一种计算复合材料等效弹性性能的有限元方法

在最小二乘意义下提出了一种计算复合材料等效弹性性能的有限元方法.这种方法由于考虑了等效弹性张量各分量之间的耦合关系,所求得的等效弹性常数比传统方法更可靠,可适用于求解含任意形状的夹杂和夹杂物问题.通过算例计算了在不同弹性模量对比度下两相复合材料的等效弹性性能,并与相关的理论及数值结果进行了比较,结果表明,利用该方法计算含夹杂复合材料等效弹性常数是可行的.     

类桁架夹层板的等效弹性常数研究

从应变能等效出发,将具有周期性分布的夹层板的类桁架夹芯与各向异性连续材料等效,给出了相应的宏观等效弹性常数,进而用有限元方法计算了实际夹层板和等效夹层板的结构响应,用一个算例证明了该文方法的有效性.通过对类桁架夹芯的等效弹性常数的计算,结果表明该文方法可以得到较为准确的等效弹性常数,且较其它类型的均匀化方法大大降低了计算量.     

倾斜内锁型三维机织陶瓷基复合材料的细观力学模型

利用平均化方法提出了倾斜内锁型三维机织陶瓷基复合材料弹性性能分析的三维细观力学模型,对材料的弹性性能进行了预测。这个力学模型考虑了倾斜内锁型三维机织陶瓷基复合材料经向纤维束的弯曲和纬向纤维束的平直,纤维束的横截面形状尺寸和相邻纤维束之间的孔洞以及材料制造过程中碳纤维性能下降对弹性性能的影响。基于层合板理论,提出两种单胞应变状态假设分别对材料的九个弹性常数进行了推导计算,结果表明两种方法理论的预测值非常接近。计算结果与实验值比较吻合,表明所提出的细观力学模型是合理的,可以为纺织陶瓷基复合材料的优化设计提供有价值的参考。     

考虑材料各向异性的熔丝制造PLA点阵结构弹性各向同性设计

增材制造技术的兴起激发了国内外学者对结构创新设计的热情. 然而, 增材制造材料的各向异性为结构力学性能的预测与设计带来了一定的困难. 为了准确预测熔丝制造聚乳酸(PLA)材料和点阵结构的弹性性能, 并实现点阵结构的弹性各向同性设计, 首先, 本文采用正交各向异性弹性模型来描述PLA材料的弹性行为, 通过实验和计算得到了正交各向异性模型需要的9个独立的弹性常数. 然后, 设计了一种力学性能可调的二维组合桁架点阵结构, 基于代表体元法, 在不考虑材料各向异性的情况下推导出了其平面内等效弹性性能的解析表达式及弹性各向同性条件. 最后, 根据PLA材料的各向异性调整点阵结构内部杆件的弹性模量和厚度, 并基于代表体元法重新推导出了点阵结构平面内等效弹性性能的解析表达式及其弹性各向同性条件. 研究结果表明, 正交各向异性弹性模型适用于描述熔丝制造PLA材料的弹性行为, 基于该模型能够准确预测PLA材料在任意方向上的弹性模量. 在预测与设计熔丝制造点阵结构的力学性能时需要充分考虑材料的各向异性. 在考虑材料的各向异性之后, 基于代表体元法调整点阵结构的几何尺寸, 能够实现部分点阵结构的弹性各向同性设计.      

基于迭代法的非线性弹性均质化研究

微观结构对复合材料的宏观力学性能具有至关重要的影响,通过合理设计复合材料微观结构可以得到期望的宏观性能.均质化方法作为一种有效的设计方法,它从微观结构的角度出发,利用均匀化的概念,实现了对复合材料宏观力学性能的预测和设计.而当考虑非线性因素,均质化的实现就非常困难.本文利用双渐近展开方法,将位移按照宏观位移和微观位移展开,推导了非线性弹性均质化方程.通过直接迭代法,对非线性弹性均质化方程进行了求解,并给出了具体的迭代方法和实现步骤.本文基于迭代步骤和非线性弹性均质化方程编写MATLAB程序,对3种典型本构关系的周期性多孔材料平面问题进行了计算,对比细致模型的应变能、最大位移和等效泊松比,对程序及迭代方法的准确性进行了验证.之后对一种三元橡胶基复合材料进行多尺度均质化,将其分为芯丝尺度和层间尺度.用线弹性的均质化方法得到了芯丝尺度的等效弹性参数,并将其作为层间尺度的材料参数.在层间尺度应用非线性弹性均质化方法对结构进行计算,得到材料的宏观等效性能,并以实验结果为基准进行评价.     

基于细观力学方法的底部充填封装芯片接合层的热应力计算

底部充填是一种用来提高电子产品在恶劣环境下工作的稳定性及可靠性的技术,是电子制造产业的常用方法．本文基于细观力学方法建立了计算底部充填封装芯片热应力的方法．针对底部充填封装芯片焊锡-充填物接合层的结构特点,我们建立了接合层的均一化模型,并从理论上推导了接合层的等效弹性常数、热膨胀系数和导热系数．运用该均一化模型,我们对封装芯片工作产热导致的热传导和热应力问题进行了有限元数值模拟,计算的结果与接合层未均一化的模型具有较好的一致性,而计算效率极大提高,显示了该方法在计算底部充填封装芯片热应力方面的可行性．     

基于迭代法的非线性弹性均质化研究

微观结构对复合材料的宏观力学性能具有至关重要的影响, 通过合理设计复合材料微观结构可以得到期望的宏观性能. 均质化方法作为一种有效的设计方法, 它从微观结构的角度出发, 利用均匀化的概念, 实现了对复合材料宏观力学性能的预测和设计. 而当考虑非线性因素, 均质化的实现就非常困难. 本文利用双渐近展开方法, 将位移按照宏观位移和微观位移展开, 推导了非线性弹性均质化方程. 通过直接迭代法, 对非线性弹性均质化方程进行了求解, 并给出了具体的迭代方法和实现步骤. 本文基于迭代步骤和非线性弹性均质化方程编写MATLAB 程序, 对3种典型本构关系的周期性多孔材料平面问题进行了计算, 对比细致模型的应变能、最大位移和等效泊松比, 对程序及迭代方法的准确性进行了验证. 之后对一种三元橡胶基复合材料进行多尺度均质化, 将其分为芯丝尺度和层间尺度. 用线弹性的均质化方法得到了芯丝尺度的等效弹性参数, 并将其作为层间尺度的材料参数. 在层间尺度应用非线性弹性均质化方法对结构进行计算, 得到材料的宏观等效性能, 并以实验结果为基准进行评价.      

一类多孔固体的等效偶应力动力学梁模型

一维多孔固体结构可采用等效连续介质梁模型来研究其动力学行为. 当类梁结构的高度尺寸和多孔固体单胞结构尺寸相近时,等效模型的力学行为会产生尺寸效应现象. 等效经典模型由于不包含尺度参数而无法描述尺寸相关特点,而广义连续介质力学模型则可以准确地考虑尺寸效应的影响. 基于偶应力理论,对一类单胞含有圆形孔洞的周期性多孔固体类梁结构,给出了分析其横向自由振动的等效连续介质铁木辛柯梁模型. 通过对单胞分析,在应变能等价和几何平均的意义下,定义了等效偶应力介质的材料常数. 利用已有的材料常数,推导了等效铁木辛柯梁的动力学微分方程. 将实际多孔固体结构进行完全的动力学有限元离散计算,所获得的解作为精确解以检验等效梁模型所获得的频率和振型的精度. 振型的比较借助于模态置信准则矩阵方法. 大量算例表明,等效偶应力铁木辛柯梁模型在频率和振型两方面均具有较高的计算精度. 重点研究了单胞孔径的相对大小、类梁结构高度与单胞尺寸比以及类梁结构长高比对等效梁模型精度的影响. 在此基础上,偏保守地建议了多孔固体类梁结构自振分析方法.      

考虑面层约束时蜂窝芯弹性常数的确定

本文研究了面板约束效应对蜂窝芯弹性性能的影响并基于六边形蜂窝芯夹层板的代表性体单元建立了考虑面板约束效应的蜂窝芯位移模式.根据真实蜂窝芯代表性单元与其等效材料的代表性单元在宏观均匀应变作用下的总弹性应变能相等,导出了蜂窝芯材料等效弹性常数的公式,进一步探讨了蜂窝几何参数对其弹性常数的影响规律.通过与现有理论结果、有限元结果和实验数据进行对比证实本文导出的弹性常数公式具有较好的预报精度.结果表明面板约束对蜂窝芯等效弹性常数有显著影响.     

三参量固体模型粘弹性输流管道的动力特性分析

推导了三参量固体模型粘弹性输流管道的振动微分方程 ,计算了在不同无量纲松弛系数和弹性常数比下管道的无量纲临界流速和无量纲自振复频率 ,并给出了前三阶复频率与流速的关系 .计算结果表明 ,质量比、无量纲松弛系数及无量纲弹性常数比对输流管道的动力特性均有影响 .     

The response of circular composite plates to underwater blast: Experiments and modelling

We present a new experimental technique to allow laboratory-scale observation of underwater blast loading on circular plates, including dynamic deformation and failure of the plates as well as the sequence of cavitation events in water. The apparatus is used to measure and compare the responses of a quasi-isotropic glass/vinylester composite and of a woven carbon/epoxy plate. Dynamic explicit FE simulations are conducted and their predictions are found in good agreement with experiments. Measurements and FE predictions are used to validate a recently developed theoretical model for the response of elastic orthotropic plates to underwater blast.     

蜂窝夹层板结构等效模型比较分析

在对蜂窝夹层板结构进行有限元分析时,要对其进行等效处理,采取等效方法的合理性将直接影响到计算结果的准确性.分别采用Reissner理论、Hoff理论、三明治夹芯板理论三种不同的等效方法建立有限元模型,然后进行了静力分析和模态分析,并将每种等效方法的计算结果与实体单元建立的蜂窝夹层板模型计算结果进行了比较.与Reissn...     

Compatible model for herringbone bond masonry: Linear elastic homogenization,failure surfaces and structural implementation

A simplified kinematic procedure at a cell level is proposed to obtain in-plane elastic moduli and macroscopic masonry strength domains in the case of herringbone masonry. The model is constituted by two central bricks interacting with their neighbors by means of either elastic or rigid-plastic interfaces with friction, representing mortar joints. The herringbone pattern is geometrically described and the internal law of composition of the periodic cell is defined.A sub-class of possible elementary deformations is a-priori chosen to describe joints cracking under in-plane loads. Suitable internal macroscopic actions are applied on the Representative Element of Volume (REV) and the power expended within the 3D bricks assemblage is equated to that expended in the macroscopic 2D Cauchy continuum. The elastic and limit analysis problem at a cell level are solved by means of a quadratic and linear programming approach, respectively.To assess elastic results, a standard FEM homogenization is also performed and a sensitivity analysis regarding two different orientations of the pattern, the thickness of the mortar joints and the ratio between block and mortar Young moduli is conducted. In this way, the reliability of the numerical model is critically evaluated under service loads.When dealing with the limit analysis approach, several computations are performed investigating the role played by (1) the direction of the load with respect to herringbone bond orientation, (2) masonry texture and (3) mechanical properties adopted for joints.At a structural level, a FE homogenized limit analysis is performed on a masonry dome built in herringbone bond. In order to assess limit analysis results, additional non-linear FE analyses are performed, including a full 3D numerical expensive heterogeneous approach and models where masonry is substituted with an equivalent macroscopic material with orthotropic behavior and possible softening. Reliable predictions of collapse loads and failure mechanisms are obtained, meaning that the approach proposed may be used by practitioners for a fast evaluation of the effectiveness of herringbone bond orientation.     

The dynamic response of clamped rectangular Y-frame and corrugated core sandwich plates

The dynamic response of fully clamped, monolithic and sandwich plates of equal areal mass has been measured by loading rectangular plates over a central patch with metal foam projectiles. All plates are made from AISI 304 stainless steel, and the sandwich topologies comprise two identical face-sheets and either Y-frame or corrugated cores. The resistance to shock loading is quantified by the permanent transverse deflection at mid-span of the plates as a function of projectile momentum. At low levels of projectile momentum both types of sandwich plate deflect less than monolithic plates of equal areal mass. However, at higher levels of projectile momentum, the sandwich plates tear while the monolithic plates remain intact. Three-dimensional finite element (FE) calculations adequately predict the measured responses, prior to the onset of tearing. These calculations also reveal that the accumulated plastic strains in the front face of the sandwich plates exceed those in the monolithic plates. These high plastic strains lead to failure of the front face sheets of the sandwich plates at lower values of projectile momentum than for the equivalent monolithic plates.     

Nonlinear analysis of thick plates on an elastic foundation by HT FE with p-extension capabilities

The paper is concerned with the development of hybrid-Trefftz (HT) p-element for nonlinear analysis of Reissner-Mindlin plates resting on an elastic foundation. The foundation may be of Winkler-type or Pasternak-type. Exact solutions of the Lame-Navier equations are used for the in-plane intraelement displacement field and an incremental form of the basic equations is adopted. With the aid of incremental form of these equations, all nonlinear terms may be taken as pseudo-loads. Moreover, some modifications have been made on the nonlinear boundary equations to simplify the ensuing derivation. As a result, the in-plane and out-of-plane equations are uncoupled, and then the derivation for the HT finite element (FE) formulation becomes very simple. The practical efficiency of the new element model has been assessed through several examples.     

An Experimental–Numerical Methodology for a Rapid Prototyped Application Combined with Finite Element Models in Vertebral Trabecular Bone

In the present study, a novel evaluation method involving rapid prototyped (RP) technology and finite element (FE) analysis was used to study the elastic mechanical characteristics of human vertebral trabecular bone. Three-dimensional (3D) geometries of the RP and FE models were obtained from the central area of vertebral bones of female cadavers, age 70 and 85. RP and FE models were generated from the same high-resolution micro-computed tomography (μCT) scan data. We utilized RP technology along with FE analysis based on μCT for high-resolution vertebral trabecular bone specimens. RP models were used to fabricate complex 3D objects of vertebral trabecular bone that were created in a fused deposition modeling machine. RP models of vertebral trabecular bone are advantageous, particularly considering the repetition, risks, and ethical issues involved in using real bone from cadaveric specimens. A cubic specimen with a side length of 6.5 mm or a cylindrical specimen with a 7 mm diameter and 5 mm length proved better than a universal cubic specimen with a side length of 4 mm for the evaluation of elastic mechanical characteristics of vertebral trabecular bones through experimental and simulated compression tests. The results from the experimental compression tests of RP models closely matched those predicted by the FE models, and thus provided substantive corroboration of all three approaches (experimental tests using RP models and simulated tests using FE models with ABS and trabecular bone material properties). The RP technique combined with FE analysis has potential for widespread biomechanical use, such as the fabrication of dummy human skeleton systems for the investigation of elastic mechanical characteristics of various bones.     

非均匀Winkler弹性地基上变厚度矩形板自由振动的DTM求解

针对非均匀Winkler弹性地基上变厚度矩形板的自由振动问题,通过一种有效的数值求解方法——微分变换法（DTM）,研究其无量纲固有频率特性。已知变厚度矩形板对边为简支边界条件,其他两边的边界条件为简支、固定或自由任意组合。采用DTM将非均匀Winkler弹性地基上变厚度矩形板无量纲化的自由振动控制微分方程及其边界条件变换为等价的代数方程,得到含有无量纲固有频率的特征方程。数值结果退化为均匀Winker弹性地基上矩形板以及变厚度矩形板的情形,并与已有文献采用的不同求解方法进行比较,结果表明,DTM具有非常高的精度和很强的适用性。最后,在不同边界条件下分析地基变化参数、厚度变化参数和长宽比对矩形板无量纲固有频率的影响,并给出了非均匀Winkler弹性地基上对边简支对边固定变厚度矩形板的前六阶振型。     

基于FE重构方法的冲击破碎仿真

提出了一种结合FE和SPH的3D冲击破碎问题仿真方法——FE重构法。通过立方体FE单元填充的方式对任意几何体进行离散,并建立粒子一形心重合模型,然后将用LS-dyna软件对粒子模型进行SPH撞击仿真;基于每一个步长的仿真结果,进行FE单元的重构,并结合失效准则进行失效分析,最终得到FE与SPH混合的仿真结果。针对超高速...     

A new analytical model for the elastic–plastic behaviour of spot welded joints subjected to orthogonal load

An analytical procedure for the evaluation of the elastic–plastic stiffness behaviour of spot welded joints is presented. The procedure is based on a new model of spot weld region: a circular plate having variable thickness with a central rigid nugget, which is resolved using an original analytical method.The closed-form solution allows to describe the displacement of a rigid nugget when an axial orthogonal load is applied on the plate while plasticity and large deflections are present. The goal is to reach a reliable spot weld region model which can be used as the basis to develop a spot weld element in FE analysis even when plasticity and large deflections are in effect.The procedure is as completely original as no other can be found in the technical literature, and it has been applied to some examples of plates usually employed for spot weld analysis. The analytical results obtained by using the new general relations precisely match those obtained modelling spot weld area by FEA.     

Compressive response and failure of braided textile composites: Part 2—computations

In this, the second part of a two part paper, results obtained by using the finite element (FE) method in conjunction with micromechanics to predict the effective elastic stiffness and strength of a carbon 2D triaxially braided composite (2DTBC), are presented. The 3D FE based micromechanics study was carried out on one representative unit cell (RUC) of the carbon 2DTBC (the “micromodel”). The FE models were first used to determine the macroscopic elastic orthotropic stiffnesses of the 2DTBC. The micromodel was deemed acceptable (in terms of the number of elements used in the mesh of the micromodel) if the elastic stiffnesses it displayed were within 5% of the elastic properties found experimentally. Subsequently, buckling eigenmodes were determined for the FE RUC under uniaxial and biaxial loading states, corresponding to the experimental investigation reported in part I of this two part paper. The lowest symmetric modes were identified and these mode shapes were used as imperfections to the FE model for a subsequent nonlinear response analysis using an arc-length method in conjunction with the ABAQUS commercial FE code. The magnitude of the imperfections was left as a parameter and its effect on the predicted response was quantified. The present micromechanics computational model provides a means to assess the compressive and compressive/tensile biaxial strength of the braided composites and its dependence on various microstructural parameters. It also serves as a tool to assess the most significant parameter that affects compressive strength.