含椭圆孔有限板应力集中的复变函数直接解法

采用复变函数级数展开方法研究了含椭圆孔的有限大矩形板在承受拉伸和剪切载荷时的应力场和应力集中系数,通过直接对边界力的差值进行最小化求取级数中的待定系数,避免了通常采用的将椭圆孔变换成圆孔的保角变换过程,从而极大地简化了求解过程.与有限元计算的对比分析表明,对于承受单向拉伸载荷的含中心椭圆孔(两轴比在0.7至2之间)的有限尺寸矩形板,计算精度高,且较之传统的保角变换法更简单,易于应用.另外,给出了计算含中心椭圆孔(两轴比为0.8)的细长板在拉伸载荷作用下以及含中心圆孔的细长板在面内剪切载荷作用下孔边应力集中系数的经验公式,便于工程应用.     

压缩载荷作用下复合材料开孔补强稳定性分析

运用有限元软件MSC.Nastran分别分析了压缩载荷作用下的复合材料板在无孔、开孔及开孔补强后的稳定性问题.在开孔复合材料板稳定性分析中,讨论了开孔孔径和开孔位置的影响;在补强中,分别选取不同开孔孔径和开孔位置研究补强参数对板稳定性的影响.研究表明:开孔降低了复合材料板的稳定性,通过补强可提高其稳定性;开孔孔径和开孔位置对复合材料板稳定性的影响较大,补强参数随开孔孔径和开孔位置改变而改变,且对复合材料板的稳定性有所影响;补强后板的稳定性要好于无孔复合材料板的稳定性.     

带孔有限宽板孔边应力集中系数的修正解法

 通过弹性力学方法可以得到带孔无限大(宽) 板应力场的理论解, 但带孔有限宽板的理论解却比较难于得到. 本文从二者孔边应力分布的相似性出发, 引入应力分布函数的修正系数, 从而建立了带孔有限宽板孔边应力集中系数的修正解法, 对于多种不同宽度的带孔板, 孔边应力集中系数的修正解与有限元数值解进行了比较, 误差在允许范围内, 修正因子具有其工程应用合理性.     

集中载荷作用下正交复合材料板奇异应力场的焦散线模拟实验

本文利用焦散线理论和复合材料力学的弹性理论封闭解，对集中载荷作用下半无限正交复合材料板的奇异应力场进行了光力学可视化分析，系统地推导了奇异区域应力集中问题的焦散线及初始曲线参数方程，建立了应用集中载荷与焦散斑特征尺寸的相互依赖关系，并对不同类型正交复合材料在集中载荷作用下应力奇异区的焦散线与初始曲线进行了模拟，分析了集中载荷作用区域的应力奇异特征，并与实验结果进行了比较。     

不同铺层角含孔复合材料板的损伤研究

针对0o、45o、90o铺层角复合材料层合板的含孔结构损伤问题,提出了一种基于层合板各铺层孔边应力解析解的首次损伤载荷系数分析计算模型。根据非均匀各向异性层合板的弹性特性,采用复变函数曲线映射方法获取了层合板孔边界积分方程,计算获得了0o、45o、90o角度铺层层合板各铺层的孔边纤维主方向和垂直于纤维主方向的应力分量;采用Tsai-Hill强度理论,对层合板各铺层进行孔边首次损伤载荷系数计算。分析结果表明:试件左右两端面在受到均布拉伸载荷p的作用下,各铺层中具有90o铺层角的铺层首次损伤载荷系数最小,具有0o铺层角的铺层首次损伤载荷系数最大,说明具有90o铺层角的铺层最先出现损伤,对应铺层首次损伤出现在孔边90o方向区域。将计算值与现有文献结果进行比较,误差小于10%,二者具有较好的一致性。     

热超弹性薄板非对称拉伸的分岔和稳定性

本文应用超弹性材料的有限变形理论分析了在面内等双向拉伸死载荷作用下不可压热超弹性方形薄板发生非对称变形的分岔及其稳定性问题.给出了方板变形的分岔曲线和临界载荷,发现对受面内等双向拉伸载荷作用的均匀方板,当拉伸载荷值较小时,方板双向等伸长变形,发生对称的拉伸变形;但当此载荷值大于某一临界值时,从方板的对称拉伸变形中分岔出非对称的变形,方板在两个方向的变形不再相等.通过变形发生分岔前后的能量比较发现,分岔后的对称变形是不稳定的,而非对称变形是稳定的.同时,给出了板中的应力分布曲线,并由不同温度下变形的分岔曲线和应力分布曲线讨论了温度对方板变形和板中的应力分布的影响.     

双向加载条件下尼龙6-橡胶复合材料的应力松弛研究

在双向测试系统上进行了不同纵向应变与不同横向应变的双向松弛实验,研究了在双向拉伸载荷作用下单向尼龙6-橡胶复合材料的应力松弛特性．为了预测尼龙6-橡胶复合材料的应力松弛规律,提出了一个松弛型本构模型．当试件承受双向拉伸载荷作用时,将松弛型本构模型获得的理论曲线和实验数据进行了对比,二者取得了较好的一致性．     

各向异性叠层矩形板大挠度弯曲问题

本文以板的中心挠度为摄动参数,采用摄动方法获得承受均布载荷,四边固定的对称角交叠层板的大挠度弯曲问题的近似解.与文献[12]不同,本文在每一级近似中,应用伽辽金方法求出各级近似解.文中计算了碳纤维复合材料对称角交叠层板的数值结果,绘出了载荷与中心挠度关系曲线以及列出有代表性的几点的应力计算公式.另外,本文研究了玻璃纤维复合材料正交对称叠层方板的大挠度特性,与文献[6]采用有限差分法所得的结果比较表明,采用本文的方法所得结果与试验值吻合得较好.     

高炉炉壳开孔位置对应力集中的影响

考虑到冶金行业中高炉炉壳开孔的实际情况，本文应用有限元分析的方法研究受远场均匀拉伸载荷，二维有限区域内菱形分布的圆孔中间不同开孔位置下的应力分布，得到最大应力集中系数随孔位置变化的三维变化曲面。此外，孔沿座标轴及沿原孔边缘位置变化对应力集中系数的影响被详细研究，从而为合理设计炉壳开孔提供了理论依据。     

横向爆炸载荷下开孔板的动应力集中因子

基于ANSYS 5.7/LS-DYNA程序,对3 m3 m0.25 m四边固支和简支、中心具有0.3 m0.3 m方孔的开孔板和无孔板对应点在两种下三角爆炸载荷作用下的应力响应进行了分析;由开孔板和无孔板边对应点的主应力时程曲线,对提出的能量密度时间分布函数的绝对值平方进行变上限积分,按其比值确定动应力集中因子,该方法简单易行。     

Buckling stresses of composite tubes under biaxial compressive loads

An analytical model describing the instability of specially orthotropic composite tubes with geometric imperfections subject to biaxial compressive loads and under clamped-clamped boundary conditions is developed. Furthermore, the range of validity of the present solution is clarified, and comparisons are made to some studies on isotropic cylindrical shells. Six E-glass woven fabric-epoxy composite tubes with the same internal radius and different thicknesses and longitudinal lengths were fabricated and subjected to various combinations of external hydrostatic pressure and axial compressive load simultaneously. The normalized buckling stresses were found to agree in general with the theoretical predictions at various biaxial loadings. The buckling envelopes in normalization form provide useful design data on the strength of specially orthotropic composite tubes under a realistic range of biaxial loading conditions.     

Mixed numerical–experimental technique for orthotropic parameter identification using biaxial tensile tests on cruciform specimens

This paper presents a mixed numerical–experimental method for the identification of the four in-plane orthotropic engineering constants of composite plate materials. A biaxial tensile test is performed on a cruciform test specimen. The heterogeneous displacement field is observed by a CCD camera and measured by a digital image correlation (DIC) technique. The measured displacement field and the subsequently computed strain field are compared with a finite element simulation of the same experiment. The four independent engineering constants are unknown parameters in the finite element model. Starting from an initial value, these parameters are updated till the computed strain field matches the experimental strain field. Two specimen geometries are used: one with a centered hole to increase the strain heterogeneity and one without a hole. It is found that the non-perforated specimen yields the most accurate results.     

ANALYTICAL SOLUTIONS TO STRESS CONCENTRATION PROBLEM IN PLATES CONTAINING RECTANGULAR HOLE UNDER BIAXIAL TENSIONS

The stress concentration problem in structures with a circular or elliptic hole can be investigated by analytical methods. For the problem with a rectangular hole, only approximate results are derived. This paper deduces the analytical solutions to the stress concentration problem in plates with a rectangular hole under biaxial tensions. By using the U-transformation technique and the finite element method, the analytical displacement solutions of the finite element equations are derived in the series form. Therefore, the stress concentration can then be discussed easily and conveniently. For plate problem the bilinear rectangular element with four nodes is taken as an example to demonstrate the applicability of the proposed method. The stress concentration factors for various ratios of height to width of the hole are obtained.     

Shape optimization of the hole in an orthotropic plate

The exploration in this work is how to minimize the stress concentration around the edge of the hole in an orthotropic plate. The study first presents the analytical solution of the stress distribution around arbitrary holes using the complex variable method and then carries out the shape optimization using the mixed penalty function method. In the optimization process, optimal holes and stress distributions under the different factors are investigated, i.e., the loading, the Young’s modulus, and the fiber direction. Finally, we come to the conclusion that in the biaxial compressive load state, the shape and the stress are mainly affected by the loading, followed by the fiber direction and the Young’s modulus. In the pure shear condition, all three factors determine the optimum results.     

Triangular grid method for stress-wave propagation in 2-D orthotropic materials

A triangular grid method is presented to calculate propagation problems of elastic stress waves in 2-D orthotropic materials. This method is based on the dynamic equilibrium equations of the computational cells formed among the auxiliary triangular grids. The solution is obtained by calculating alternately the nodal displacements and the central point stresses of the spatial grids. The numerical results are compared with the corresponding solutions of the finite element method. Comparisons show that the triangular grid method yields a higher calculational speed than the finite element method. The stress concentrations are investigated from wave-field analyses when the stress wave propagates within an orthotropic plate with a hole. Finally, the presented numerical method is used to study the features of wave propagation and diffraction in a square orthotropic plate with a hole when an impact load is applied to the top of the plate.This work was supported by National Natural Science Foundation of China (Nos. 10025212 and 10232040) and Natural Science Foundation of Liaoning province (No. 20021070).     

Stress Concentration in an Orthotropic Plate with a Circular Hole under Dynamic Loading

The paper sets forth a photoelastic method for the determination of the dynamic stress concentration factor near a hole in an orthotropic plate. The stress distribution at the periphery of a circular hole is analyzed. The stress concentration factors for orthotropic and isotropic plates under dynamic and statical loading are compared     

Plane-stress fracture testing of finite sheets under biaxial loads

A procedure which combines the Williams series-type stress- and displacement-field expressions at the crack-tip neighborhood with a suitable numerical scheme away from the crack-tip was employed in the determination of the plane-stress fracture properties of four finite 7076-T6 aluminum sheets containing cracks emanating from a circular hole under four biaxial loads. The compatibility of the analytical and numerical displacements at the nodal points along the boundary of the crack-tip neighborhood was utilized in formulating displacement-continuity expressions containing some undetermined constants which solution depends on the nature of the boundary loading conditions. By linear superposition of the displacement due to remote uniaxial load and the displacements due to remotely applied transverse load in the neighborhood of the crack-tip, biaxial-displacement-continuity expressions containing these important fracture properties—namely, the opening Mode I stress-intensity factorK, the nonsingular stress term associated with the stresses in the direction parallel to the plane of cracksA and the integration termB associated with the displacement in this direction—were evaluated. Because no known biaxial testing of this geometry had been reported prior to this research, the analytical procedure was used to select the optimum geometry required in a biaxial fracture test of a finite-sheet specimen containing cracks emanating from a circular hole. This geometric optimization of the specimen guaranteed uniformity of stress all over the volume of specimen and also made the alteration of the existing MTS test fixtures unnecessary. Four square sheets of 7075-T6 aluminum alloy containing a central hole with two collinear cracks emanating radially at the edge of the hole were then fabricated in accordance with the analytically determined geometric requirements. The biaxial fracture test was then conducted under four biaxial load factors (λ) of 0.0, 0.5, 1.0 and 1.5. The fracture toughness obtained in this research was compared with those reported for uniaxial loading of large panels. It was found that there is a good correlation between the reported fracture toughness and this work.     

Elastoplastic cracks moving in orthotropic crystals

The stress field, crack-tip plastic zones and total plastic displacement created around an infinite row of collinear elastoplastic constant width Griffith-type strip cracks moving within an orthotropic crystal are considered using the powerful method of dislocation layers. The method is applied with the BCS modelled elastoplastic cracks moving under mode III loading at constant crack-tip velocity, according to the Yoffe model. Simultaneously the analysis provides solutions for a corresponding single crack moving similarly within a finite orthotropic plate and a finite plate containing a surface crack. Analogous results for the corresponding mode I, mode II and purely elastic cracks can be deduced.     

Hole-shape optimization in a finite plate in the presence of auxiliary holes

Minimizing the stress concentration around holes in uniaxially loaded finite plates is an important consideration in engineering design. One method for reducing the stress concentration around a central circular hole in a uniaxially loaded plate is to introduce smaller auxiliary holes on either side of the original hole to help smooth the flow of the tensile principal-stress trajectories past the original hole. This method has been demonstrated by Heywood and systematically studied by Erickson and Riley. Erickson and Riley show that for a central-hole diameter-to-plate width ratio of 0.222, the maximum stress reduction is up to 16 percent. In recent work, Durelliet al. show that the stress concentrations around holes in uniaxially loaded plates can be minimized by changing the hole shape itself till an optimum hole profile with constant stress values respectively on the tensile and compressive segments of the hole boundary is reached. By this technique the maximum stress reduction obtained for the above case is up to 20 percent. In the present work, starting with the optimum sizes and locations of central and auxiliary circular holes for a finite plate given by Erickson and Riley, a systematic study of the hole-shape optimization is undertaken. A two-dimensional photoelastic method is used. For a central-hole diameter-to-plate width ratio of 0.222, the reduction in stress-concentration factor obtained after hole-shape optimization is about 30 percent. It is also shown that it is possible to introduce the ‘equivalent ellipse’ concept for optimized holes.     

Convex polynomial yield functions

It is shown that some of the recently proposed orthotropic yield functions obtained through the linear transformation method are homogeneous polynomials. This simple observation has the potential to simplify considerably their implementation into finite element codes. It also leads to a general method for designing convex polynomial yield functions with powerful modeling capabilities. Convex parameterizations are given for the fourth, sixth and eighth order plane stress orthotropic homogeneous polynomials. Illustrations are shown for the modeling of biaxial and directional yielding properties of steel and aluminum alloy sheets. The parametrization method can be easily extended to general, 3D stress states.