多输入多输出柔顺机构几何非线性拓扑优化

多自由度柔顺机构在微动精密定位和精密操作等领域有广泛的应用,柔顺机构拓扑实际上是一个几何非线性问题,因而研究多自由度柔顺机构几何非线性拓扑优化就显得十分必要.基于此,给出一种多输入多输出柔顺机构几何非线性拓扑优化设计的新方法.首先,建立增量形式平衡方程,采用Total-Lagrange描述方法和Newton-Raphson载荷增量求解技术获得几何非线性的结构响应.其次,推导描述多输入多输出柔顺机构柔性的几何增益公式和描述机构刚性的应变能公式,研究抑制耦合输出策略,给出描述输出耦合效应的计算公式,在此基础上建立考虑抑制输出耦合效应时多输入多输出柔顺机构的多目标几何非线性拓扑优化数学模型.目标函数敏度分析采用伴随求解技术,拓扑优化采用固体各向同性材料插值方法,并用移动近似算法进行迭代求解.最后,通过算例说明以上方法的正确性和有效性.研究结果表明,拓扑优化后柔顺机构可以按照预定要求运动,输出耦合现象得到了有效抑制,同时也说明了对柔顺机构进行几何非线性拓扑优化的必要性.     

基于材料-结构协同设计的层合板多级优化方法

提出一种以材料参数与结构参数为变量的复合材料层合板多级优化设计新方法。以单层纤维含量、层厚和铺层角为设计参数,建立了刚度和强度约束下的结构减重设计模型,基于有限元分析,运用所提出的三级优化策略完成结构轻量化设计。本文给出了不同载荷类型和位移边界条件下层合板优化算例,设计结果验证了方法的有效性。     

Nonlinear bending analysis of variable cross-section laminated plates using the dynamic relaxation method

This paper tries to analyze the laminated plates with variable cross section, using the Dynamic relaxation method for solving the governing equations of the thin composite plate, obtained from the CPT theory. Comprehensive comparison and parametric studies prove the accuracy and efficiency of the utilized approach with interesting specifications such as fully vector calculations, independency to the lamina scheme (angle and number of plies) and boundary conditions so that the laminated plates with uniform, variable one direction and variable two direction of cross section could be analyzed. Results show that the behaviour of the composite plates depends on both lamina scheme (the stacking sequences and the number of the plies), and the cross section variation of the laminated plate. In this manner, utilizing the laminated plates with variable two direction of cross section could absorb more potential energy in comparison with uniform and variable one direction of cross section, so that they are useful for using in passive control mechanisms in which the kinetic energy should be removed from the structure by transforming to the potential energy.

     

基于最大应力约束的柔顺机构拓扑优化设计

采用拓扑优化方法获得柔顺机构构型容易出现类铰链结构,导致应力集中、疲劳可靠性差。为了抑制类铰链结构,提出了一种基于最大应力约束的柔顺机构拓扑优化设计方法。采用改进的固体各向同性材料惩罚模型（Solid isotropic material with penalization,SIMP）,以柔顺机构的互应变能最大化作为目标函数,采用P范数方法对所有单元的局部应力凝聚化成一个全局化应力约束,利用自适应约束缩放法使得P范数应力更加接近最大应力,以机构的最大应力和体积作为约束,建立柔顺机构最大应力约束拓扑优化模型,采用全局收敛移动渐近线算法求解柔顺机构最大应力约束拓扑优化问题。结果表明,采用P范数方法进行柔顺机构最大应力约束拓扑优化设计,能够有效抑制类铰链结构。随着应力约束极限值减少,获得机构构型由集中式柔顺机构逐渐转变为分布式柔顺机构,应力分布更加均匀,但机构的互应变能逐渐减小。     

基于转动约束策略的柔顺机构拓扑优化

柔顺机构在航天航空、生物医疗、及仿生机器人等高新科技领域的精密微机械系统中拥有巨大的应用潜力。目前,拓扑优化是柔顺机构构型设计的主要方法之一。为了解决传统柔顺机构拓扑优化设计中存在虚铰的问题,首先,将旋转角引入柔顺机构构型设计中,以旋转角为观测指标,分析拓扑优化结果中存在虚铰的原因。其次,通过约束设计域内的旋转角平方的平均值不超过许用值,建立无铰链式柔顺机构拓扑优化模型,并且利用伴随法推导与之相应的灵敏度分析列式。最后,采用反向位移机构与柔性夹钳这两个经典算例的拓扑优化设计验证了所提优化模型的可行性和有效性。研究结果表明：基于转动约束策略获得的具有类桁架构型无铰链式柔顺机构,虽然在输入位移与输出位移方面表现出一定程度的减少,但避免了局部应变过大、应力集中问题的出现。     

Interlaminar stress analysis of general composite laminates

In this study, based on the reduced from of elasticity displacement field for a long laminate, an analytical method is established to exactly obtain the interlaminar stresses near the free edges of generally laminated composite plates under the extension and bending. The constant parameters, which describe the global deformation of a laminate, are properly computed by means of the improved first-order shear deformation theory. Reddy's layerwise theory is subsequently utilized for analytical and numerical examinations of the boundary layer stresses within arbitrary laminated composite plates. A variety of numerical results are obtained for the interlaminar normal and shear stresses along the interfaces and through the thickness of laminates near the free edges. Finally the effects of end conditions of laminates on the boundary-layer stress are examined.     

Spring-joint method for topology optimization of planar passive compliant mechanisms

There is seldom approach developed for the initial topology design of flexure-based compliant mechanisms. The most commonly-used approaches, which start with an existing rigid-body mechanism, do not consider the performances between different topologies. Moreover, they rely heavily on the rigid-body topology, therefore limit the diversity of compliant mechanisms topology. To obtain the optimal initial topology of such mechanisms directly from problem specifications without referencing to the existing mechanism topologies, a spring-joint method is presented for a restricted class of the serial passive flexure-based compliant mechanisms, which are the building blocks of parallel compliant mechanisms. The topology of the compliant mechanisms is represented by a serial spring-joint mechanism（SSJM） that is a traditional rigid-body mechanism with a torsional spring acting on each joint, and is described by position vectors of the spring-joints. A simplified compliance matrix, determined by the position vectors, is used to characterize the tip of the SSJM kinematically, and is optimized to ensure the desired freedoms of the compliant mechanisms during optimization. The topology optimization problem is formulated as finding out the optimal position of the spring-joints in a blank design domain with an objective function derived from the simplified compliance matrix. In design examples, syntheses of the compliant mechanisms with both single freedom and two decoupled freedoms are presented to illustrate the proposed method. The proposed method provides a new way for the initial design of flexure-based compliant mechanisms.     

Effect of fiber orientation on interfacial fracture toughness for adhesively bonded composite plates

In this study, interfacial fracture toughness was investigated experimentally and numerically in laminated composite plates with different fiber reinforcement angles bonded with adhesive. The composite plates are four-layered and the layer sequence is [0º/θ]_s. DCB test was applied to composite plates reinforced with epoxy resin matrix and unidirectional carbon fiber. The experimental sample model for the DCB test was made using the ANSYS finite element package program. In the numerical study, four layered composites were prepared in three dimensions. Under critical displacement value; mode I fracture toughness at the crack tip was calculated using VCC (virtual crack closure) technique. Numerical values consistent with experimental results have presented in graphical forms. At 60o and 75° the greatest fracture toughness was obtained. In addition, numerical results have shown that fiber orientation prevents the uniform distribution of stress on the interface crack tip and causes stress accumulation, especially at the edge of the plate.

     

Thermal buckling behavior of laminated composite plates: a finite-element study

In this paper, the thermal buckling behavior of composite laminated plates under a uniform temperature distribution is studied. A finite element of four nodes and 32 degrees of freedom (DOF), previously developed for the bending and mechanical buckling of laminated composite plates, is extended to investigate the thermal buckling behavior of laminated composite plates. Based upon the classical plate theory, the present finite element is a combination of a linear isoparametric membrane element and a high precision rectangular Hermitian element. The numerical implementation of the present finite element allowed the comparison of the numerical obtained results with results obtained from the literature: 1) with element of the same order, 2) the first order shear deformation theory, 3) the high order shear deformation theory and 4) the three-dimensional solution. It was found that the obtained results were very close to the reference results and the proposed element offers a good convergence speed. Furthermore, a parametrical study was also conducted to investigate the effect of the anisotropy of composite materials on the critical buckling temperature of laminated plates. The study showed that: 1) the critical buckling temperature generally decreases with the increasing of the modulus ratio E _L/E _T and thermal expansion ratio α _T/α _L, and 2) the boundary conditions and the orientation angles significantly affect the critical buckling temperature of laminated plates.     

Thermomechanical buckling of laminated composite and sandwich plates using global–local higher order theory

In this paper, a global–local higher order theory has been used to study buckling response of the laminated composite and sandwich plates subjected to thermal/mechanical compressive loads. The present global–local theory satisfies the free surface conditions and the geometric and stress continuity conditions at interfaces, and the number of unknowns is independent of the layer numbers of the laminate. Based on this higher-order theory, a refined three-noded triangular element satisfying C¹ weak-continuity conditions has been also proposed. The present theory not only predicts accurately the buckling response of general laminated composite plates but also calculates the critical buckling loads of the soft-core sandwich plates. However, numerical results show that the global higher-order theories as well as first order theories encounter some difficulties and overestimate the critical buckling loads for the sandwich plates with a soft core.     

Free-edge stresses in general composite laminates

In the present study, by starting from the reduced form of elasticity displacement field for a long flat laminate, an analytical method is developed in order to accurately calculate the interlaminar stresses near the free edges of generally laminated composite plates under extension. The constant parameter appearing in the reduced displacement field, which describes the global rotational deformation of a laminate, is appropriately obtained by employing an improved first-order shear deformation theory. The accuracy and effectiveness of the proposed first-order theory are verified by means of comparison with the results of Reddy's layerwise theory as a three-dimensional benchmark. Reddy's layerwise theory is then utilized for analytical and numerical investigations of the boundary-layer stresses within arbitrarily laminated composite plates. Various numerical examples are presented for the interlaminar normal and shear stresses along the interfaces and through the thickness of laminates in the vicinity of the free edges. The effects of end conditions of laminates, fibers orientation angles as well as the stacking sequences of the layers within laminates, and geometric parameters on the boundary-layer stresses are presented and discussed.     

柔顺机构几何非线性拓扑优化设计

对柔顺机构几何非线性拓扑优化设计理论进行了深入研究。首先,建立增量形式平衡方程,采用Total-Lagrange描述方法和Newton-Raphson载荷增量求解技术获得几何非线性的结构响应。其次,基于固体各向同性材料插值方法,建立体积约束下,输出位移最大为目标函数的柔顺机构几何非线性拓扑优化数学模型,目标函数敏度分析采用伴随求解技术,并用移动近似算法进行迭代求解。最后,通过算例说明以上方法的正确性和有效性。研究结果表明,应用上述方法对柔顺机构进行几何非线性拓扑优化设计能够得到合理拓扑图,并比线性分析所得机构的稳定性更高,同时也说明了对柔顺机构进行几何非线性拓扑优化的必要性。     

Mixed-type finite element formulation of higher order shear deformation theory for the linear and nonlinear analyses of a laminated composite plate

For the linear and nonlinear analyses of a laminated composite plate structure, the mixed type finite element program is developed on the basis of higher order shear deformation theory of laminated plates. The accuracy of this program is checked by means of comparing with the existing results for laminated rectangular plates and is found to agree well with them. Deformations and interlaminar stresses of laminated plates are calculated according to the variation of layer numbers, fiber orientations, and plate thicknesses, so that the shear and nonlinear effects on their behaviors are studied. It is found that plate deformations are reduced by means of arranging the fiber direction into the angle-ply and increasing layer numbers.     

航空电子设备复合材料结构优化设计概述

复合材料由于其良好的性能而在航空电子设备中的应用越来越广泛。讨论了航空电子设备复合材料结构优化设计技术,对优化的数学模型展开论述,介绍了优化的五个层次的材料工艺优化、拓扑优化、位置优化、尺寸优化和铺层优化,同时阐述了它们的特点和相应的优化算法。继而针对航空电子设备,研究了复合材料结构综合优化方法。通过对某型天线罩进行结构优化设计,结果表明了优化方法的可行性。     

Analysis of rectangular laminated composite plates via FSDT meshless method

A meshless approach based on the reproducing kernel particle method is developed for the flexural, free vibration and buckling analysis of laminated composite plates. In this approach, the first-order shear deformation theory (FSDT) is employed and the displacement shape functions are constructed using the reproducing kernel approximation satisfying the consistency conditions. The essential boundary conditions are enforced by a singular kernel method. Numerical examples involving various boundary conditions are solved to demonstrate the validity of the proposed method. Comparison of results with the exact and other known solutions in the literature suggests that the meshless approach yields an effective solution method for laminated composite plates.     

Hygrothermal effects on the postbuckling of shear deformable laminated plates

The influence of hygrothermal effects on the postbuckling of shear deformable laminated plates subjected to a uniaxial compression is investigated using a micro-to-macro-mechanical analytical model. The material properties of the composite are affected by the variation of temperature and moisture, and are based on a micro-mechanical model of a laminate. The governing equations of a laminated plate are based on Reddy's higher-order shear deformation plate theory that includes hygrothermal effects. The initial geometric imperfection of the plate is taken into account. Two cases of the in-plane boundary conditions are considered. A perturbation technique is employed to determine buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling behavior of perfect and imperfect, antisymmetric angle-ply and symmetric cross-ply laminated plates under different sets of environmental conditions. The influences played by temperature rise, the degree of moisture concentration, the character of in-plane boundary conditions, transverse shear deformation, plate aspect ratio, total number of plies, fiber orientation, fiber volume fraction and initial geometric imperfections are studied.     

考虑不确定性的柔性机构拓扑优化设计

柔性机构在制造和运行过程中会存在各种不确定因素。基于多椭球凸模型描述,考虑荷载及材料属性的不确定性,采用人工弹簧方法和几何非线性有限元分析手段,提出以输出端位移最大化为目标、具有最小输入端性能约束的柔性机构拓扑优化数学模型。采用伴随法给出设计变量灵敏度计算公式,提出数值计算不稳定性的简易处理方法,利用数学规划法实现优化问题的求解。反向器机构和微夹钳机构的设计算例验证了所提出优化模型的正确性及算法的有效性,并通过与确定性设计结果的比较,说明了在柔性机构拓扑设计阶段考虑不确定性的重要意义。     

拓扑优化技术在机翼前缘设计中的应用

针对柔性机构实现机翼前缘变形问题,应用连续体拓扑优化技术,以实际位移与目标位移之间的偏差为目标函数,材料用量和屈服应力为约束,并考虑到机翼表面受载荷约束等实际情况,建立SIMP(solid isotropic material with penalization)密度刚度插值的拓扑优化模型。分别采用Mat-lab及Ansys软件对柔性机构优化设计和仿真分析,并最终进行了铝合金实物模型形变实验。研究结果显示:机翼前缘断面模型在0~1 N/mm均布外载约束下,可实现0~6.7°理想的机翼前缘变形。     

实现高载荷下机翼前缘形状变化的柔性机构优化设计

为使柔性机构在高载荷作用下能实现预期的形状变化,提出了柔性机构的二次优化设计方法。以柔性机构的变形边界与目标边界间的最小平方差(LSE)为优化目标。采用遗传算法(GA),对柔性机构进行全局优化,求得其初始拓扑解;再采用约束随机探索法进行二次优化,求得柔性机构尺寸的精确解。以柔性机构实现机翼前缘形状变化问题为例,运用MATLAB7.1进行编程计算。结果表明,通过对GA初始拓扑解的二次优化,最小平方差下降了31.48%。最后运用ANSYS验证其变形结果基本一致。     

Nonlinear free and forced vibration of simply supported shear deformable laminated plates with piezoelectric actuators

This paper deals with the nonlinear vibration and dynamic response of simply supported shear deformable cross-ply laminated plates with piezoelectric actuators subjected to mechanical, electrical and thermal loads. The material properties are assumed to be independent of the temperature and electric field. Theoretical formulations are based on the higher order shear deformation plate theory and general von Kármán-type equation, which includes thermo-piezoelectric effects. Due to the bending and stretching coupling effects, a nonlinear static problem is first solved to determine the pre-vibration deformation caused by temperature field and control voltage. By adding an incremental dynamic state to the pre-vibration state, the equations of motion are solved by an improved perturbation technique to determine nonlinear frequencies and dynamic responses of hybrid laminated plates. The numerical illustrations concern nonlinear vibration characteristics of unsymmetric cross-ply laminated plates. The results presented show the effects of temperature rise, applied voltage and stacking sequence on the nonlinear vibration and dynamic response of the plates.