一种基于复合材料加筋板结构效率的稳定性优化方法

提出一种以承载效率最高作为目标的新设计方法, 对复合材料加筋板的承载能力进行优化。讨论了不同压缩与弯曲刚度的匹配模式与加筋板临界失稳载荷的关系。将全局失稳载荷、局部失稳载荷与静载荷的接近程度作为结构承载效率的量化标准, 通过静载荷的控制, 使结构的稳定性向着效率最高的方向优化。以宏观的加筋板压缩与弯曲刚度参数作为设计变量, 构建了一种可用于结构效率优化的代理模型, 避免了局部最优点的出现, 更便于数值寻优。通过有限元分析验证, 优化后壁板的临界失稳载荷与所施加的静载荷基本一致, 反映出较高的效率, 从而验证了该方法的可靠性。      

考虑屈曲的复合材料加筋壁板铺层顺序优化

提出了一种考虑屈曲的复合材料加筋壁板铺层顺序优化方法。基于复合材料加筋壁板屈曲载荷求解的能量法,系统推导了轴压载荷作用下复合材料加筋壁板蒙皮、筋条局部屈曲载荷的显示表达式,考虑了加筋壁板各板元之间的弹性支持作用及筋条下缘条的影响,引入工程法求解了加筋壁板整体屈曲载荷。基于国产自主结构分析软件HAJIF中的复合材料铺层工程数据库,以铺层参数为中间变量,利用本文提出的复合材料加筋壁板屈曲载荷求解方法,构建了考虑屈曲的复合材料加筋壁板铺层顺序优化设计流程并完成程序实现,将最小二乘法用于最优铺层顺序与工程铺层数据库的匹配。相比于传统有限元计算方法,本文提出的复合材料加筋壁板屈曲载荷求解方法具备较好的求解精度及求解效率。复合材料加筋壁板优化算例表明,采用本文提出的加筋壁板屈曲载荷分析及其优化方法,在结构重量不变的前提下,屈曲载荷提高约17%,且铺层顺序优化结果可直接从铺层工程数据库中提取并用于工程实际。      

Design of efficient stiffened shells of revolution

A method to produce efficient piecewise uniform stiffened shells of revolution is presented. The approach uses a first order differential equation formulation for the shell prebuckling and buckling analyses and the necessary conditions for an optimum design are derived by a variational approach. A variety of local yielding and buckling constraints and the general buckling constraint are included in the design process. The local constraints are treated by means of an interior penalty function and the general buckling load is treated by means of an exterior penalty function. This allows the general buckling constraint to be included in the design process only when it is violated. The self adjoint nature of the prebuckling and buckling formulations is used to reduce the computational effort. Results for four conical shells and one spherical shell are given.     

Computational strategy for multiobjective optimization of composite stiffened panels

This paper presents a multiobjective optimization methodology for composite stiffened panels. The purpose is to improve the performances of an existing design of stiffened composite panels in terms of both its first buckling load and ultimate collapse or failure loads. The design variables are the stacking sequences of the skin and of the stiffeners of the panel. The optimization is performed using a multiobjective evolutionary algorithm specifically developed for the design of laminated parts. The algorithm takes into account the industrial design guidelines for stacking sequence design. An original method is proposed for the initialization of the optimization that significantly accelerates the search for the Pareto front. In order to reduce the calculation time, Radial Basis Functions under Tension are used to approximate the objective functions. Special attention is paid to generalization errors around the optimum. The multiobjective optimization results in a wide set of trade-offs, offering important improvements for both considered objectives, among which the designer can make a choice.     

Multilevel Optimization Framework for Hierarchical Stiffened Shells Accelerated by Adaptive Equivalent Strategy

In order to improve the post-buckling optimization efficiency of hierarchical stiffened shells, a multilevel optimization framework accelerated by adaptive equivalent strategy is presented in this paper. Firstly, the Numerical-based Smeared Stiffener Method (NSSM) for hierarchical stiffened shells is derived by means of the numerical implementation of asymptotic homogenization (NIAH) method. Based on the NSSM, a reasonable adaptive equivalent strategy for hierarchical stiffened shells is developed from the concept of hierarchy reduction. Its core idea is to self-adaptively decide which hierarchy of the structure should be equivalent according to the critical buckling mode rapidly predicted by NSSM. Compared with the detailed model, the high prediction accuracy and efficiency of the proposed model is highlighted. On the basis of this adaptive equivalent model, a multilevel optimization framework is then established by decomposing the complex entire optimization process into major-stiffener-level and minor-stiffener-level sub-optimizations, during which Fixed Point Iteration (FPI) is employed to accelerate convergence. Finally, the illustrative examples of the multilevel framework is carried out to demonstrate its efficiency and effectiveness to search for the global optimum result by contrast with the single-level optimization method. Remarkably, the high efficiency and flexibility of the adaptive equivalent strategy is indicated by compared with the single equivalent strategy.     

Surrogate-based multi-objective optimization of a composite laminate with curvilinear fibers

A variable stiffness design can increase the structural performance of a composite plate and provides flexibility for trade-offs between structural properties. In this paper, we examine the simultaneous optimization of stiffness and buckling load of a composite laminate plate with curvilinear fiber paths. The problem, which falls in the area of multi-objective optimization, is formulated and solved through a surrogate-based optimization algorithm capable of finding the set of optimum Pareto solutions. We integrate surrogate modeling into an evolutionary algorithm to reduce the high computational cost required to solve the optimization process. The results show that a curvilinear fiber path can increase both buckling load and stiffness simultaneously over the quasi-isotropic laminate. Furthermore, the optimum direction for varying the fiber angle is dependent on the loading direction and boundary conditions. The results for a plate under uniform compression with free transverse edges shows that varying the fiber orientation perpendicular to the loading direction can increase the buckling load by 116% with respect to that of a quasi-isotropic laminate.     

复合材料帽型加筋板轴压试验及承载能力预测

随着复合材料的广泛使用,复合材料帽型加筋板在飞机结构上的使用也越来越多。为研究复合材料帽型加筋板承受轴向压缩的能力,首先对不同蒙皮半径、蒙皮厚度及长桁间距的复合材料帽型加筋板进行了轴压试验,得到了局部屈曲载荷、破坏载荷与加筋板曲率系数、长桁间距的关系,然后,通过引入曲率修正系数,修正了现有加筋板屈曲载荷的工程估算公式;最后,利用分段处理法结合有效宽度概念改进了加筋板轴压极限承载的工程算法。结果表明:帽型复合材料加筋板局部屈曲载荷及最终破坏载荷与曲率系数正相关;改进的方法能对复合材料加筋板的极限承载进行准确预测。所得结果表明该方法为复合材料加筋板结构设计及载荷估算提供了一种新方法,具有一定的工程应用价值。      

New conceptual design of aeroelastic wing structures by multi-objective optimization

Internal structural layouts and component sizes of aircraft wing structures have a significant impact on aircraft performance such as aeroelastic characteristics and mass. This work presents an approach to achieve simultaneous partial topology and sizing optimization of a three-dimensional wing-box structure. A multi-objective optimization problem is assigned to optimize lift effectiveness, buckling factor and mass of a structure. Design constraints include divergence and flutter speeds, buckling factor and stresses. The topology and sizing design variables for wing internal components are based on a ground element approach. The design problem is solved by multi-objective population-based incremental learning (MOPBIL). The Pareto optimum results lead to unconventional wing structures that are superior to their conventional counterparts.     

Optimum buckling design of composite stiffened panels using ant colony algorithm

Optimal design of laminated composite stiffened panels of symmetric and balanced layup with different number of T-shape stiffeners is investigated and presented. The stiffened panels are simply supported and subjected to uniform biaxial compressive load. In the optimization for the maximum buckling load without weight penalty, the panel skin and the stiffened laminate stacking sequence, thickness and the height of the stiffeners are chosen as design variables. The optimization is carried out by applying an ant colony algorithm (ACA) with the ply contiguous constraint taken into account. The finite strip method is employed in the buckling analysis of the stiffened panels. The results shows that the buckling load increases dramatically with the number of stiffeners at first, and then has only a small improvement after the number of stiffeners reaches a certain value. An optimal layup of the skin and stiffener laminate has also been obtained by using the ACA. The methods presented in this paper should be applicable to the design of stiffened composite panels in similar loading conditions.     

CURRENT EXPERIENCE OF THE USE OF THE STIFFENED PANEL DESIGN SOFTWARE VICONOPT IN OPTIMUM DESIGN OF AIRCRAFT

VICONOPT is an optimum design program for prismatic plate assemblies based on exact methods of eigenvalue analysis. It has proved to be reliable and efficient in the optimum design of stiffened aerospace panels. Parametric design studies have been made for panels with longitudinal voids, skewed panels and variants of benchmark aircraft wing panels, including estimation of the effects of allowance for transverse shear deformation. Current developments include efficient methods for the design of multi-cell wing boxes, the use of random design moves to escape from a local optimum, a generic minimum cost design procedure and an exploration of parallel methods for optimum design.     

A moving superimposed finite element method for structural topology optimization

Level set methods are becoming an attractive design tool in shape and topology optimization for obtaining efficient and lighter structures. In this paper, a dynamic implicit boundary‐based moving superimposed finite element method (s‐version FEM or S‐FEM) is developed for structural topology optimization using the level set methods, in which the variational interior and exterior boundaries are represented by the zero level set. Both a global mesh and an overlaying local mesh are integrated into the moving S‐FEM analysis model. A relatively coarse fixed Eulerian mesh consisting of bilinear rectangular elements is used as a global mesh. The local mesh consisting of flexible linear triangular elements is constructed to match the dynamic implicit boundary captured from nodal values of the implicit level set function. In numerical integration using the Gauss quadrature rule, the practical difficulty due to the discontinuities is overcome by the coincidence of the global and local meshes. A double mapping technique is developed to perform the numerical integration for the global and coupling matrices of the overlapped elements with two different co‐ordinate systems. An element killing strategy is presented to reduce the total number of degrees of freedom to improve the computational efficiency. A simple constraint handling approach is proposed to perform minimum compliance design with a volume constraint. A physically meaningful and numerically efficient velocity extension method is developed to avoid the complicated PDE solving procedure. The proposed moving S‐FEM is applied to structural topology optimization using the level set methods as an effective tool for the numerical analysis of the linear elasticity topology optimization problems. For the classical elasticity problems in the literature, the present S‐FEM can achieve numerical results in good agreement with those from the theoretical solutions and/or numerical results from the standard FEM. For the minimum compliance topology optimization problems in structural optimization, the present approach significantly outperforms the well‐recognized ‘ersatz material’ approach as expected in the accuracy of the strain field, numerical stability, and representation fidelity at the expense of increased computational time. It is also shown that the present approach is able to produce structures near the theoretical optimum. It is suggested that the present S‐FEM can be a promising tool for shape and topology optimization using the level set methods. Copyright © 2005 John Wiley & Sons, Ltd.     

T型截面多级加筋柱壳的缺陷敏感性及优化研究

该文基于非线性显式动力学方法进行后屈曲分析,获得了四种加筋柱壳(均匀加筋柱壳、矩形截面双向多级加筋柱壳、T型截面单向和双向多级加筋柱壳)整个后屈曲过程的轴压位移-载荷曲线,并以模态缺陷为例,比较了四者的缺陷敏感性,结果显示T型截面双向多级加筋柱壳呈现出显著的低缺陷敏感性和较强的可设计性。该文还将缺陷敏感性分析结果与对应的完善结构后压溃稳定平衡路径进行了对比,发现两者一定程度上的趋势一致性。这表明对完善结构运用显式动力学方法进行单次后屈曲分析,即可同时获得其承载能力和缺陷敏感性,大大减少计及缺陷敏感性结构设计的计算量。最后,该文进一步构造了面向低缺陷敏感性的T型截面多级加筋柱壳优化模型,算例表明该方法可以高效地获得可靠性更强的优化解。     

Effect of Stiffening Configurations on Fracture of Aluminium Structures

Abstract:  Traditionally, marine structures have been designed to resist yielding, buckling and fatigue, but not fracture. This is because existing data regarding fracture on large-scale models are limited. Consequently, adequate methods and procedures to design vessels to resist fracture have not been developed, although the shipbuilding industry is seeking to achieve advanced and more efficient concepts and designs for vessels with improved safety and performance using optimised structural design. The rapidly increasing application of lightweight materials and thin-walled structures in several industries requires fundamental understanding of mechanisms and mechanics of fracture that govern stiffened panels. Therefore, a comprehensive tool consisting of application of advanced fracture models, material calibration, and validation through component testing is provided that will increase the survivability envelope of new vessels. This paper presents the effect of stiffening configurations on fracture of aluminium structures by studying the structural response of various stiffened plates which are compared with unstiffened plates represented by small-scale compact tension (CT) specimens. It is shown that mapping of crack patterns in stiffened plates is feasible and can enable ship designers to evaluate critical areas within a structure with respect to crack initiation, propagation and optimum material usage.     

Stacking sequence optimization to maximize the buckling load of blade-stiffened panels with strength constraints using the iterative fractal branch and bound method

Laminated carbon fiber reinforced polymer (CFRP) composites have widespread applications in aerospace structures, and thus optimization of the stacking sequences in these composites is indispensable. Here, a fractal branch and bound method (FBB) is proposed for optimizing the stacking sequences. This method requires only low computational costs, and an optimal result can be obtained rapidly by means of the deterministic process. For practical stacking sequence optimizations, more than two laminates have to be optimized, because a practical aerospace structural component usually comprises a panel and stiffeners made from composite laminates. Since the stacking sequences of the skin panel and stiffeners affect the buckling load of the stiffened panel, the optimization of both laminates must be performed simultaneously. In the present study, a new method to implement a strength constraint for the FBB method is proposed for the simultaneous optimization of more than two laminates (such as a panel and stiffeners). Moreover, a quadratic polynomial objective function, which includes lamination parameter variables of the two laminates: the stiffeners and the panel, is adopted. The strength constraint is implemented by means of a response surface. The new method is applied to the buckling load maximization of a blade-stiffened composite panel, in which the strength constraint is demonstrated as a feasibility study. The method successfully obtained optimal stacking sequences with the strength constraint at low computational cost.     

复合材料加筋板屈曲/后屈曲分析的应用

研究了复合材料加筋板翼面结构稳定性问题,分析了加筋板在压缩和剪切等载荷作用下的稳定性安全裕度。利用计算复合材料加筋板屈曲及后屈曲承载能力的方法,验证复杂受载情况下结构的稳定性。验证对象是一个优化后的满足强度、刚度和工艺制造要求的复合材料机翼。该机翼在各种载荷工况下的内力分布情况由MSC.NASTRAN分析得到,通过本文提出的方法得到每块蒙皮的稳定性承载能力。然后给出复合材料层合板在复杂载荷下的屈曲及后屈曲安全裕度的计算准则,验证优化后的机翼加筋板是否满足稳定性设计要求。该方法可作为约束集成到结构优化系统平台中。     

Simultaneous single-loop multimaterial and multijoint topology optimization

As the aerospace and automotive industries continue to strive for efficient lightweight structures, topology optimization (TO) has become an important tool in this design process. However, one ever-present criticism of TO, and especially of multimaterial (MM) optimization, is that neither method can produce structures that are practical to manufacture. Optimal joint design is one of the main requirements for manufacturability. This article proposes a new density-based methodology for performing simultaneous MMTO and multijoint TO. This algorithm can simultaneously determine the optimum selection and placement of structural materials, as well as the optimum selection and placement of joints at material interfaces. In order to achieve this, a new solid isotropic material with penalization-based interpolation scheme is proposed. A process for identifying dissimilar material interfaces based on spatial gradients is also discussed. The capabilities of the algorithm are demonstrated using four case studies. Through these case studies, the coupling between the optimal structural material design and the optimal joint design is investigated. Total joint cost is considered as both an objective and a constraint in the optimization problem statement. Using the biobjective problem statement, the tradeoff between total joint cost and structural compliance is explored. Finally, a method for enforcing tooling accessibility constraints in joint design is presented.     

离散变量结构优化设计的拟满应力遗传算法

以力学准则法为基础,提出了一种求解离散变量结构优化设计的拟满应力方法;这种方法能直接求解具有应力约束和几何约束的离散变量结构优化设计问题.通过在遗传算法中定义拟满应力算子,建立了一种离散变量结构优化设计的混合遗传算法拟满应力遗传算法.算例表明;这种混合遗传算法对于离散变量结构优化设计问题具有较高的计算效率.     

Optimization methods for advanced design of aircraft panels: a comparison

Advanced nonlinear analyses developed for estimating structural responses for recent applications for the aerospace industry lead to expensive computational times. However optimization procedures are necessary to quickly provide optimal designs. Several possible optimization methods are available in the literature, based on either local or global approximations, which may or may not include sensitivities (gradient computations), and which may or may not be able to resort to parallelism facilities. In this paper Sequential Convex Programming (SCP), Derivative Free Optimization techniques (DFO), Surrogate Based Optimization (SBO) and Genetic Algorithm (GA) approaches are compared in the design of stiffened aircraft panels with respect to local and global instabilities (buckling and collapse). The computations are carried out with software developed for the European aeronautical industry. The specificities of each optimization method, the results obtained, computational time considerations and their adequacy to the studied problems are discussed.     

Design of hat-stiffened composite panels loaded in axial compression

An integrated step-by-step analysis procedure for the design of axially compressed stiffened composite panels is outlined. The analysis makes use of the effective width concept. A computer code, BUSTCOP, is developed incorporating various aspects of buckling such as skin buckling, stiffener crippling and column buckling. Other salient features of the computer code include capabilities for generation of data based on micromechanics theories and hygrothermal analysis, and for prediction of strength failure. Parametric studies carried out on a hat-stiffened structural element indicate that, for all practical purposes, composite panels exhibit higher structural efficiency. Some hybrid laminates with outer layers made of aluminium alloy also show great promise for flight vehicle structural applications.     

Application of an iterative global approximation technique to structural optimizations

An iterative global approximation technique based on the Kriging method is proposed. The technique is validated through analytical test cases and then applied to solve two practical optimization problems: the optimization of aluminium-foam filled absorbers against crashworthiness requirements and the optimization of composite stiffened panels against buckling and strength constraints. The absorbers of the first application consist of two co-axial aluminium alloy tubes filled with lightweight aluminium foam. They were optimized to collapse at a controlled force level and to be the lightest possible. Explicit Finite element analyses were performed to evaluate the structural behavior of the absorbers in the sample points used to build the approximation. In the second application stiffened panels were optimized against buckling and strength constraints. The Tsai-Wu criterion was used to estimate first-ply failures as strength limit of the structure. Non-linear Riks analyses were performed with ABAQUS/Standard to evaluate the shell behavior in the sample points used to build the response surfaces. Basing on the obtained results the proposed iterative procedure seems a promising alternative to the classic a-priori building of response surface allowing better accuracy and saving of sample points.