跨内支撑杆及阶梯杆屈曲的一种解析法分析

针对跨内含支撑的杆和变截面阶梯杆的弹性屈曲问题，提出一种分段作屈曲分析再叠加重组的分析方法．首先在杆两端引入横向和旋转弹簧，用以模拟弹性边界条件．其次建立两端弹性约束杆屈曲方程的通用形式，并通过屈曲方程求得几种边界约束杆端部弹性刚度因子的解析表达式．最后，建立拆分杆段连接处的平衡方程和协调条件，综合杆段的屈曲方程和节点的补充刚度条件得到整个杆件的屈曲方程，从而求得临界力．本文还提出一种基于泰勒展开求解屈曲特征方程近似根的方法．算例中将本方法所得结果与既有文献和有限元软件计算结果对比，验证本方法的适用性和准确度．所提方法属于解析方法，得到简洁、严密和易用的解析公式，可为多跨结构和变截面杆件的屈曲分析提供新参考．     

正交各向异性Kagome蜂窝材料宏观等效力学性能

由于微结构的布局和尺寸的方向性,人造和天然的蜂窝材料都会不同程度呈现各向异性,其中正交各向异性的蜂窝材料较为常见.该文采用桁架模型推导了正交各向异性Kagome单胞蜂窝材料等效刚度和强度的解析表达式,给出了初始屈服函数和近似弹性屈曲强度,讨论了等效刚度与各向异性率和相对密度的关系.等效刚度的解析结果与单胞壁杆采用梁单元建模的刚架模型均匀化结果进行比较,结果令人满意.需要说明的是这类"组合蜂窝"材料具有多功能性和潜在的可设计性,正在受到人们关注.     

立方晶粒任意集合下的格林函数和有效弹性刚度张量

为了推导多晶体材料的有效弹性刚度张量,给出立方晶粒任意集合的格林函数封闭但近似的表达式,该格林函数表达式包含三个单晶弹性常数和多晶体材料五个织构系数,它考虑取向分布函数的影响直至织构系数的线性项,它适用于弱织构多晶体材料或具有弱各向异性晶粒的多晶体材料(如金属铝),它与Nishioka格林函数近似式的比较通过三个算例给出;Synge的格林函数积分式则直接通过数值计算完成,它可作为问题的精确解供参考．该文还简单介绍了多晶体材料有效弹性刚度张量的推导过程,并把所得结果和有限元计算结果进行比较。     

弹性约束正交各向异性板屈曲精度改进分析

对单轴压缩下受载边处于简支边界约束非受载边处于竖向及旋转弹性边界约束的正交各向异性矩形板的屈曲问题进行了精度改进的理论研究.在运用瑞利-里兹法进行理论推导中,确保了形函数同时精度满足力边界约束和位移边界约束,从而获得了具有较高精度(与有限元对比,误差小于1%)的闭合形式解析解及常用于工程分析设计的显式公式.这些结果可用于判别单轴压缩下竖向及旋转弹性边界约束正交各向异性矩形板的屈曲承载能力,进而应用到复合材料薄壁结构的局部稳定性前期分析设计中.     

构造上正交各向异性凹凸板等效刚度的研究

针对构造上正交各向异性凹凸板等效刚度的研究问题,考虑经典弹性薄板理论和凹凸板的几何周期特性,划分出了以凸起为中心的典型单元,首先研究了典型单元的刚度特性,再通过刚度组合方法得到了凹凸板的等效弯曲刚度;然后以四边简支正交各向异性凹凸板为例,基于经典薄板理论中纳维二重三角级数推广到正交各向异性板的解,利用本文的等效刚度公式分别计算了在集中载荷作用下板的挠度和其自身的固有频率。计算结果与ANSYS有限元的模拟结果进行对比,理论计算与有限元模拟结果一致,验证了本文等效解析方法的合理性和精确性。最后讨论了凹凸板的各项尺寸参数对刚度等效精度的影响,并对其原因进行了分析。本文给出的等效刚度解析方法便于工程应用,尤其在应对大规模凹凸板刚度求解中具有计算简便的优点,研究结果对凹凸板静力学和动力学的研究以及实际工程应用具有重要的指导意义。     

用于正交各向异性织物仿真的弹簧质点模型

针对正交各向异性织物,本文提出了一种含附加节点的三角形弹簧质点模型．通过冗余自由度的引入和缩聚,能够实现有限元模型和弹簧质点模型三角形单元刚度矩阵的精确相等;据此,针对一般正交各向异性材料常数和单元形状,推导出弹簧质点模型中弹簧刚度系数及附加节点位置的解析表达式,有效解决了传统弹簧质点模型在正交各向异性织物仿真中存在的计算精度不高、弹簧参数选取随意等缺陷;并进一步完善了基于弹簧质点模型的柔性织物空间变形算法．数值模拟表明本文提出的弹簧质点模型和变形算法在进行织物仿真计算时,具有精度好、通用性强等优点．     

变截面Timoshenko梁的单元刚度矩阵

变截面构件在工程中应用广泛,在对变截面梁进行数值计算时,需要建立变截面梁单元的刚度矩阵。该文采用势能驻值原理,考虑了轴力引起的几何非线性和剪切变形的影响,将梁截面刚度的变化率作为小量,得到了近似到二阶的单元刚度矩阵。在构造位移模式时,从梁的微分平衡方程出发,得到同样近似到二阶、分别以三次和五次多项式表示的剪切和弯曲位移模式。该文还证明了单元刚度矩阵的奇异性,给出了轴压刚度的表达式,定量论证了与某些精确解的误差,表明在一定范围内,该文的结果具有足够的精度。最后以一个计算实例说明该文的单元刚度矩阵具有较快的收敛性。     

以环肋加强的圆柱壳在液压作用下的总体稳定

本文给出了以环肋加强的圆柱壳在液压作用下屈曲形态和临界载荷的计算方法.根据组合结构的方法,建立了一组肋和肋间壳段的稳定微分方程组.在肋的截面高度、偏心距、截面总面积ΣF_r、总抗弯刚度ΣE_rI_(G_ra)不变的前提下,而使环肋的数目趋于无穷大,从而得到了作为组合的环肋加强壳的初次近似的正交各向异性壳模型及其弹性关系.可以进一步寻求方程组的级数解,其首项代表零阶近似解,亦即上述等效正交各向异性壳的解,其余各项代表逐次渐近的修正解,或等效壳和真实的环肋加强组合壳解的误差.根据误差的估计可以给出简化为等效各向异性壳的判据.最后给出了算例并与其它作者的方法进行了比较.计算结果表明与实验符合得很好.     

粘弹性铰对梁结构模态性能的影响分析

研究以连接铰结构中置入粘弹性材料的,预紧力大小发迹时引起铰点约束刚度变化对模态性能的影响,给出了平移约束刚度和旋转约束刚度变化时结构模态参数变化的解析表达式,可以分析两个参数同时变化的固有频率和损耗因子变化的三科。可获得对了大损耗因子约束参数,可为结构的被动控制设计提供一定的指导。     

不同模量理论弹性支承连续梁及框架

弹性支承连续梁及框架结构的内力不仅与各杆件的刚度有关，而且与支承结构的刚度有关．当引入拉压不同模量后，各杆件的抗弯刚度EI不再为常数(与经典力学不同)，而是内力的函数，使结构内力计算成为非线性问题．用分段积分法推导出不同模量弹性支承连续梁及框架的中性轴公式和内力计算表达式并编制非线性内力计算迭代程序．通过实例计算对比分析不同模量与经典力学相同模量两种方法计算结果的差异，最后提出对该类结构计算的合理建议以及利用不同模量对结构进行优化的结论．     

Unilateral contact buckling of lightly profiled skin sheets under compressive or shearing loads

Thin, profiled steel sheets forming the skin of concrete-filled composite wall panels and similar members benefit from the unilateral (tensionless) restraint provided by fill of sufficient elastic modulus. This paper investigates the buckling of such skin sheets in panels subjected to compressive or shearing loads. The profiled skins are modelled as infinite, thin orthotropic plates resting on tensionless rigid foundations, allowing the local buckling response to be simulated by the single-wave buckling mode of an unrestrained plate section of appropriate aspect ratio. Solution of the governing differential equations leads to the determination of the plate buckling coefficients. Simplified formulas for the buckling coefficients in terms of the parameters describing the skin sheets are developed and shown to agree well with published results and finite element analyses for particular limiting cases.     

钢-混凝土组合梁负弯矩区畸变屈曲弯矩计算公式

侧向弯曲屈曲及侧向弯扭屈曲均为钢-混凝土组合梁负弯矩区钢梁的重要屈曲模式,而现有计算方法通常只考虑到侧向弯曲屈曲,未考虑到侧向弯扭屈曲,因此有一定局限性。本文在钢梁腹板对钢梁下翼缘的转动约束刚度及侧向约束刚度的计算公式上,结合弹性介质中薄壁杆件的屈曲理论推导了工形钢-混凝土组合梁负弯矩区的侧向弯曲屈曲弯矩及侧向弯扭屈曲弯矩计算公式。实例分析表明,现有计算方法均存在一定理论缺陷,本文计算方法更为合理;同时,本文计算式比现有文献中同类型计算式更为简洁,便于手算,实用性强并适于工程应用。     

正交各向异性加筋板屈曲分析方法研究

为简化正交各向异性加筋板屈曲分析,本文将筋条位移场用其所在位置的板的位移表达,建立加筋板总势能,通过离散位移场,利用最小势能原理,推导出基于里兹法的正交各向异性加筋板屈曲分析控制方程,采用Matlab进行求解.基于本文推导的方程对单筋和三筋加筋板在不同压剪比下的屈曲荷载和模态进行分析,得到与Abaqus基本一致的结果.加筋板的屈曲荷载随着筋条数增加明显增大;压剪比为1∶1时,各阶屈曲荷载均最小;随着位移函数阶数提高,本文算法计算精度提高,但相应的计算量也显著增大.     

梯度弹性基础上正交异性薄板的屈曲分析

基于双参数弹性基础模型,研究了梯度弹性基础上正交异性薄板的屈曲问题. 首先,基于能量法与变分原理,给出了梯度弹性基础上正交异性薄板的屈曲控制方程,并得到了梯度弹性基础刚度系数K₁ 与K₂的计算式;进而,通过将位移函数采用三角函数展开的方法,给出了单向压缩载荷作用下、四边简支正交异性弹性基础板屈曲载荷的计算式;在算例中,通过将该文的解退化到单纯的正交异性板,并与经典弹性解比较,证明了理论的正确性;最后,求解了弹性模量在厚度方向上呈幂律分布的梯度基础上的薄板屈曲问题,分析了基础上下表层材料弹性模量比与体积分数指数对屈曲载荷的影响.     

Elasto-plastic buckling analysis of laminated plates including interfacial damage

Elasto-plastic buckling of orthotropic laminated plates, which include interfacial damage, is analyzed in detail. Firstly, a novel mixed hardening yield criterion, as an improvement of Hill’s counterpart, is proposed for the orthotropic materials on the basis of the plastic theory. And differing from Hill’s theory, the present yield criterion is related to the spherical tensor of stress. Then, the incremental elasto-plastic constitutive relations of the mixed hardening orthotropic materials are presented. Secondly, the incremental static equilibrium equations for laminated plates including interfacial damage are established based on Von-Karman type theory and the principle of minimum potential energy. Finally, the elasto-plastic buckling of laminated plates are solved by adopting the Galerkin method and iteration scheme. The numerical results show that buckling of the plate occurs easier due to the existence of interfacial damage, and the critical load trends to constant when the interfacial damage approaches a certain degree. Also, the effect of anisotropy on buckling is obvious and the analysis of elasto-plastic buckling is necessary.     

Plate/shell structure topology optimization of orthotropic material for buckling problem based on independent continuous topological variables

The purpose of the present work is to study the buckling problem with plate/shell topology optimiza-tion of orthotropic material.A model of buckling topology optimization is established based on the independent,con-tinuous, and mapping method, which considers structural mass as objective and buckling critical loads as constraints. Firstly, composite exponential function (CEF) and power function(PF)as filter functions are introduced to recognize the element mass,the element stiffness matrix,and the ele-ment geometric stiffness matrix.The filter functions of the orthotropic material stiffness are deduced. Then these fil-ter functions are put into buckling topology optimization of a differential equation to analyze the design sensitiv-ity.Furthermore,the buckling constraints are approximately expressed as explicit functions with respect to the design vari-ables based on the first-order Taylor expansion.The objective function is standardized based on the second-order Taylor expansion. Therefore,the optimization model is translated into a quadratic program.Finally,the dual sequence quadratic programming(DSQP)algorithm and the global convergence method of moving asymptotes algorithm with two different filter functions(CEF and PF)are applied to solve the opti-mal model.Three numerical results show that DSQP&CEF has the best performance in the view of structural mass and discretion.     

Buckling and vibration of rectangular laminates with cut off regions

The pure global buckling and vibration of four sides simply-supported as well as clamped orthotropic rectangular laminates having multiple rectangular cut off regions that are symmetric with respect to mid-plane have been studied by treating the remaining cut off regions as uniform plates with reduced stiffnesses. The variation of stiffness of the plate is represented by Fourier series. Some numerical results for the pure global buckling bad prediction due to its reduced flexural stiffness for typical cases of rectangular middle-plane symmetric cut off regions are presented.     

正交各向异性薄板的弹塑性屈曲分析

本文应用混合硬化正交各向异性塑性理论和屈曲的能量法则，推导了正交各向异性薄板在面内压缩情况下的弹塑性稳定方程，计算了相应的临界荷载，并讨论几何形状、边界条件及诱导荷载比等对临界应力的影响。分析表明材料的各向异性性质对弹塑性临界应力的有较大的影响。     

Buckling load and critical length of nanowires on an elastic substrate

This paper considers the stability of nanowires on an elastic substrate. The problem is converted to a generalized Euler problem containing rotational spring restraint. When distributed loading and tip forces are simultaneously applied, the buckling problem of a heavy nanocolumn with rotational spring junction is reduced to an integral equation. An approximate buckling load equation is derived explicitly. The critical length of nanocantilevers is given in closed form. Results indicate that spring stiffness increases the critical length of nanowires. The effect of self-weight on the critical length is pronounced for small tip forces, and becomes weaker for larger tip forces.     

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 K′arm′an assumption,the governing equations of equilibrium for the micro-classical plate considering 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/E2and 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.