithm is more efficient than those in the literature. Especially, it is found that the direct treatment for a max-value cost function is more efficient than the transformation treatment for all the design cases. © 1998 John Wiley & Sons, Ltd.     

旋转压电复合圆柱的弹性分析

针对由各向同性弹性核和压电层组成的两层复合圆柱的旋转问题,给出了弹性力学解。先从压电层的静电平衡方程出发,得到含一个待定常数的电位移形式解,并由此分别给出弹性核和压电层的位移通解,然后利用力学和电学边界条件以及界面处的连续条件确定出所有各层中引入的待定常数,最终得到原问题的解。数值结果表明：当压电层的内外表面均接地时,压电层中的径向应力幅值随弹性核材料的杨氏模量增大而增大,而环向应力则正好相反。弹性核材料的泊松比及外加在压电层内外表面上的电势对旋转两层复合圆柱内的应力响应均有显著的影响。     

An improvement of Kriging based sequential approximate optimization method via extended use of design of experiments

When Kriging is used as a meta-model for an inequality constrained function, approximate optimal solutions are sometimes infeasible in the case where they are active at the constraint boundary. This article explores the development of a Kriging-based meta-model that enhances the constraint feasibility of an approximate optimal solution. The trust region management scheme is used to ensure the convergence of the approximate optimal solution. The present study proposes a method of enhancing the constraint feasibility in which the currently infeasible design is replaced by the most feasible-usable design during the sequential approximate optimization process. An additional convergence condition is also included to reinforce the design accuracy and feasibility. Latin hypercube design and (2n+1) design are used as tools for design of experiments. The proposed approach is verified through a constrained mathematical function problem and a number of engineering optimization problems to support the proposed strategies.     

Procedure of optimization of the structure of composite plates under dynamic loads

We analyze the applicability of the methods of the theory of nonlinear programming to the development of the optimal design of laminated plates with maximum damping. Translated from Problemy Prochnosti, No. 6, pp. 91–99, November–December, 2008.     

复合载荷作用变刚度复合材料回转壳屈曲优化

通过曲线纤维轨迹设计,变刚度复合材料回转壳将拥有比常刚度（直线纤维）回转壳更好的抗屈曲稳定性,为此,研究了复合载荷作用下曲线纤维铺层形式和几何参数对变刚度复合材料回转壳屈曲性能的影响规律。首先根据回转壳横截面圆弧变化改进曲线纤维角度线性描述方法,建立了变刚度复合材料回转壳的参数化有限元模型;其次,结合序列二次响应面方法和回转壳屈曲优化模型,搭建了复合材料回转壳曲线纤维轨迹优化的设计流程;最后,以准各向同性铺层复合材料回转壳为比较基准,对弯扭载荷作用变刚度圆柱壳和轴压、弯矩和扭矩分别作用变刚度椭圆柱壳在不同铺层方式、不同几何参数下的屈曲性能进行了优化比较。结果表明:弯扭载荷作用下,变刚度圆柱壳的屈曲性能随弯矩载荷占比增加而提高,且均好于准各向同性圆柱壳,但扭矩载荷占优时,优化常刚度圆柱壳的屈曲性能更具有优势;不同载荷作用下,具有较小截面方向比的变刚度椭圆柱壳屈曲性能要明显好于对应的准各向同性椭圆柱壳,且横截面越接近圆形,曲线纤维对椭圆柱壳屈曲性能的改善越弱。      

An engineering method for complex structural optimization involving both size and topology design variables

This work presents an engineering method for optimizing structures made of bars, beams, plates, or a combination of those components. Corresponding problems involve both continuous (size) and discrete (topology) variables. Using a branched multipoint approximate function, which involves such mixed variables, a series of sequential approximate problems are constructed to make the primal problem explicit. To solve the approximate problems, genetic algorithm (GA) is utilized to optimize discrete variables, and when calculating individual fitness values in GA, a second-level approximate problem only involving retained continuous variables is built to optimize continuous variables. The solution to the second-level approximate problem can be easily obtained with dual methods. Structural analyses are only needed before improving the branched approximate functions in the iteration cycles. The method aims at optimal design of discrete structures consisting of bars, beams, plates, or other components. Numerical examples are given to illustrate its effectiveness, including frame topology optimization, layout optimization of stiffeners modeled with beams or shells, concurrent layout optimization of beam and shell components, and an application in a microsatellite structure. Optimization results show that the number of structural analyses is dramatically decreased when compared with pure GA while even comparable to pure sizing optimization.     

Hybrid approximation algorithm with Kriging and quadratic polynomial‐based approach for approximate optimization

This paper describes a new hybrid algorithm that uses a Kriging and quadratic polynomial‐based approach for approximate optimization. The Kriging method is used for generating a global approximation model, and the polynomial‐based approximation method is used for generating a local approximation model. The Kriging system is only used to construct a polynomial‐based locally approximate model by estimating some function values and Hessian components of an estimated surface. The number of Kriging estimations can be reduced in comparison with direct Kriging‐based optimization, and a local optimum solution on an approximated surface can be clearly estimated without use of an optimization procedure based on a local appropriate quadratic polynomial model. Numerical examples of engineering optimization using the proposed method illustrate validity and effectiveness of the proposed method. Copyright © 2006 John Wiley & Sons, Ltd.     

复合材料点阵夹芯结构平压性能不确定分析与优化

考虑一体化成型工艺制备的复合材料点阵夹芯结构及其不确定性,采用区间向量实现不确定参数定量化,建立复合材料点阵夹芯结构平压性能区间分析模型.考虑结构功能状态判断的模糊性,分别在不考虑设计容差与考虑设计容差情形下,建立了不确定平压载荷作用下含区间参数模糊可靠性分析与优化模型.研究结果表明:材料参数及结构参数不确定性,特别是设计容差对复合材料点阵夹芯结构平压性能影响明显,因此在工程优化中不仅需要充分考虑材料参数与外部载荷等不确定性,而且需要充分重视传统不确定设计方法中未计及的设计容差的影响.本研究实现了理论成果与工程应用的有机结合,为工程领域复合材料点阵夹芯结构平压性能分析与优化提供有效理论方法.     

复合材料点阵夹芯结构平压性能不确定分析与优化

考虑一体化成型工艺制备的复合材料点阵夹芯结构及其不确定性, 采用区间向量实现不确定参数定量化, 建立复合材料点阵夹芯结构平压性能区间分析模型。考虑结构功能状态判断的模糊性, 分别在不考虑设计容差与考虑设计容差情形下, 建立了不确定平压载荷作用下含区间参数模糊可靠性分析与优化模型。研究结果表明: 材料参数及结构参数不确定性, 特别是设计容差对复合材料点阵夹芯结构平压性能影响明显, 因此在工程优化中不仅需要充分考虑材料参数与外部载荷等不确定性, 而且需要充分重视传统不确定设计方法中未计及的设计容差的影响。本研究实现了理论成果与工程应用的有机结合, 为工程领域复合材料点阵夹芯结构平压性能分析与优化提供有效理论方法。     

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.     

Bending analysis of thick laminated plates using extended Kantorovich method

This study is concerned with bending of moderately thick rectangular laminated plates with clamped edges. The governing equations, based on Reissner first-order shear deformation plate theory; in terms of deflection and rotations of the plate include a system of three second-order, partial differential equations (PDEs). Application of extended Kantorovich method (EKM) to the system of partial differential equations reduces the governing equations to a double set of three second-order ordinary differential equations in the variables x and y. These sets of equations were then solved in an iterative manner until convergence was achieved. Normally three to four iterations are enough to get the final results with desired accuracy. It is demonstrated that, unlike other weighted residual methods, in the extended Kantorovich method initial guesses to start iterations are arbitrary and not even necessary to satisfy the boundary conditions. Results of this study also reveal that the convergence of the EKM is rapid and the method is an efficient way to solve system of PDEs of the same type. To compare the results of this study, the problem was also analyzed using commercial finite element software, ANSYS. Results show reasonably good agreement with the finite element analysis.     

复合材料格栅圆柱筒稳定性数值仿真与试验

作为一种典型的航空航天结构,复合材料格栅圆柱筒的轴压稳定性决定了航天器结构的极限承载能力。现有的均匀化等效法和梁-壳有限元法模拟均存在一定的不足。考虑到肋条的局部应力和稳定性问题,将肋条等效为壳单元,提出了全壳有限元法。结合某型号飞行器复合材料格栅承力筒,分别采用这3种方法进行了轴压稳定性研究,同时设计了全尺寸轴压破坏试验。对比数值计算和试验结果得知两者的一致性较好,并且验证了该型号飞行器设计的合理性。均匀化等效法、梁-壳有限元法和全壳有限元法得到的结果与试验值的偏差分别为14.9%、9.5%和5.2%。全壳有限元法精度最高,并且能准确预测结构破坏位置,为同类结构的设计提供了参考。     

Buckling analysis of composite laminates under end shortening by higher‐order shear deformable finite strips

A higher‐order shear deformable finite strip is developed and employed in the buckling analysis of laminated composite plates when subjected to uniform end shortening. This enables the transverse shear deformation to be accurately incorporated. The permitted laminate material properties are quite general, encompassing anisotropy and full coupling between in‐plane and out‐of‐plane behaviour. Results with respect to the number of plies, thickness of laminate and ratios of E₁₁/E₂₂ are presented for unsymmetric cross‐ply and angle‐ply lay‐ups and for laminates with arbitrary lay‐up arrangements. Copyright © 2002 John Wiley & Sons, Ltd.     

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.     

An uncertain multidisciplinary design optimization method using interval convex models

This article proposes an uncertain multi-objective multidisciplinary design optimization methodology, which employs the interval model to represent the uncertainties of uncertain-but-bounded parameters. The interval number programming method is applied to transform each uncertain objective function into two deterministic objective functions, and a satisfaction degree of intervals is used to convert both the uncertain inequality and equality constraints to deterministic inequality constraints. In doing so, an unconstrained deterministic optimization problem will be constructed in association with the penalty function method. The design will be finally formulated as a nested three-loop optimization, a class of highly challenging problems in the area of engineering design optimization. An advanced hierarchical optimization scheme is developed to solve the proposed optimization problem based on the multidisciplinary feasible strategy, which is a well-studied method able to reduce the dimensions of multidisciplinary design optimization problems by using the design variables as independent optimization variables. In the hierarchical optimization system, the non-dominated sorting genetic algorithm II, sequential quadratic programming method and Gauss–Seidel iterative approach are applied to the outer, middle and inner loops of the optimization problem, respectively. Typical numerical examples are used to demonstrate the effectiveness of the proposed methodology.     

基于离散元法的双组份复合涂料搅拌螺杆参数优化

为了提高双组份复合涂料的混合均匀度,对搅拌螺杆的参数进行优化。以混合销钉式搅拌螺杆为对象,建立其三维模型后导入EDEM软件,然后基于离散元法对双组份复合涂料在该搅拌螺杆中的搅拌过程进行仿真分析,研究了螺杆的转速、螺距和长径比对混合均匀度的影响。最后通过单轴压缩实验对螺杆参数优化后的搅拌效果进行了对比验证。结果表明：螺杆转速、螺距和长径比分别通过改变颗粒抛撒程度、螺旋叶片间隙和螺杆长度来影响复合涂料的混合均匀度;稳定出料后,螺杆转速为200 r/min、螺距为80 mm、长径比为5.57∶1时的搅拌效果最佳;实验验证了利用优化后搅拌螺杆搅拌时复合涂料的力学性能优于手工搅拌时的。研究结果可为自动化搅拌螺杆的结构设计和参数优化提供理论依据。     

航空发动机复合材料主轴优化方案设计方法

提出了航空发动机复合材料主轴优化设计方法,建立了以质量最轻为目标函数,以强度、临界转速和外径尺寸为约束,以轴芯厚度、复合材料层数、各层厚度和各层铺设角度为优化设计变量的优化数学模型。基于ANSYS软件,建立了发动机复合材料主轴优化方案设计平台,着重解决了可同时进行离散和连续设计变量优化的问题。以低压涡轮主轴为例,进行了金属基复合材料主轴优化设计,设计的复合材料主轴质量比同负荷金属轴减少36.16%。     

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.