多应变速率下尺寸效应对黄铜微尺度塑性变形本构及损伤演化的影响

准静态微尺度塑性变形中,特征尺寸效应与晶粒尺寸效应会直接影响韧性断裂的应变能及断裂强度,其直接原因是由于表面层自由晶粒所占比例随着样品尺寸的缩小或晶粒尺寸的增大而逐渐增加从而影响流动应力。在高应变速率下,特征尺寸效应和晶粒尺寸效应对金属流动应力和损伤的影响则较少被提及。通过分离式霍普金森压杆试验得出高应变速率下黄铜微尺度等温流动应力,以Johnson-Cook本构模型为基础构建了包含尺寸系数的微尺度高应变速率本构模型,并将其与Freudenthal非耦合断裂准则相结合,提出了多应变速率微尺度混合损伤模型,量化了不同应变速率下特征尺寸效应及晶粒尺寸效应对金属损伤的影响,为飞刀切削样品表面改善提供了理论依据。     

微细辊对平板辊压成形工艺建模与尺度效应分析

带有功能性表面微细结构特征的金属构件在诸多领域得到越来越多的应用。当微细特征的尺寸小于1 mm时,成形模具的模腔几何尺寸和材料的晶粒尺寸决定着金属材料的流动行为,微特征的成形质量受到尺度效应的严重影响。传统的工艺设计方法难以有效指导微细成形工艺参数的设计。研究一种高效的金属构件表面微细结构加工方法——微细辊对平板(Roll-to-plate,R2P)辊压成形工艺。针对不同晶粒尺度的铜试样,研究晶粒尺度对材料力学性能的影响规律;构建R2P微细辊压成形工艺仿真模型,分析辊压模腔尺寸、材料晶粒尺寸等工艺参数对微特征成形质量的影响规律;基于自主开发的R2P微细辊压成形原型系统,进行辊压成形试验研究,验证仿真预测模型的有效性。研究结果显示,在模腔几何尺寸中,模槽宽度对材料的流动行为有着显著地影响。而且,不同的晶粒尺寸也显著影响着微特征的形成过程。     

基于Cosserat理论的微梁振动特性的尺度效应

不少微观实验已经证实,微尺度领域材料的力学性能存在尺度效应.采用偶应力理论(又称Cosserat理论)研究微梁振动特性(主要是固有频率)的尺度效应.文中首先对偶应力理论进行简介,然后采用Hamilton变分原理推导基于Cosserat理论的微梁无阻尼自由振动的微分方程,分析微梁固有频率对微尺度的依赖性.结果表明,当微梁的厚度减小到可以和材料的本征长度相比时,微梁的固有频率将显著增大.     

核反应堆控制棒驱动机构驱动杆屈曲分析

驱动杆是核反应堆控制棒驱动机构的关键零部件,对整机的运行起到重要作用。以具有细长杆特征的驱动杆为研究对象,建立了基于ANSYS线性屈曲分析、非线性屈曲分析原理的驱动杆模型,分析计算两种情况下驱动杆受轴向力时的屈曲模态以及临界载荷。研究结果表明:非线性屈曲分析驱动杆得到的临界载荷小于线性屈曲分析,其值为线性屈曲分析结果的92%,更符合实际情况;所求临界载荷能更全面的反映驱动杆的稳定极限承载能力,可进一步指导驱动杆的设计优化。     

欧拉压杆超低频水平隔振系统

研制一种新型超低频水平隔振系统，该系统采用细长压杆作为水平隔振弹簧。通过对一端固定，一端自由的细长压杆在纵横载荷联合作用下的力学特性进行分析，得出当压杆承受的纵向载荷达到临界载荷时，其横向刚度趋于零，从而可以获得极低的固有频率，实现水平方向的超低频宽频带隔振。     

初始挠度及中间弹性支撑对压杆稳定的影响分析

实际工程结构中的细长杆受压时,当存在初始挠度及中间弹性支撑时,不能用经典的欧拉公式计算杆件的屈曲临界载荷.利用有限元软件ANSYS对实际工程结构进行非线性屈曲分析,能够考虑到杆件的初姑挠度以及中间弹性支撑对临界失稳载荷的影响.计算结果表明:机车径向转向架耦合杆初妊挠度为10 mm时,对应的临界失稳载荷相对欧拉公式计算结...     

有初始缺陷粘弹性压杆的蠕变屈曲

研究有初始缺陷粘弹性压杆的蠕变屈曲,讨论分析了瞬时临界载荷和耐久临界载荷对粘弹性压杆蠕变屈曲的影响。     

基于ANSYS机车牵引杆屈曲分析

实际工程结构中经常存在细长杆受压的形式,需要对其进行屈曲分析。为准确计算屈曲临界载荷,利用有限元软件ANSYS对实际工程结构进行线性和非线性屈曲分析。计算结果表明：有限元软件可对工程结构进行线性和非线性屈曲分析;实际结构由于材料弹塑性能,发生屈曲失稳时,有可能发生塑性变形,降低了屈曲临界载荷,非线性计算结果为线性计算结果的95%左右。对结构进行非线性屈曲分析得出更偏于安全的计算结果。     

耦合场中小尺寸碳纳米管的组合扭转屈曲行为

针对小尺寸碳纳米管在多物理场耦合作用下的组合扭转屈曲问题,提出了基于非局部理论耦合场作用下的力学模型,并研究了该模型的组合扭转屈曲行为.首先,采用连续弹性壳模型,引进热-电-力多场耦合作用下的本构关系,通过引入非局部弹性理论来考虑小尺寸碳纳米管的尺度效应;然后针对多壁碳纳米管层间范德华力和周边弹性介质的影响,建立了基于非局部理论多场耦合作用下碳纳米管的屈曲控制方程.最后,在轴力组合扭转载荷及温度与电压变化影响的工况下,研究了各因素对碳纳米管组合扭转屈曲行为的影响.得到的结果显示了小尺寸碳纳米管组合扭转屈曲行为在多场耦合作用下的响应,揭示了各物理场与组合扭转屈曲行为的关系;同时指出非局部理论下的屈曲载荷与经典理论下的屈曲载荷比值总小于1,说明经典理论高估了小尺寸碳纳米管的组合扭转屈曲行为.     

含结构惯性载荷作用桁架结构的弯曲应力及其控制

结构惯性载荷所占成分较大的桁架结构,需考虑其对杆单元弯曲应力的影响及其控制。针对该问题,可用桁架结构分析方法求解杆内轴向应力,再用受横向均布载荷梁的分析方法求解杆内最大弯曲应力,将两者相加以确定杆内最大总应力。继而,采用控制细长比的方法,以控制横向惯性载荷引起的最大弯曲应力,并讨论相应的屈曲条件以确定许用轴向压应力。运用应力比法对多工况下应力约束桁架结构进行最轻化设计,以含惯性载荷作用的3杆和10杆桁架结构优化为例,验证该控制最大弯曲应力方法的必要性与有效性。     

细长压杆失稳时最大挠度的确定

针对国内工程力学教材普遍认为细长压杆失稳变形挠曲线线性化方程中的挠度值不确定的错误观点,指出其对细长压杆失稳变形挠曲线线性化方程推导存在误区,以两端铰支细长压杆为例,建立了其失稳变形挠曲线线性化方程后,又考虑了压杆失稳后两端截面形心产生轴向位移参数,通过消参,确定了细长压杆失稳时最大挠度值。结果表明：压杆失稳后两端截面形心产生轴向位移以及临界压力的确定这两个条件缺一不可才能在线性化下确定细长压杆失稳时最大挠度值,挠度值的大小与轴向压力直接有关。     

Comparative study of thermal post-buckling analysis of uniform slender & shear flexible columns using rigorous finite element and intuitive formulations

Thermal post-buckling analysis of uniform, isotropic, slender and shear flexible columns is presented using a rigorous finite element formulation and a much simpler intuitive formulation. The ends of the columns are axially restrained to move and consequently any temperature rise above the stress free condition of the column produces an equivalent constant compressive mechanical load that causes the column to buckle at a critical temperature. Further increase in temperature beyond critical temperature results in the thermal post-buckling phenomenon. As a result of constraints imposed on the axial displacement at the ends of the column, the post-buckling phenomenon is governed by the von-Karman strain displacement relation applicable to one dimensional problems. Empirical formula for ratio of nonlinear axial load to critical load (equivalent constant mechanical load for a given temperature rise) as a function of the central deflection are obtained using both the rigorous finite element and intuitive formulations for various boundary conditions. The boundary conditions considered are the classical such as hinged-hinged, clamped-clamped and clamped-hinged conditions and nonclassical boundary conditions like the hinged-guided or the clamped-guided conditions. Post-buckling analysis results pertaining to nonclassical boundary conditions are meagre in the literature. It is observed that results obtained from both the formulations are in excellent agreement for all boundary conditions considered. Also the accuracy and simplicity of the intuitive formulation is aptly demonstrated to slender and shear flexible columns.     

Buckling of columns: Allowance for axial shortening

This paper investigates the effect of axial shortening on (i) the elastic buckling of columns with a continuous elastic restraint, (ii) the elastic buckling of rotating columns and (iii) the free vibration of columns under a static axial load. These column problems can be solved in a unified approach because the resulting energy functional is similar. The field differential equation is derived by minimizing the energy functional with respect to the lateral displacement function via calculus of variations. The buckling load or fundamental frequency may be obtained by analytically solving the two-point boundary-value problem. It was found that the boundary conditions and the restraint parameter or angular velocity parameter affect the influence of axial shortening on the buckling load. In vibrating columns, tensile forces enhance the effect of axial stretching on the fundamental frequency.     

Morphology and mechanical properties of polypropylene micro-arrays by micro-injection molding

To study the effects of particular process conditions and micro size factor on microstructures manufactured by micro-injection molding, four types of polypropylene micro column arrays are fabricated. The filling performance, morphology, and mechanical properties of these column arrays are investigated by polarized light microscopic, SEM, X-ray microbeam diffraction, nanoindentation, and microindentation. The process parameters are optimized by analyzing the filling performance of these micro columns under different process conditions. These micro columns represent “skin-core” structure and spherulite size diminishes gradually with the decrease of diameter of micro columns. Micro columns contain both α and β phase. The hardness and modulus of the same micro column increase from core zone to skin layer. There is no obvious difference of hardness among the micro columns with different diameters.     

Exact static analysis of partially composite beams and beam-columns

The ordinary differential equations and general solutions for the deflection and internal actions and, especially, the pertaining consistent boundary conditions for partially composite Euler–Bernoulli beams and beam-columns are presented. Static loading conditions, including transverse and axial loading and first- and second-order analyses are considered. The theoretical procedure is applicable to general loading and boundary conditions for uniform composite beams and beam-columns with interlayer slip. Further, the exact closed form characteristic equations and their associated exact buckling length coefficients for composite columns with interlayer slip are derived for the four Euler boundary conditions. It is shown that these coefficients are the same as those for ordinary fully composite (solid) columns, except for the Euler clamped-pinned case. For the clamped-pinned case, the difference between the exact buckling length coefficient and the corresponding value for solid columns is less than 1.8% depending on the so-called composite action parameter and relative bending stiffness parameter. Correspondingly, the maximum deviation between the exact and approximate buckling load is at most 2.5%. These small differences can in most practical cases be neglected. Also, the maximum theoretical range for the relative bending stiffness for partially composite beams and beam-columns is derived. An effective bending stiffness, valuable in the determination of the critical buckling load for partially composite members, is derived. This effective bending stiffness is also suitable for analysing approximate deflections and internal actions or stresses in composite beams with flexible shear connection. The beam-column analysis is applied to a specific case. The difference in the approaches to the first- and second-order analysis is illustrated and the results clearly show the magnification in the actions and displacements due to the second-order effect. The magnification of the internal axial forces is different from magnifications obtained for the other internal actions, since only that portion of an internal axial force that is induced by bending is magnified by the second-order effect.     

Analytical solutions for buckling of multi-step non-uniform columns with arbitrary distribution of flexural stiffness or axial distributed loading

In this paper, the function for describing the distribution of flexural stiffness K(x) of a non-uniform column is arbitrary, and the distribution of axial distributed loading N(x) acting on the column is expressed as a function of K(x) and vice versa. The governing equation for buckling of a one-step non-uniform column is reduced to a differential equation of the second-order without the first-order derivative by means of variable transformation. Then, this kind of differential equation is reduced to Bessel equations and other solvable equations for 14 cases. The analytical buckling solutions of one-step non-uniform columns are thus found. Then the obtained analytical solutions are used to derive the eigenvalue equation for buckling of a multi-step non-uniform column for several boundary supports by using the transfer matrix method. A numerical example shows that the proposed procedure is an efficient method for buckling analysis of multi-step non-uniform columns.     

弹性圆柱壳的稳定性优化设计

研究任意轴对称边界条件下和受均布法向载荷作用圆柱壳的稳定性优化设计问题，即极大化屈曲临界载荷。利用能量原理分析轴对称变厚度圆柱壳的分支点屈曲，将求解屈曲临界载荷变成求解广义特征值方程，使圆柱壳稳定性优化设计成为极大化最小特征值问题。实际算例验证了本方法的有效性。研究结果可用于圆柱壳的加肋优化设计。     

Theoretical study of dynamic elastic buckling of columns subjected to intermediate velocity impact loads

Dynamic elastic buckling of simply supported columns subjected to intermediate velocity impact is theoretically studied in this paper. The dynamic buckling equation is set up. Theoretical solution of dynamic responses of columns subjected to a half-sine shape intermediate velocity impact load is derived. Based on the characteristics of the theoretical solution, a dynamic buckling criterion is proposed to determine the critical buckling condition and to estimate the dynamic buckling critical load. Theoretical results obtained in this study are compared with experimental data. They are also compared with numerical results obtained by other authors. Good agreements between them are observed.     

Nonconservative dynamic axial–torsional buckling of structural frames using power series

Axial deformation is not involved in the formulation of linear buckling caused by axial force. Likewise, twisting is not present in linear buckling caused by axial torque. The dynamic axial–torsional buckling of structural frames in the presence of follower axial force will be solved by means of dynamic stiffness using power series. Variationally consistent natural boundary conditions are given so that the resulting dynamic stiffness is symmetrical for conservative loading. Some parts of the boundary forces disappeared for follower axial forces due to consistent tangency to the neutral axis. The deficiency of the power series method to deal with non-uniform sections is highlighted. New instability phenomena for a simple column are studied in detail. It is shown that columns can buckle under direct follower tension. Follower tension decreases the natural frequency initially and then increases it rapidly after a turning point. The first pair of modes about the major axis and that about the minor axis of a rectangular section column meet at one crossing point. A very small axial torque will change the crossing into flutter-like tongues. These tongues are common in compressive follower force. These tongues caused by axial torque are reported here for the first time.     

Nonlocal beam models for buckling of nanobeams using state-space method regarding different boundary conditions

Buckling analysis of nanobeams is investigated using nonlocal continuum beam models of the different classical beam theories namely as Euler-Bernoulli beam theory (EBT), Timoshenko beam theory (TBT), and Levinson beam theory (LBT). To this end, Eringen’s equations of nonlocal elasticity are incorporated into the classical beam theories for buckling of nanobeams with rectangular cross-section. In contrast to the classical theories, the nonlocal elastic beam models developed here have the capability to predict critical buckling loads that allowing for the inclusion of size effects. The values of critical buckling loads corresponding to four commonly used boundary conditions are obtained using state-space method. The results are presented for different geometric parameters, boundary conditions, and values of nonlocal parameter to show the effects of each of them in detail. Then the results are fitted with those of molecular dynamics simulations through a nonlinear least square fitting procedure to find the appropriate values of nonlocal parameter for the buckling analysis of nanobeams relevant to each type of nonlocal beam model and boundary conditions.analysis.