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.     

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.     

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.     

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.     

An eigenelement method of periodical composite structures

Eigenelement method is an eigenvector expansion based finite element method, which was proposed by the authors to solve the macro behaviors of composites with less computational cost. To improve the macroscopic accuracy of the classical eigenelement method (CEEM), a serendipity eigenelement method (SEEM) is proposed, which takes the geometry and elastic properties of different phases of composites into account to some extent. Moreover, the shape function and its construction method of a multiscale eigenelement method (MEM) are presented, and the results of SEEM and MEM are compared with that of CEEM and the mathematical homogenization method (MHM) whose physical interpretation is revealed for the first time. It is shown that MEM is the most accurate eigenelement, SEEM is more accurate than CEEM, and MEM satisfies the two essential homogenization conditions: the strain energy equivalence and the deformation similarity. The extensive numerical comparison is given for stresses, displacements and frequencies.     

A strength-based multiple cutout optimization in composite plates using fixed grid finite element method

The design of interior cutouts in laminated composite panels is of great importance in aerospace, automobile and structural engineering. Based on the Tsai–Hill failure criterion of the first ply, this paper presents a newly developed Fixed (FG) Grid Evolutionary Structural Optimization (ESO) method to explore shape optimization of multiple cutouts in composite structures. Different design cases with varying number of cutouts, ply orientations and lay-up configurations are taken into account in this study. The examples demonstrate that the optimal boundaries produced by FG ESO are much smoother than those by traditional ESO. The results show the remarkable effects of different opening numbers and various lay-up configurations on resulting optimal shapes. The paper also provides an in-depth observation in the interactive influence of the adjacent cutouts on the optimal shapes.     

Optimum stacking sequence design of laminated composite circular plates with curvilinear fibres by a layer-wise optimization method

The optimum stacking sequence design for the maximum fundamental frequency of symmetrically laminated composite circular plates with curvilinear fibres is investigated for the first time using a layer-wise optimization method. The design variables are two fibre orientation angles per layer. The fibre paths are constructed using the method of shifted paths. The first-order shear deformation plate theory and a curved square p-element are used to calculate the objective function. The blending function method is used to model accurately the geometry of the circular plate. The equations of motion are derived using Lagrange’s method. The numerical results are validated by means of a convergence test and comparison with published values for symmetrically laminated composite circular plates with rectilinear fibres. The material parameters, boundary conditions, number of layers and thickness are shown to influence the optimum solutions to different extents. The results should serve as a benchmark for optimum stacking sequences of symmetrically laminated composite circular plates with curvilinear fibres.     

Multi-criteria optimization of large composite parts

The objective of the current study is the optimization of the structure and manufacturing processes of large composite plastic parts. The main attention is paid to strengthening of plastic preformed shell by adding variable thickness glass–fiber composite layers and optimizing the material concentrations of the reinforcement layer. The final properties of the part are determined by minimizing the cost and production time simultaneously. The multistage optimization procedure has been applied. According to this approach, the solution of the posed optimization problem has been decomposed into FEA (including free size optimization), meta-modeling and global optimization. Multiple criteria analysis (MCA) is used for evaluating decision options against multiple criteria. Search for global optimum has been performed using of genetic algorithm. The solution has been implemented in MATLAB code. The product family of the composite plastic bathtub, together with the derivate products and their production technologies, is designed using proposed methodology.     

Detection of surface lattice defects using line scan method

The presence of different kinds of surface lattice defects such as missing atom, interstitial atom, line defects, in graphite single crystal have been identified by using scanning tunneling microscope. These defects cause displacement of atoms from their mean position and lattice strain is introduced. By measuring the displacement of atoms from their mean position. lattice strain has been calculated. It is found that among single point defects, vacancies cause maximum lattice strain. Paper presented at the poster session of MRSI AGM V1, Kharagpur, 1995     

Exact 3D stress analysis of laminated composite plates by sampling surfaces method

A paper focuses on the use of the efficient approach to exact 3D elasticity solutions of cross-ply and angle-ply laminated composite plates. This approach is based on the new method of sampling surfaces (SaS) developed recently by the authors. We introduce inside the nth layer I_n not equally spaced SaS parallel to the midsurface of the plate and choose displacements of these surfaces as fundamental plate unknowns. Such an idea permits the representation of the proposed higher order layer-wise plate theory in a very compact form. This fact gives in turn the opportunity to derive the exact 3D solutions of elasticity for thick and thin laminated composite plates with a prescribed accuracy by utilizing a sufficiently large number of SaS, which are located at interfaces and Chebyshev polynomial nodes.     

Design of multifunctional structure with embedded electronic circuitry using composite laminate optimization techniques

This research investigates the optimization of a multifunctional structure with embedded electronic circuitry, following traditional composite laminate optimization methods. A heavily ‘de-featured’ finite element model provides thermal and mechanical analyses of the structure. The model places point heat sources at the surface component locations, and the optimization problem enforces strain constraints at these locations. A simple problem seeks the least-mass I-beam whose shear web contains a simple circuit, subject to strength and strain constraints. A second problem finds the lowest mass unmanned aerial vehicle (UAV) wing box configuration containing embedded circuitry subject to strength, deflection and strain constraints under two load cases. Sequential unconstrained minimization techniques and sequential quadratic programming perform the optimization; combinatorial methods are computationally impractical. Despite the model de-featuring and the use of calculus-based methods, the problem requires significant computational effort. The surface-component strain constraints result in structures with more mass than those without surface components.     

Buckling optimization of composite laminated adaptive structures

This paper deals with the optimal design of laminated composite plates with integrated piezoelectric actuators. Refined finite element models based on equivalent single layer high-order shear deformation theories are used. These models are combined with simulated annealing, a stochastic global optimization technique, in order to find the optimal location of piezoelectric actuators and also to find the optimal fiber reinforcement angles in both cases having the objective of maximizing the buckling load of the composite adaptive plate structure. To show the performance of the proposed optimization models, two illustrative and simple examples are presented and discussed. In one of these examples a comparison between the simulated annealing technique and a gradient based optimization scheme, is carried out.     

Measurement of residual stresses in thick composite cylinders by the radial-cut-cylinder-bending method

Thick fabric composite cylinders for nozzle parts in solid rocket motors should be designed to endure the extreme temperature and pressure of combustion gas. As the thickness of the composite cylinder increases, fabricational residual stresses due to the anisotropic thermal expansion or shrinkage of fabric composites also increase, which induces inter-laminar failures. Therefore, the accurate estimation of the residual stresses is indispensable for the development of thick fabric composite cylinders.

In this paper, the residual stresses in thick cylinders made of carbon fabric phenolic composites were measured by a new radial-cut-cylinder-bending method. To obtain the residual stresses from the measured relative strains during the radial-cut operation, a bending test of the cylinder with the radial-cut was performed instead of measuring the material properties with respect to radial positions. The thermal residual stresses were also calculated by finite element method considering shear deformation of fabric layers, and compared with the measured residual stresses by the new method, from which it was found that the new simple method estimated the residual stresses pretty well. Also the inter-laminar tensile strength at the position of maximum radial residual stress could be obtained from the bending test.     

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.     

Transient dynamic analysis of tapered FRP composite transmission poles using finite element method

Power transmission poles are subjected to dynamic cantilever bending due to wind gusts and cable unilateral failure, or may also be subjected to vehicle impacts. In this paper, transient dynamic analysis of tapered fiber-reinforced polymer (FRP) composite transmission poles with circular thin-walled cross-section subjected to dynamic cable tension and vehicle impacts is investigated by combination of tapered beam finite element and precise time integration method. It is assumed that the material behavior is linearly elastic and the laminate of the cross-section of the wall is symmetric or antisymmetric angle-ply. The effect of fiber type and orientation, the pole geometry, and the concentrated mass at the pole tip are evaluated by performing the dynamic analysis of FRP poles under step, triangular and sine pulses. There is a good agreement between the results of the present method and those obtained from the poles modeled by ANSYS commercial finite element software and existed literatures. Also, there is a significant shorter run-time in the present method. It is concluded that beyond 10 layers for the laminate with constant thickness of the wall, the pole tip deflection does not change.     

Analysis of cracked steel members reinforced by pre-stress composite patch

Pre‐stress bonded composite patch is a promising technique to reinforce steel member damaged by fatigue. The effectiveness of this technique was verified by fatigue tests on notched steel plates. Results showed that the application of carbon fibre reinforced plastic (CFRP) strips and, eventually, the introduction of a compressive stress by pretension of the CFRP strips prior to bonding produced a significant increment of the remaining fatigue life. In this paper, the stress intensity factor in the notched plates is computed by a two‐dimensional finite element model in connection with the three‐layer technique in order to reduce the computational effort. Due to high stress concentration at the plate crack tip, debond is assumed at the adhesive–plate interface. The goal is to illustrate the influence of some reinforcement parameters such as the composite strip stiffness, the pre‐stress level, the adhesive layer thickness and the size of the debonded region on the effectiveness of the composite patch reinforcement.     

基于节点分析法斯特林发动机的参数优化

以斯特林发动机为研究对象,将斯特林发动机划分为6个控制容积,采用三阶节点分析法模拟了GPU-3斯特林发动机,得出其内部压力、温度、功率和效率等参数的动态变化规律。在此基础上对影响斯特林发动机工作腔容积与死容积的参数进行了优化分析,得到了发动机输出功达到最大时各参数的最优值。