Size-dependent effect on biaxial and shear nonlinear buckling analysis of nonlocal isotropic and orthotropic micro-plate based on surface stress and modified couple stress theories using differential quadrature method

The size-dependent effect on the biaxial and shear nonlinear buckling analysis of an isotropic and orthotropic micro-plate based on the surface stress, the modified couple stress theory （MCST）, and the nonlocal elasticity theories using the differential quadrature method （DQM） is presented. Main advantages of the MCST over the classical theory （CT） are the inclusion of the asymmetric couple stress tensor and the consideration of only one material length scale parameter. Based on the nonlinear von Karman assumption, the governing equations of equilibrium for the micro-classical plate consid- ering midplane displacements are derived based on the minimum principle of potential energy. Using the DQM, the biaxial and shear critical buckling loads of the micro-plate for various boundary conditions are obtained. Accuracy of the obtained results is validated by comparing the solutions with those reported in the literature. A parametric study is conducted to show the effects of the aspect ratio, the side-to-thickness ratio, Eringen＇s nonlocal parameter, the material length scale parameter, Young＇s modulus of the surface layer, the surface residual stress, the polymer matrix coefficients, and various boundary conditions on the dimensionless uniaxial, biaxial, and shear critical buckling loads. The results indicate that the critical buckling loads are strongly sensitive to Eringen＇s nonlocal parameter, the material length scale parameter, and the surface residual stress effects, while the effect of Young＇s modulus of the surface layer on the critical buckling load is negligible. Also, considering the size dependent effect causes the increase in the stiffness of the orthotropic micro-plate. The results show that the critical biaxial buckling load increases with an increase in G12/E2 and vice versa for E1/E2. It is shown that the nonlinear biaxial buckling ratio decreases as the aspect ratio increases and vice versa for the buckling amplitude. Because of the most lightweight micro-composite materials with high strength/weight and stiffness/weight ratios, it is anticipated that the results of the present work are useful in experimental characterization of the mechanical properties of micro-composite plates in the aircraft industry and other engineering applications.

PRACTICAL ANALYSIS OF ORTHOTROPIC PLATES SUPPORTED IN ONE DIRECTION

A practical method for computing the one-way rectangular orthotropicplate(isotropic plate as a special case)is suggested in this paper.The supported condi-tions in two opposite edges may be simply supported,continuous or supportednonsymmetrically and the other two opposite edges are slide-supported or free.A series ofsimplified formulas are given for calculating the bending moments along the cross section(loaded section),in which the acting point of the concentrated load or the center of a rec-tangular uniform load is located.The valid range and accuracy of these formulas were stud-ied and the approximate results were examined and compared extensively with those by thetriangular series solution or finite element method.

Bending stress of rolling element in elastic composite cylindrical roller bearing

A new structure design method of elastic composite cylindrical roller bearing is proposed, in which PTFE is embedded into a hollow cylindrical rolling element, according to the principle of creative combinations and through innovation research on cylindrical roller bearing structure. In order to systematically investigate the inner wall bending stress of the rolling element in elastic composite cylindrical roller bearing, finite element analysis on different elastic composite cylindrical rolling elements was conducted. The results show that, the bending stress of the elastic composite cylindrical rolling increases along with the increase of hollowness with the same filling material. The bending stress of the elastic composite cylindrical rolling element decreases along with the increase of the elasticity modulus of the material under the same physical dimension. Under the same load, on hollow cylindrical rolling element, the maximum bending tensile stress values of the elastic composite cylindrical rolling element after material filling at 0° and 180° are 8.2% and 9.5%, respectively, lower than those of the deep cavity hollow cylindrical rolling element. In addition, the maximum bending-compressive stress value at 90° is decreased by 6.1%.

Using Refined Theory to Studied Elastic Wave Scattering and Dynamic Stress Concentrations in Plates with Two Cutouts

In this paper, based on complex variables and conformal mapping methods, using the refined dynamic equation of plates, elastic wave scattering and dynamic stress concentrations in plates with two cutouts were studied. Applying the orthogonal function expansion method, the problem to be solved can be reduced into the solution of a set of infinite algebraic equations. According to free boundary conditions, numerical results of dynamic moment concentration factors in thick plates with two circular cutouts analyze that: there will be more complex interaction changes between two-cutout situation than single cutout situation. In the case of low frequency or high frequency and thin plate, the hole-spacing in the absence of coupling interactions was larger or smaller. The numerical results and method can be used to analyze the dynamics and strength of plate-like structures.

Bending and Vibrations of a Thick Plate with Consideration of Bimoments

The paper is dedicated to the development of the theory of orthotropic thick plates with consideration of internal forces, moments and bimoments. The equations of motion of a plate are described by two systems of six equations. New equations of motion of the plate and the boundary conditions relative to displacements, forces, moments, and bimoments are given. As an example, the problems of free and forced oscillations of a thick plate are considered under the effect of sinusoidal periodic load. The problem is solved by Finite Difference Method. Eigenfrequencies of the plate are determined, numeric maximum values of displacements, forces and moments of the plate are obtained depending on the frequency of external force. It is shown that when the value of the frequency of external effect approaches the eigenfrequency, there occurs an increase in displacement, force and moment values;that testifies a gradual transition of the motion of plate points into the resonant mode.

Three-Dimensional Thermo-Elastic-Plastic Finite Element Method Modeling for Predicting Weld-Induced Residual Stresses and Distortions in Steel Stiffened-Plate Structures

The objective of the present paper is to develop nonlinear finite element method models for predicting the weld-induced initial deflection and residual stress of plating in steel stiffened-plate structures. For this purpose, three-dimensional thermo-elastic-plastic finite element method computations are performed with varying plate thickness and weld bead length (leg length) in welded plate panels, the latter being associated with weld heat input. The finite element models are verified by a comparison with experimental database which was obtained by the authors in separate studies with full scale measurements. It is concluded that the nonlinear finite element method models developed in the present paper are very accurate in terms of predicting the weld-induced initial imperfections of steel stiffened plate structures. Details of the numerical computations together with test database are documented.

Computational Complex Method for Finite Elastic Plane Problem with Multiple Elliptical Holes

把多复变量应力函数和边界配点最小二乘法相结合，计算含有任意多个椭圆孔有限大小弹性板的应力场．每个孔的大小、位置为任意．板的边界由下列四种边界条件以及它们的组合所组成：１）已知Ｐｘ和Ｐｙ的应力边界，２）已知Ｖｘ和Ｖｙ的位移边界，３）已知法向位移ＶＮ和切向力ＰＴ的混合边界，４）已知法向力ＰＮ和切向位移ＶＴ的混合边界．编制了相应的ＦＯＲＴＲＡＮ程序，进行考题和算例分析，结果表明本方法行之有效．

A mechanical study of personalised Ti6Al4V tibial fracture fixation plates with grooved surface by finite element analysis

Low shape matching and high stress shielding rates between bone plate and human bone are not conducive to the primary healing of fracture.In this study,taking the fracture site of the lower one‐third of human tibia as an application case,six types of personalised Ti6Al4V tibial plates with grooved surface were designed and evaluated by reverse en-gineering and finite element analysis.The results showed that the grooved design can reduce the stress shielding rate of bone plate and promote the facture healing.Among the six types of bone plates,the‘OUT-MI’bone plate has the lowest stress shielding rate and the most uniform stress distribution.Meanwhile,with the increasing tibial load during the convalescence,the average stress and maximum axial displacement of the tibial fracture surface increased,which can effectively improve the bone regeneration in the tibial fracture area.Moreover,there was no significant difference in four-point bending performance between the‘OUT-MI’bone plate and the‘STR-BE’bone plate,indicating that the mechanical properties of this bone plate were reliable.The results provide a theoretical basis for the design of fracture fixation plates on clinical treatment.

基于正交异性等效的双向加筋板结构变形简化分析方法

[目的]随着船舶不断向大型化、复杂化发展,舱段级以上的船体结构有限元模型的网格数量将急剧增加,导致碰撞、冲击、接触等大型非线性力学问题均难以求解,故提出一种基于正交异性等效的双向加筋板结构变形简化方法。[方法]首先,将现行成熟的单向加筋板平面应力简化方法推广至更复杂的双向加筋板平面弯曲问题,并引入正交方向上加筋板总惯性矩与板的惯性矩之比来反映结构的正交异性;然后,将惯性矩比值代入推广所得的加筋板等效平面弯曲本构方程,以实现材料正交异性的转化,从而在力学层面上兼顾结构的抗变形能力和中性轴移轴产生中面力的影响;最后,利用有限元计算,根据不同的位移分布对四边固支加筋板的变形模式进行分类,并将加筋板实际结果与该方法及传统方法的等效结果进行误差对比分析。[结果]对比结果表明,在船舶双向加筋板结构中,该方法最多可减少84%的网格数量,且3种变形模式下的等效误差均可控制在6%以内,远低于2种传统方法。[结论]该方法的精度较高、适用范围更广、大幅了节省计算资源,可为大型船体结构非线性力学问题的直接建模仿真计算提供解决方案。

弹性复合圆柱滚子轴承结构设计研究

根据组合创新原理,通过对圆柱滚子轴承的结构进行创新研究,提出了一种在空心圆柱滚动体中嵌入聚四氟乙烯(PTFE)材料的弹性复合圆柱滚子轴承新结构的设计方法。为确定弹性复合圆柱滚动体的结构尺寸,定义滚动体的填充度K=d/D(D为滚动体直径,d为材料填充直径),用ANSYS软件对弹性复合圆柱滚子轴承进行有限元建模,分析了重载工况下弹性复合圆柱滚子轴承的接触应力、von Mises应力、弯曲应力以及变形量对滚动体结构尺寸的影响。结果表明,在重载工况下,弹性复合圆柱滚子轴承滚动体填充度最优值为55%,并通过试验验证了分析结果的正确性。所得结果为弹性复合圆柱滚子轴承的设计提供了基础性数据。

无缝线路稳定性分析有限元模型

利用有限元法建立包含钢轨、扣件、轨枕和道床阻力为一体的轨道框架模型。研究在温度力作用下无缝线路的臌曲失稳问题。推导相应的数值计算公式并编制了计算程序。轨道框架模型由4种单元组成:用考虑钢轨非线性变形的平面梁单元代表钢轨;无几何尺寸的两结点弹簧单元模拟钢轨扣件;弹性基础上的普通平面梁单元表示轨枕;弹簧单元模拟道床的横向、纵向阻力,并考虑了道床阻力的非线性特性。运用该模型,分析道床横向阻力、轨枕失效、曲线半径和线路初始弯曲对无缝线路稳定性的影响,得到不同工况下钢轨横向位移—温度曲线、钢轨内应力分布及钢轨和轨枕的横向变形分布曲线。

钢-超薄UHPC层轻型组合桥面性能研究

提出一种钢-超薄UHPC（Ultra-High Performance Concrete）层轻型组合桥面,既使得该组合桥面能运用于铺装层较薄的桥面结构,又降低了正交异性钢桥面的疲劳开裂风险,避免了沥青铺装的病害问题。以某大桥为工程背景,从有限元分析和试验两方面对此结构的性能进行研究。结果表明：35 mm UHPC层对正交异性钢桥面板受力性能改善明显,顶板应力幅下降达到68.72%,U肋和横隔板接近14.74%~34.11%,可大大降低钢桥面板疲劳开裂风险。试验得出的UHPC层横桥向开裂强度26.3 MPa,大于有限元计算下车辆荷载作用产生的最大应力7.36 MPa,证明了此组合桥面结构的可行性。

多孔有限大弹性薄板弯曲应力集中问题

应用弹性力学的复变函数理论,采用多保角变换的方法,推出了含有任意多孔有限大弹性薄板弯曲的多复变量应力函数的表达式。在内边界上进行复Fourier级数展开,在外边界采用配点法来确定应力函数的未知系数,从而计算有限大弹性薄板的应力场。本文以外边界为矩形,内边界为任意多椭圆孔的有限薄板为例,编制了相应的计算程序,进行了算例分析。结果表明本方法对处理多孔有限大弹性平面问题是简单且行之有效的。

多孔弹性平板弯曲或扭转的应力集中

针对含有任意多孔无限大弹性平板弯曲或扭转应力集中的计算问题,应用弹性力学的复变函数理论,采用多保角变换的方法,推出了多复变量应力函数的表达式。在边界上进行复Fou-rier级数展开,用待定系数法确定应力函数的未知系数,从而计算弹性板的应力场。以含有任意多圆孔的无限板为例,进行了算例分析,给出了各种载荷下孔距对应力集中的影响因素和孔边周向弯矩的分布图。结果表明:该方法对处理多孔弹性平板弯曲或扭转问题是行之有效的。

弹性半空间地基上正交异性矩形板弯曲通解

本文先对受任意边界约束的正交各向异性矩形薄板,在各种形式荷载作用下的弯曲问题,构造了四次逐项可导的带有补充项的双重正弦傅里叶级数新通解.该解析解既不需要叠加,对不同的物性参数又不需要分类,而且待定系数少又具有明确的物理含义,这使得正交各向异性矩形薄板的弯曲问题求解统一化、简单化、规律化。然后将新通解与弹性半空间受任意竖向荷载作用下的静力位移积分变换解相结合,得出弹性半空间地基上受任意边界约束的正交各向异性矩形板,在任意竖向荷载作用下的弯曲解析解。本文还给出了算例分析,其结果与文献吻合良好,证明本文的方法是切实可行的。

横观各向同性弹性半空间地基上正交异性矩形中厚板弯曲解析解

对横观各向同性体通解进行双重傅里叶变换,获得了直角坐标系下横观各向同性弹性半空间地基受任意竖向荷载作用下的位移积分变换解;在此基础上建立了板与地基的变形协调方程,并与三个广义位移变量描述的弹性地基上四边自由正交各向异性矩形中厚板的弯曲控制方程相结合,用三角级数法,得出横观各向同性弹性半空间地基上四边自由正交异性矩形中厚板受任意竖向荷载作用的弯曲解析解。相关算例分析表明,本文方法是有效的。

面板结构设计对正交异性板疲劳性能的影响研究

为量化面板结构形式对正交异性钢桥面板疲劳性能的影响,以军山长江大桥钢箱梁正交异性板为例进行研究。采用有限元分析软件ANSYS建立4节段钢箱梁仿真分析模型,研究采用5种面板结构形式时正交异性板各疲劳构造细节的最不利应力幅和疲劳寿命系数。研究结果表明:面板刚度增加对面板开裂构造疲劳性能改善作用最大,对加劲肋开裂构造疲劳性能改善作用次之,对横隔板开裂构造疲劳性能改善作用最小;与增加面板厚度相比,采用钢-混组合桥面结构可以大幅降低正交异性板各构造细节疲劳应力幅,提高其疲劳寿命,这一点值得进一步深入研究。

双参数弹性地基上自由矩形中厚板问题分析尝试

为了解决中厚板与双参数弹性地基的共同作用,基于弹性板理论,推导出中厚板弯曲的一种近似方法,求得了双参数地基上自由矩形中厚板弯曲问题的解析解.对数值算例编程求解,与Winkler弹性地基上自由矩形中厚板的解进行比较,并与有限元解、差分解、福氏级数解、叠加解和复级数解进行对比,结果十分接近,证明该方法可行.

板弯曲与平面弹性问题的多类变量变分原理

进一步完善板弯曲与平面弹性问题的多类变量变分原理，给出了相关边界积分项的具体表达式．多类交量变分原理涵盖了平衡、应力函数、应力、位移一应变、协调和物性共五大类基本方程和所有边界条件，是一个具有更加广泛意义的变分原理．

弹性地基上的正交异性矩形薄板弯曲问题的一般解析解

建立了弹性地基上的正交异性矩形薄板弯曲挠度函数微分方程的一般解.可以求解任意载荷作用下任意边界的弯曲问题.以四边自由中部受均布载荷作用的正方形板为例进行了计算,用这种解析法给出了一个精确解.其理论分析简单、计算容易,并适合于实际工程.