DESIGN SENSITIVITY ANALYSIS AND OPTIMAL DESIGN OF COMPOSITE STRUCTURES USING HIGHER ORDER DISCRETE MODELS

This paper deals with the structural optimization of multilaminated composite plate structures of arbitrary geometry and layup, using single layer higher order shear deformation theory discrete models. The structural and sensitivity analysis formulation is developed for a family of C° Lagrangian elements. The design sensitivities of static response for objective and/or constraint functions, such as maximum displacements, stress failure criterion and elastic strain energy, with respect to ply angles and ply thickness are presented. The objectives of the design are the minimization of the structural elastic strain energy, minimization of maximum deflection and/or the minimization of the structure volume. The accuracy and relative performance of the proposed discrete models are compared and discussed among developed elements and alternative models. Several test designs are optimized to show the applicability of the proposed refined discrete models.     

Multiple eigenvalue optimization of composite structures using discrete third order displacement models

This paper deals with the implementation and test of a non-smooth eigenfrequency based criterion to evaluate the directional derivatives applied to multilaminated plate structures, when non-differentiable multiple eigenfrequencies occur during the structural optimization process. The algorithm is applied to a family of C⁰ Lagrangian higher order shear deformation theory discrete models. Angle ply design variables and vectorial distances from the laminate middle surface to the upper surface of each ply are considered as design variables. The efficiency and accuracy of the algorithm developed is discussed with an illustrative case. The analytical single and/or directional derivatives are compared to forward finite difference derivatives for the developed discrete models.     

Particle swarm-based structural optimization of laminated composite hydrokinetic turbine blades

Composite blade manufacturing for hydrokinetic turbine application is quite complex and requires extensive optimization studies in terms of material selection, number of layers, stacking sequence, ply thickness and orientation. To avoid a repetitive trial-and-error method process, hydrokinetic turbine blade structural optimization using particle swarm optimization was proposed to perform detailed composite lay-up optimization. Layer numbers, ply thickness and ply orientations were optimized using standard particle swarm optimization to minimize the weight of the composite blade while satisfying failure evaluation. To address the discrete combinatorial optimization problem of blade stacking sequence, a novel permutation discrete particle swarm optimization model was also developed to maximize the out-of-plane load-carrying capability of the composite blade. A composite blade design with significant material saving and satisfactory performance was presented. The proposed methodology offers an alternative and efficient design solution to composite structural optimization which involves complex loading and multiple discrete and combinatorial design parameters.     

钢筋混凝土深梁的拓扑优化模型

钢筋混凝土深梁的拓扑优化模型的获取是一个既有理论意义又有工程背景的设计问题。由于钢筋混凝土材料的特殊性,特别是混凝土拉压性能极端差异的特点以及变量的离散性使得问题复杂化。介绍了一种基于演化原理的结构优化算法——演化结构优化算法(GESO算法),这种算法通过以一定的概率淘汰构件中利用率不高的材料获取构件的优化桁架模型。在计算中考虑钢筋混凝土构件的受力特点,充分发挥钢筋受拉和混凝土受压的优势,给出能反映钢筋混凝土深梁工作机理的拓扑优化桁架模型。给出的钢筋混凝土简支梁和开孔深梁的计算实例,说明了方法的有效性和可行性。     

On the Role of Lengthscale in the Prediction of Failure of Composite Structures: Assessment and Needs

The role of modeling in the design of structural composite components against failure is discussed. Composite materials fail due to damage processes operating at several lengthscales. The interactions between these processes offer the principal challenges to applying mechanism-based models at structural scales beyond the ply level. A methodology is proposed to increase the efficiency of the design process, analogous to the 'building block' approach, which provides a framework for integrating mechanism-based models with the current experimentally-based design process. Available models are reviewed and their key elements identified. General concepts are illustrated via a discussion of the particular issues pertaining to notched components. Key steps needed to allow the evolution of the design process to the envisioned process are identified.     

分析复合材料螺栓连接接头静强度的一种方法

根据复合材料机械连接区逐点逐层破坏的物理本质,采用了每层破坏单元刚度退化和应力空间二阶张量破坏准则,用有限元素法,计算了T300/648碳纤维复合材料21种不同铺层情况的接头强度,分析了它们的破坏模式和破坏过程并与试验结果进行了比较.      

Structural assessment of microvascular self-healing laminates using progressive damage finite element analysis

This paper presents a progressive damage analysis methodology to numerically analyse the effect of microvascular open channels on the structural properties of self-healing fibre–polymer laminates. The tensile and compression properties of self-healing carbon–epoxy laminates containing microvascular systems are analysed using finite element models which consider progressive in-plane ply damage and intra-ply damage (matrix and delamination cracking). The models predict with good accuracy (often within 5%) the stiffness and strength of laminates containing circular or elliptical microvascular channels of different sizes and orientations. The model calculates a progressive reduction in structural properties with increasing size of microvascular channels due to increased ply waviness, which was confirmed using experimental property data. The model also predicts the location and progression of damage under increasing tensile or compression loading to final failure. The model has application as a tool for the design of microvascular systems in self-healing composites used for structural applications.     

Uncertainty propagation in inverse reliability-based design of composite structures

An approach for the analysis of uncertainty propagation in reliability-based design optimization of composite laminate structures is presented. Using the Uniform Design Method (UDM), a set of design points is generated over a domain centered on the mean reference values of the random variables. A methodology based on inverse optimal design of composite structures to achieve a specified reliability level is proposed, and the corresponding maximum load is outlined as a function of ply angle. Using the generated UDM design points as input/output patterns, an Artificial Neural Network (ANN) is developed based on an evolutionary learning process. Then, a Monte Carlo simulation using ANN development is performed to simulate the behavior of the critical Tsai number, structural reliability index, and their relative sensitivities as a function of the ply angle of laminates. The results are generated for uniformly distributed random variables on a domain centered on mean values. The statistical analysis of the results enables the study of the variability of the reliability index and its sensitivity relative to the ply angle. Numerical examples showing the utility of the approach for robust design of angle-ply laminates are presented.     

A PROCEDURE TO SELECT THE BEST MATERIAL COMBINATIONS AND OPTIMALLY DESIGN HYBRID COMPOSITE PLATES FOR MINIMUM WEIGHT AND COST

The optimal layup with least weight or cost for a symmetrically laminated plate subject to a buckling load is determined using a hybrid composite construction. A hybrid construction provides further tailoring capabilities and can meet the weight, cost and strength constraints while a non-hybrid construction may fail to satisfy the design requirements. The objective of the optimization is to minimize either the weight or cost of the plate using the ply angles, layer thicknesses and material combinations as design variables. As the optimization problem contains a large number of continuous (ply angles and thicknesses) and discrete (material combinations) design variables, a -sequential solution procedure is devised in which the optimal variables are computed in different stages. The proposed design method is illustrated using graphite, kevlar and glass epoxy combinations and the efficiencies of the hybrid designs over the non-hybrid ones are computed.     

Optimisation of geometrically non-linear composite structures based on load–displacement control

A design optimisation methodology for beam reinforced composite structures with non-linear geometric behaviour is proposed. The formulation involves displacement, stresses, buckling and size constraints. The Newton–Raphson iterative procedure and the arc-length method are used for tracing equilibrium path and later updating the buckling load and the first ply failure load. The proposed sensitivity analysis model is based on an approach of the adjoint variable method for structures with non-linear geometric behaviour. The optimal design performs on a multilevel scheme based on structural efficiency maximisation exploring the anisotropic properties of the composites and weight minimisation using the ply thickness and the cross-section variables of the stiffeners. To demonstrate the applicability of the proposed developments, optimisation problems considering first ply failure and buckling conditions are presented.     

Adaptive delamination analysis

A methodology aimed at addressing computational complexity of analyzing delamination in large structural components made of laminated composites is proposed. The classical ply‐by‐ply discretization of individual layers may increase the size of the problem by an order of magnitude in comparison with the laminated shell or plate element meshes. The paper features delamination indicators that pinpoint the onset and propagation of delamination fronts with striking accuracy. Once the location of delamination has been identified, the discrete solution space of the classical laminated plate/shell element is hierarchically enriched by a combination of weak and strong discontinuities to adaptively track the evolution of delamination fronts. The so‐called adaptive s‐method proposed herein is equivalent in terms of approximation space to the extended finite element method but offers sparser matrices and added flexibility in transitioning from weak to strong discontinuities. Numerical examples suggest that despite an overhead that comes with adaptivity, the adaptive s‐method is computationally advantageous over the classical ply‐by‐ply discretization, especially as the problem size increases. Copyright © 2015 John Wiley & Sons, Ltd.     

The harmony search heuristic algorithm for discrete structural optimization

Many methods have been developed and are in use for structural size optimization problems, in which the cross-sectional areas or sizing variables are usually assumed to be continuous. In most practical structural engineering design problems, however, the design variables are discrete. This paper proposes an efficient optimization method for structures with discrete-sized variables based on the harmony search (HS) heuristic algorithm. The recently developed HS algorithm was conceptualized using the musical process of searching for a perfect state of harmony. It uses a stochastic random search instead of a gradient search so that derivative information is unnecessary. In this article, a discrete search strategy using the HS algorithm is presented in detail and its effectiveness and robustness, as compared to current discrete optimization methods, are demonstrated through several standard truss examples. The numerical results reveal that the proposed method is a powerful search and design optimization tool for structures with discrete-sized members, and may yield better solutions than those obtained using current methods.     

复合材料机翼结构相似颤振模型的设计与实验验证

为了进行颤振实验, 依据原始金属模型, 根据结构相似方法和刚度相等的原则, 提出了基于设计元素的复合材料结构设计方法, 建立了结构缩比和复合材料结构设计软件, 并分别设计了复合材料机翼盒段和机翼模型。采用低模量复合材料制造, 进行了模态实验和风洞实验。实验结果与理论值吻合较好。设计的梁架2蒙皮复合材料机翼模型实现了结构和动力学相似, 相对于传统的蒙皮不传递载荷的梁架-维形颤振模型有了质的飞跃。      

An evolution strategy in structural optimization problems for plates and shells

For multilayered plated and shell structures the formulation of the optimization problem is strongly dependant on the definition of the design variables. Therefore, the first part of the work is devoted to the definition of design variables and the forms of objective functions. Those design variables define stacking sequences of structures have discrete fiber orientations 0°, ±45°, 90° and a finite number of key points that are required in the evaluation of the curve Γ characterizing an external boundary of the structure or a structural shape understood in the sense of a structural geometry representing a shell/plate mid-surface or thickness distribution of structures. For the curve definition we have adopted one dimensional B-splines. Each curve is formed by an assembly of subsegments passing through certain key points. The positions of key points are randomly generated so that in the generation process it is possible to fulfill the required set of equality or inequality constraints. It is necessary to emphasize that the proposed method is very general and can be applicable to a very broad class of optimization problems. The generality of the approach is confirmed by the proof of the direct equivalence and mapping between discrete fiber orientations and continuous angle ply orientations. The evolution strategy is proposed herein as the optimization algorithm. Similarly as classical ones (e.g. ACO, SS, PS or ISM) it combines all features and advantages of evolution algorithms. It is worth to note that in the evolution strategy the number of children produced in one generation is not limited and it is not necessary to conduct mutation operations as in genetic algorithms. It simplifies significantly the effectiveness of numerical procedures. Then, two numerical examples have been solved to demonstrate the effectiveness of the proposed formulations and the optimization algorithm. They deal with thickness and stacking sequence optimization problems for circular cylindrical shells subjected to various dynamic and static constraints, respectively.     

Particle swarm optimization approach for multi-objective composite box-beam design

This paper presents a multi-agent search technique to design an optimal composite box-beam helicopter rotor blade. The search technique is called particle swarm optimization (‘inspired by the choreography of a bird flock’). The continuous geometry parameters (cross-sectional dimensions) and discrete ply angles of the box-beams are considered as design variables. The objective of the design problem is to achieve (a) specified stiffness value and (b) maximum elastic coupling. The presence of maximum elastic coupling in the composite box-beam increases the aero-elastic stability of the helicopter rotor blade. The multi-objective design problem is formulated as a combinatorial optimization problem and solved collectively using particle swarm optimization technique. The optimal geometry and ply angles are obtained for a composite box-beam design with ply angle discretizations of 10°, 15° and 45°. The performance and computational efficiency of the proposed particle swarm optimization approach is compared with various genetic algorithm based design approaches. The simulation results clearly show that the particle swarm optimization algorithm provides better solutions in terms of performance and computational time than the genetic algorithm based approaches.     

Modelling and optimization of laminated adaptive shells of revolution

In this paper two shell finite element models are presented for the structural analysis of composite laminated piezoelectric shells. One is an axisymmetric conical frustum with two nodal rings and the other is a conic shell panel with eight nodes. Both models are based in a mixed laminated theory that combines a higher order shear deformation theory for the mechanical displacement field with a layerwise representation with linear functions for the electric potential through each piezoelectric layer. In order to obtain the optimal design sensitivities analysis and optimization techniques based in the nonlinear mathematical programming are used. The design objectives can be the minimization of the deformed structure or the maximization of the natural fundamental frequency and the design variables are the electric potential difference applied to the actuators or the ply thicknesses among others.     

Spatial Evolution of the Thickness Variations over a CFRP Laminated Structure

Ply thickness is one of the main drivers of the structural performance of a composite part. For stress analysis calculations (e.g., finite element analysis), composite plies are commonly considered to have a constant thickness compared to the reality (coefficients of variation up to 9% of the mean ply thickness). Unless this variability is taken into account reliable property predictions cannot be made. A modelling approach of such variations is proposed using parameters obtained from a 16-ply quasi-isotropic CFRP plate cured in an autoclave. A discrete Fourier transform algorithm is used to analyse the frequency response of the observed ply and plate thickness profiles. The model inputs, obtained by a mathematical representation of the ply thickness profiles, permit the generation of a representative stratification considering the spatial continuity of the thickness variations that are in good agreement with the real ply profiles spread over the composite part. A residual deformation FE model of the composite plate is used to illustrate the feasibility of the approach.     

基于离散宏单元的砌体结构高效非线性分析方法

砌体结构由力学性能不同的块体和砂浆构成，材料的各向异性使结构非线性行为体现出高度复杂性。砌体结构非线性分析模型主要包括分离式和整体式两种:分离式模型将块体、砂浆及二者粘结界面分开建模，可以精细化揭示砌体非线性行为和破坏形态，但非线性分析计算量大，多用于局部构件的细部分析和模拟；整体式模型将块体和砂浆假定为连续的匀质体，建模过程简单、易行，适用于整体结构的宏观分析。无论是分离式还是整体式，结构非线性计算分析中大规模刚度矩阵的实时更新与分解降低了分析效率。该文提出了一种基于整体式空间离散宏单元模型的砌体结构高效非线性分析方法，该方法采用剪切单元模拟砌体墙的斜截面剪切破坏模式，采用无厚界面单元模拟砌体墙的正截面弯曲破坏模式、正截面剪切滑移破坏模式和平面外剪扭破坏模式，进一步将剪切单元等效斜向弹簧的轴向变形和无厚界面单元上下表面的相对变形分解为线弹性和非线性两部分，并引入塑性自由度描述分离出的非线性部分，可将任意时刻的切线刚度矩阵表示为初始弹性刚度矩阵的低秩摄动形式，引入Woodbury公式进行求解，该文方法避免了大规模整体刚度矩阵的迭代更新，非线性分析的主要计算量仅集中于小规模非线性矩阵的更新与分解，显著提升了计算效率。     

Minimum cost design of framed structures by the mini-max dual method

Minimum cost design of a framed structure is considered by using the mini-mas dual method. Stress and/or displacement constraints are imposed as behavioural constraints. The minimum cost design problem has a discrete objective function and discrete design variables. A sequence of approximate optimization problems in created by using the first-order Taylor series expansion for displacements with respect to the reciprocals of cross-sectional areas and moments of inertia. Each approximate problem is solved in the dual space. Two simple structural examples are given to show the appropriateness and efficiency of the proposed procedure. Approximate solutions are obtained within five structural analysis.     

Investigation of thermally induced bistable behaviour for tow-steered laminates

Traditionally, bistable laminates have been developed from prepreg plies stacked up together to achieve a layup which is either constant or discretely varying over the planform of the laminate. Laminates with discrete variation in layup are, in particular, of interest as they offer the prospect of easier blending. Moreover, such laminates can be manufactured to have Variable Angle Tows (VATs) in a ply using a tow-steering technique, doing so, ensures fibre-continuity and may impart additional structural strength. This paper presents an approach to develop finite element (FE) models which can accurately predict the cured shape(s) of tow-steered laminates that are designed to be bistable. Manufactured laminates are characterised using microscopy and resin burn-off tests to identify resin-rich layers, ply-thicknesses and fibre volume fractions (V_f) – which are then translated into FE models. Presented data highlights the influence of the manufacturing process in the thermally induced bistable behaviour of tow-steered laminates.