多孔格栅均匀化模型平压仿真分析

为了研究均匀化方法在一种多孔格栅结构中的应用,从格栅单胞尺度入手,建立了一种适用于有限元仿真分析的三维周期性边界条件.以ABAQUS作为分析平台,对周期性边界条件下的格栅单胞模型进行了平压仿真分析,并将仿真结果与文献实验结果对比,验证了该边界条件的可靠性.利用均匀化理论建立了格栅单胞力学平衡方程,得到了格栅均匀化模型....     

双周期平面裂纹问题的特征展开-变分方法

根据弹性力学的变分原理,利用双周期问题位移场的双准周期性质和应力应变场的双周期性质,构造了双周期平面问题的单胞泛函变分表达式. 然后结合针对裂纹问题的复应力函数特征展开式,发展了基于单胞模型的双周期裂纹平面问题的特征展开-变分方法. 由于该方法考虑了最一般的双周期边界条件,因而能够分析一般非对称排列的双周期裂纹问题. 通过结果的收敛性分析说明了该方法具有计算效率和精度都高的优点. 最后,对于裂纹呈平行四边形排列的情况,分析了不同的裂纹排列对应力强度因子的影响.      

基于修正高精度广义胞元法的复合材料细观力学分析

高精度广义胞元法是多尺度分析复合材料模量和微观应力应变场的有效方法之一．然而，由于位移插值函数中缺少二次耦合项，很大程度上影响了复合材料局部应力、应变场，特别是剪切场的计算精度．本文通过引入二次方向耦合项，提出了一种修正的高精度广义胞元法插值函数．在施加周期性边界条件、平均应力和平均位移连续性条件后，可以确定位移插值函数中的系数．通过对多相复合材料弹性模量和局部场分析，并且与有限元分析和实验测量结果比较，验证了修正高精度广义胞元法的准确性．与高精度广义胞元相比，本文提出的修正高精度广义胞元法在不需要引入额外未知变量，不影响计算效率的前提下，对复合材料的局部应力场计算得更加准确．     

三维编织复合材料几何建模及数值分析

论文根据三维编织复合材料的结构特点,把整体结构分为内部单胞、表面单胞和角单胞三种类型的子单胞,考虑空间纤维束的相互扭结和挤压所造成的纤维束的弯曲和截面变形,针对每种类型的子单胞,建立了相应的几何分析模型.引入周期性位移边界条件,建立了材料的弹性性能预报模型,得到了三维编织复合材料的工程弹性常数.通过数值比较可以看出,论文所给出的数值计算结果与实验结果吻合较好,从而验证了本文模型的有效性.     

高温下编织复合材料热相关参数识别方法研究

为了获取高温下编织复合材料的准确弹性参数与热膨胀系数,提出一种基于均匀化理论的热相关参数识别方法. 首先,在编织复合材料单胞有限元模型基础上,基于均匀化理论和热弹性理论,施加周期性位移边界条件和温度边界条件,预测编织复合材 料的热弹性相关参数. 然后,考虑到等效过程中编织复合材料应力分布不均匀等因素引起的误差,将复合材料精细模型的热模态数据作为补 充信息,识别编织复合材料热相关参数,对预测的材料参数进行校准. 本文在二维编织结构单胞模型基础上,开展等效预测和识别方法研 究,验证所提出方法的有效性和准确性. 对比等效和识别后热模态的误差,结果表明:本文提出的基于等效预测的参数识别方法,能够 准确识别高温下编织复合材料宏观热相关参数.      

复合材料弹塑性多尺度分析模型与算法

对材料非线性多尺度分析的计算模型与算法进行研究.在构建周期分布单胞分析算法的基础上,发展针对复合材料结构材料非线性多尺度分析的一般有限元方法.方法的特点是将所建立的单胞分析过程作为有限元分析的子程序嵌入到总程序系统当中,完成对应的高斯点应力计算,因而使所发展的方法具有实现方便的特点.给出数值计算结果,验证了方法与所发展的多尺度有限元分析程序的正确与有效性.     

高温下编织复合材料热相关参数识别方法研究

为了获取高温下编织复合材料的准确弹性参数与热膨胀系数,提出一种基于均匀化理论的热相关参数识别方法.首先,在编织复合材料单胞有限元模型基础上,基于均匀化理论和热弹性理论,施加周期性位移边界条件和温度边界条件,预测编织复合材料的热弹性相关参数.然后,考虑到等效过程中编织复合材料应力分布不均匀等因素引起的误差,将复合材料精细模型的热模态数据作为补充信息,识别编织复合材料热相关参数,对预测的材料参数进行校准.本文在二维编织结构单胞模型基础上,开展等效预测和识别方法研究,验证所提出方法的有效性和准确性.对比等效和识别后热模态的误差,结果表明:本文提出的基于等效预测的参数识别方法,能够准确识别高温下编织复合材料宏观热相关参数.     

周期性点阵类桁架材料等效弹性性能预测及尺度效应

比较了Dirichlet型和Neumann型边界条件下的代表体元法及均匀化方法对具有周期性结构的点阵类桁架材料等效弹性性能的预测结果.数值结果表明,Dirichlet型和Neumann型边界条件下的代表体元法所得结果随着参与模拟的单胞(微结构的最小周期)个数的增加,分别从上下界逼近均匀化方法的结果.对于一类具有特殊微结构的桁架材料,只需一个单胞即可充分逼近均匀化结果.指出产生尺度效应的判据是,对Dirichlet型边界条件下的代表体元法,单胞公共边界处的节点支反力是否平衡;对Neumann型边界条件下的代表体元法,单胞边界间变形是否协调.最后,我们证明了对于一类均匀化方法求解中没有广义自由度的桁架材料,其均匀化结果就是各构件性能按照体积份数加权平均得到.     

松质骨弹性模量计算的均匀化方法

对松质骨建立了六种单胞微观结构模型，采用均匀化方法和有限元方法计算松质骨的宏观等效弹性模量。给出了六种单胞模型的松质骨弹性模量与材料密度(体分比）的关系，与实验数据进行了对比，分析了不同微观结构模型在不同骨骼中的应用。结果表明，本文方法及六种单胞模型可以对松质骨微观结构和材料性能进行有效的模拟计算。同时本文又着重对松质骨的宏观等效弹性模量与体分比的指数关系进行了探讨。     

树脂基三维编织复合材料粘弹性性能的有限元分析

根据材料的细观结构,采用APDL语言分别建立了纤维束和三维编织复合材料两级单胞的参数化几何模型;推导了Prony级数表示的树脂粘弹性本构方程,对模型进行了组分材料参数设置;对纤维束单胞模型进行扫掠式网格划分,对三维编织复合材料单胞模型进行线-面-体式网格划分;对两级单胞模型均施加合理的边界条件,使单胞边界上的位移满足周期性和连续性。以有限元模型为基础,计算了三维编织复合材料的粘弹性能,并给出了材料粘弹性效应随工艺参数变化的规律。计算结果表明:三维编织复合材料编织方向的粘弹性效应随编织角的增大而增强,随纤维体积比的增大而减弱。该结果与已有实验结论一致。     

A homogenization theory for elastic-viscoplastic materials with misaligned internal structures

In this study, a homogenization theory for non-linear time-dependent materials is rebuilt for periodic elastic-viscoplastic materials with misaligned internal structures, by employing a unit cell defined for the aligned structure as an analysis domain. For this, it is shown that the perturbed velocity fields in such materials possess periodicity in the directions of misaligned unit cell arrangement. This periodicity is used as a novel boundary condition for unit cell analysis to rebuild the homogenization theory. The resulting theory is able to deal with arbitrary misalignment using the same unit cell, avoiding not only geometry and mesh generation of a unit cell for every misalignment, but also the influence of mesh dependence. To verify the theory, an elastic-viscoplastic analysis of plain-woven glass fiber/epoxy laminates with misaligned internal structures is performed. It is shown that the misalignment of internal structures affects viscoplastic properties of the plain-woven laminates both macroscopically and microscopically.     

A general super element for a curved beam

Corrugated panels have gained considerable popularity in a range of engineering applications, particularly in morphing skin applications. The optimum design of these structures needs simple models of the corrugated panels that may be incorporated into multi-disciplinary system models. Considering the geometric and mechanical properties of the corrugated panel, a generic super element of a corrugated core unit cell with elastomeric coating for morphing structures is investigated in this paper. The super element captures the small deformation of a 2D thin curved beam with variable curvature and is based on an exact analytical equivalent model which avoids any homogenization assumption. The stiffness matrix of a general curved beam element for a corrugated unit cell with elastomeric coating is derived. Different geometries are investigated to verify the accuracy and efficiency of the presented super element. The super element uses the geometric and mechanical properties of the panel as variables that may be applied for further topology optimization studies. The parametric studies of different corrugation shapes demonstrate the suitability of the proposed super element for application in further detailed design investigations.     

An eigenelement method and two homogenization conditions

Under inspiration from the structure-preserving property of symplectic difference schemes for Hamiltonian systems, two homogenization conditions for a representative unit cell of the periodical composites are proposed, one condition is the equivalence of strain energy, and the other is the deformation similarity. Based on these two homogenization conditions, an eigenelement method is presented, which is characteristic of structure-preserving property. It follows from the frequency comparisons that the eigenelement method is more accurate than the stiffness average method and the compliance average method.     

Second-order homogenization of periodic materials based on asymptotic approximation of the strain energy: formulation and validity limits

In this paper a second-order homogenization approach for periodic material is derived from an appropriate representation of the down-scaling that correlates the micro-displacement field to the macro-displacement field and the macro-strain tensors involving unknown perturbation functions. These functions take into account of the effects of the heterogeneities and are obtained by the solution of properly defined recursive cell problems. Moreover, the perturbation functions and therefore the micro-displacement fields result to be sufficiently regular to guarantee the anti-periodicity of the traction on the periodic unit cell. A generalization of the macro-homogeneity condition is obtained through an asymptotic expansion of the mean strain energy at the micro-scale in terms of the microstructural characteristic size ?; the obtained overall elastic moduli result to be not affected by the choice of periodic cell. The coupling between the macro- and micro-stress tensor in the periodic cell is deduced from an application of the generalised macro-homogeneity condition applied to a representative portion of the heterogeneous material (cluster of periodic cell). The correlation between the proposed asymptotic homogenization approach and the computational second-order homogenization methods (which are based on the so called quadratic ansätze) is obtained through an approximation of the macro-displacement field based on a second-order Taylor expansion. The form of the overall elastic moduli obtained through the two homogenization approaches, here proposed, is analyzed and the differences are highlighted. An evaluation of the developed method in comparison with other recently proposed in literature is carried out in the example where a three-phase orthotropic material is considered. The characteristic lengths of the second-order equivalent continuum are obtained by both the asymptotic and the computational procedures here analyzed. The reliability of the proposed approach is evaluated for the case of shear and extensional deformation of the considered two-dimensional infinite elastic medium subjected to periodic body forces; the results from the second-order model are compared with those of the heterogeneous continuum.     

Fully implicit formulation of elastoplastic homogenization problem for two-scale analysis

In this study, using a virtual work equation, a micro-/macro-kinematic relation and a linearized constitutive relation, a boundary value problem is fully implicitly formulated to determine perturbed displacement increment fields in elastoplastic unit cells for two-scale analysis. It is shown that this implicit homogenization problem can be iteratively solved with quadratic convergences by successively updating strain increment fields in unit cells, and that the boundary value problem formulated provides a computational algorithm which is versatile for initial setting of strain increment fields. The computational algorithm developed is then examined by performing a two-scale analysis of a holed plate with an elastoplastic micro-structure, subjected to tensile loading. This demonstrates that the convergence in iteratively solving the implicit homogenization problem strongly depends on the initial setting of strain increment fields in unit cells.     

Asymptotic analysis of perforated plates and membranes. Part 1: Static problems for small holes

Static problems for the elastic plates and rods periodically perforated by small holes of different shapes are solved using the asymptotic approach based on the combination of the asymptotic technique and the multi-scale homogenization method. Using the asymptotic homogenization method the original boundary-value problem is reduced to the combination of two types of problems. First one is a recurrent system of unit cell problems with the conditions of periodic continuation. And the second problem is a homogenized boundary-value problem for the entire domain, characterized by the constant effective coefficients obtained from the solution of the unit cell problems. The combination of the perturbation method and the technique of successive approximations is applied for the solution of the unit cell problems. Taking into the account small size of holes the method of perturbation of the shape of the boundary and the Schwarz alternating method are used. The problems of torsion of a rod with perforated cross-section; deflection of the perforated membrane loaded by a normal load; and bending of perforated plates with circular and square holes are considered consecutively. The error of the applied asymptotic techniques is estimated and the high accuracy of the obtained solutions is demonstrated.     

一种模拟动边界绕流的锐利界面浸入边界法

为避免复杂贴体网格的更新和畸形对动边界流场计算效率、精度的影响,以充分掌握结构场的受力特性,采用一种改进的锐利界面（sharp-interface）浸入边界法模拟具有动边界绕流的流动问题。该方法将计算域中的固体视为流体,固体边界离散为若干个拉格朗日网格点,通过在界面单元处插值重构流动参数（速度）,将其直接作为流动求解器的边界条件,由此来反映固体边界的影响。即通过构造“虚拟点—受力点—垂足点”的计算结构,借助双线性插值得到虚拟点的速度,再通过强制满足固体边界的无滑移条件计算出受力点的速度,以此为边界条件,最终求解基于浸入边界法的耦合系统方程,实现复杂动边界的流动数值模拟。采用C++编写该浸入边界法的数值程序,以单圆柱绕流为验证算例,通过与文献和实验结果的对比,验证了该方法的准确性和可靠性。在此基础上,对主动运动椭圆柱绕流问题进行了精细计算,探讨了不同轴长比(A_R)、不同攻角($ \theta $)下的椭圆柱对尾涡结构分布特征和水力不稳定现象的影响。捕捉到了反对称S型、“P+S” Ⅰ型、“P+S” Ⅱ型尾涡脱落模态,漩涡强度、涡脱频率和升阻比随A_R和$ \theta $的变化规律,以及确定了升阻比临界攻角(25°)。