THE SOLUTION TO THE DESTABILIZING CRITICAL LOAD OF CIRCULAR DOUBLE ARTICULATED ARCH UNDER GOING VERTICAL DISTRIBUTIVE LOAD g0/cos2θ

In this paper, after taking the effect of axis force on bending into consideration, the general potential energy for the circular double articulated arch is established undergoing vertical distributive load g₀/cos²θ. With sufficient engineering precision, the fourth approximations to the destabilizing critical load of the arch under t his load are obtained by Ritz method. The approximations to the critical load ta ble are listed for various center angles of arch, and are contrasted with the critical load circular arch undergoing radial uniform load. Some reference results have been obtained.     

The shape of the strongest column

The problem of determining that shape of column which has the largest critical buckling load is solved, assuming that the length and volume are given and that each cross section is convex. The strongest column has an equilateral triangle as cross section, and it is tapered along its length, being thickest in the middle and thinnest at its ends. Its buckling load is 61.2% larger than that of a circular cylinder. For columns all of whose cross sections are similar and of prescribed shape-not necessarily convex—the best tapering is found to increase the buckling load by one third over that of a uniform column. This result, which was independently obtained by H. F. Weinberger, is originally due to Clausen (1851). For a uniform column, triangularizing is shown to increase the buckling load by 20.9% over that of a circular cylinder. The results lead to isoperimetric inequalities for the buckling loads of arbitrary columns. The research reported in this paper has been sponsored by the Office of Naval Research under Contract No. (285) 46.     

拱暨索拱面内稳定性研究的传递矩阵法

为探究拱桥面内稳定问题求解的新途径,应用传递矩阵法对径向均布荷载作用下的圆拱面内屈曲微分方程进行解答,利用边界条件导出其特征方程,从而求得其屈曲荷载。同时,结合力法以及拱上荷载集度与轴力的关系,将该理论方法推广到承受集中荷载的变截面拱以及索拱组合结构的稳定分析中,并和有限元ANSYS计算结果进行对比,验证了本文理论和方法的正确性。最后,研究了不同荷载工况下的边界条件、圆心角和截面惯性矩对拱结构面内稳定性的影响。结果表明,索拱结构的面内稳定性优于纯拱结构。     

固支圆板安定性的实验研究

本文利用机动法求解固支圆板在循环集中力作用下的安定问题,得到了安定载荷的理论解;利用激光全息的实验方法研究固支圆板的塑性累积现象,测得了安定载荷的上下限,并对实验结果进行了分析研究.     

Nonlinear vibration and buckling of circular sandwich plate under complex load

The nonlinear vibration fundamental equation of circular sandwich plate under uniformed load and circumjacent load and the loosely clamped boundary condi- tion were established by von Karman plate theory,and then accordingly exact solution of static load and its numerical results were given.Based on time mode hypothesis and the variational method,the control equation of the space mode was derived,and then the amplitude frequency-load character relation of circular sandwich plate was obtained by the modified iteration method.Consequently the rule of the effect of the two kinds of load on the vibration character of the circular sandwich plate was investigated.When circumjacent load makes the lowest natural frequency zero,critical load is obtained.     

用广义阶梯函数简化计算简支圆板在复杂荷载作用下的极限荷载

本文将广义阶梯函数应用于薄板的塑性极限分析问题，用以简化计算简支圆板在复杂荷载作用下的极限荷载。文中针对简支圆板在任意局部均布荷载和线性分布荷载共同作用下的塑性极限分析问题，并考虑荷载的五种不同的分布形式，给出相应的极限荷载的计算公式。     

圆板动力反直观行为实验研究

对受子弹正向撞击的铝合金圆板进行了动力反直观行为的实验研究。描述了不同撞击速度下板的响应模式,发现了圆板中的反直观现象,即板的最终变形与子弹撞击方向相反,并记录了板在整个变形过程中典型点的位移历史曲线,进一步证实了结构动力响应的反直观行为是一种客观存在的弹塑性动力行为。     

考虑几何与压电非线性行为压电层合轴对称圆板的精确解

研究可移简支及夹支边界条件下,轴对称压电层合圆板在强电场和机械荷载联合作用下的非线性变形.考虑电致伸缩的非线性压电效应及几何非线性的影响,导出轴对称压电层合圆板的控制方程.通过调整坐标轴的位置对控制方程进行简化,得到关于挠度和径向力的4阶非线性控制方程.再通过简单的积分并引入无量刚变量将控制方程等价地化为2阶非线性耦合微分方程组.利用幂级数法得到可移简支及夹支边界条件下强电场和均布荷载共同作用时的挠度、径向力及径向位移的幂级数精确解.通过对双、单压电晶片执行器的数值计算及分析,得到电场、外载对于位移、径向力的影响关系.     

加权残值法分析轴压圆柱薄壳后屈曲问题

本文首次应用了样条配点法分析了受到轴向压力的圆柱形薄壳的后屈问题,壳体的方程是L.H.Donnell的非线性正交异性圆柱形壳体方程,壳体的挠度试函数及应力函数试函数都是于轴向用了五次B样条函数基函数,周向用余弦函数。计算模型是周向为半个波长的壳块,可适应后屈曲实验变形跳跃现象。非线性代数方程组用了Newton—Rophson迭代法求解。由此所得的理论上的后屈曲曲线与国外近代实验相符。     

静载荷对夹层圆板超谐波共振的影响

研究静载荷作用下夹层圆板的超谐波共振问题．基于Hoff型夹层板理论,给出了静载荷作用下夹层圆板的非线性动力学方程．应用Galerkin法推导了静载荷作用下夹层圆板的轴对称非线性振动方程．运用多尺度法分别对系统的三次超谐波问题和二次超谐波问题进行了求解,并依据Lyapunov稳定性理论得到了系统稳态运动的稳定性判据．通过算例,得到了周边简支约束下夹层圆板三次超谐波共振和二次超谐波共振的幅频响应曲线图、振幅-静载荷响应曲线图、振幅-激励力幅值响应曲线图;研究了不同参数对系统振幅的影响规律,并对解的稳定性进行了分析．     

四种非正交边界板考虑初始荷载效应的后期荷载位移近似解

基于考虑初始荷载效应情况下板的一般形式的静力平衡微分方程,运用坐标变换得到了轴对称情形,考虑初始荷载效应后圆形板的极坐标形式的静力平衡微分方程。运用Galerkin法解得了简支等边三角形板、固支椭圆板、固支圆形板和简支圆形板四种非正交边界板考虑初始荷载效应的后期荷载位移近似解。运用相关文献提出的有限元法验证了近似解的正确性。各位移近似解表达式简单、物理意义明确,清楚地反映了初始荷载及相关因素对后期荷载位移的影响。计算分析表明：初始荷载效应提高了板的弯曲刚度,减小了板的后期荷载位移;板的初始荷载效应主要受初始荷载、跨厚比及边界条件等因素的影响。     

锯切过程中花岗石与金刚石间的摩擦效应

通过测量锯切力和计算锯切比能,获得了多种条件下的比能与单颗磨粒平均载荷的试验,从能量角度探讨了花岗石的锯石的锯切机理,并建立了单颗磨粒平均载荷与磨粒纵向切削面积平均值之间,单位宽度功率消耗与滑擦面积之间的对应关系。结果表明,锯切过程中能量主要消耗于花岗石与金刚石间的摩擦,由于单颗磨粒向切削面积平均值同时包含了磨粒切削深度与弧长的影响,更适用于描述锯切过程。锯切中锯切深度和材料去除率等因素的影响均可     

A new approach to an analysis of large deflections of thin elastic plates

For thin plates undergoing large deflections, a modified energy expression has been suggested and a new set of differential equations has been obtained in a decoupled form. Accuracy of the equations has been tested for a circular and a square plate with immovable as well as movable edge conditions under a uniform static load. Results obtained are in excellent agreement with other known results. These new equations are more advantageous than Berger's decoupled equations which fail to give meaningful results for movable edge conditions.     

Buckling of cylinders with cutouts under axial compression

An experimental study was carried out to clarify the effects of circular holes on the buckling of circular cylinders under axial compression. The effect of reinforcements was also examined by placing thin annular plates around the cutouts. Tests were performed on polyester shells with radius-to-thickness ratio of 400 and 100 and with two diametrically opposed circular holes. If a hole is small enough, there are no appreciable effects on the buckling strength of the cylinder. However larger cutouts result in a significant reduction of the buckling load. When doublers are placed around the holes, the buckling load approaches the value for the complete cylinder with no cutouts as the stiffening volume increases. Paper was presented at the 1982 SESA-JSME Joint Conference held in Oahu and Maui, HI on May 23–30, 1982.     

A contribution to the stability of circular plates

Archive of Applied Mechanics - The dynamical response of thin circular plates and their stability, resulting from the action of an arbitrary load which is a spacetime function, has been examined....     

A four-part boundary value problem in elasticity — indentation by a discontinuously concave punch

A solution is given for the frictionless indentation of an elastic half-space by a flat-ended cylindrical punch with a central circular recess, when the load is large enough to establish a circular region of contact in the recess. The problem is reduced to two simultaneous Fredholm equations using the method of complex potentials due to Green and Collins. Results are presented for the relationship between load, contact radius and penetration for various punch geometries.     

大挠度橡胶圆板的数值解及对其Hencky解的修正

将橡胶圆板视为薄膜，根据薄膜的无矩特性，巧妙采用数学方法求得橡胶圆板的膨胀状态几何特性描述，进而通过应力应变求得挠度与载荷的关系。同时，基于Hencky方法求得了挠度与载荷关系的Hencky解。对两种方法所得到的结果进行比较分析，并对Hencky解所产生的偏差进行校正的方法作了探讨。     

NONLINEAR VIBRATION OF CIRCULAR SANDWICH PLATES UNDER CIRCUMJACENT LOAD

Based on von Karman plate theory, the issue about nonlinear vibration for circular sandwich plates under circumjacent load with the loosely clamped boundary condition was researched. Nonlinear differential eigenvalue equations and boundary conditions of the problem were formulated by variational method and then their exact static solution can be got. The solution was derived by modified iteration method, so the analytic relations between amplitude and nonlinear oscillating frequency for circular sandwich plates were obtained. When circumjacent load makes the lowest natural frequency zero, critical load is obtained.     

On the effect of rotating secondary principal stresses in scattered-light photoelasticity

The lack of understanding of the effect of the rotation of secondary principal axes has been a severe limitation of the scattered-light method. The method of Poincare's equivalent system has been applied in order to develop a general formula for scattered-light intensity. Relationships among the orientation of eigenvectors and their phase retardation and stresses have been found. The method is illustrated by the solution of the problem of a circular rod loaded by a combination of torsion and axial load. An experimental procedure has also been suggested.     

带附加质量块的压电圆板能量采集器振动分析

基于圆板的压电能量采集技术在取代化学电池为低功耗电子器件提供能源方面具有巨大的潜能. 本文通过理论建模和数值仿真研究了考虑附加质量接触面积的压电圆板能量采集器的采集性能. 首先, 基于基尔霍夫薄板理论, 用广义哈密顿原理推导了带附加质量块的压电圆板能量采集器的机电耦合方程, 并用伽辽金法对方程近似离散, 通过离散方程得到电压、功率输出和最优负载阻抗的闭合解. 用有限元仿真对所提出的理论模型进行了验证, 结果表明该理论模型可以成功地预测压电圆板能量采集器输出电压和功率. 最后, 基于闭合解探讨了负载阻抗、附加质量块、压电圆板的内外半径等相关参数对压电圆板能量采集器固有频率、输出电压和功率的影响. 结果表明, 当质量块与复合板的接触半径足够小(本文中接触半径小于板半径的1/14)时, 质量块与复合圆板的接触面积可以忽略; 相较于无孔的压电片, 内径位于2.5 ~ 4 mm范围内的压电片可以提高能量采集器的采集性能; 附加质量、压电片外径和负载阻抗的合理选择既可以降低压电圆板的固有频率, 还可以提高其采集性能.