An optical system and technique for position testing of segments of the compound parabolic mirror of the radio telescope of the millimetron space observatory

An optical system and technique for position testing of segments of the compound parabolic mirror of the telescope of the Millimetron space observatory are proposed. Results of an analysis of the testing precision assured by the proposed technique are presented and recommendations for practical implementation of the technique are given. Translated from Izmeritel’naya Tekhnika, No. 5, pp. 29–31, May, 2008.     

Large deflection analysis of thermo-mechanical loaded annular FGM plates on nonlinear elastic foundation via DQM

The effects of three-parameter elastic foundations and thermo-mechanical loading on axisymmetric large deflection response of a simply supported annular FGM plate are investigated. An annular FGM plate, resting on a three-parameter elastic foundation under a transverse uniform loading and a transverse non-uniform temperature, is considered. The mechanical and thermal properties of the FGM plate are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. The mathematical modeling of the plate and the resulting nonlinear governing equations of equilibrium are derived based on the first-order shear deformation theory (FSDT) in conjunction with nonlinear von Karman assumptions. A polynomial-based differential quadrature method is used as a simple but powerful numerical technique to discretize the nonlinear governing equations and to implement the boundary conditions. Finally, the effects of certain parameters, such as nonlinear foundations stiffness, volume fraction index, and temperature, on the axisymmetric large deflection response of the FGM plate are obtained and discussed in detail.     

Crack problem for a functionally graded layer on an elastic foundation

In this paper internal and edge crack problems for an FGM layer attached to an elastic foundation are considered. This model can be used to simulate circumferential crack problem for a thin walled cylinder. It is assumed that the mechanical properties of the layer are varying in thickness direction. Crack is assumed to be perpendicular to the surfaces. For this geometry stress intensity factors are calculated for a number of different crack surface tractions. By using the calculated stress intensity factors and the principle of superposition it is possible to obtain solutions for physically meaningful cases such as fixed grip constant strain loading, membrane loading and bending. This revised version was published online in July 2006 with corrections to the Cover Date.     

饱和地基上弹性圆板的固结位移

 采用Laplace变换及Hankel变换研究弹性圆板在饱和地基上的固结位移．在Laplace变换域上建立了求解弹性圆板固结位移的第二类Fredholm积分方程，由数值反变换获得时域解，给出了对工程实践有参考价值的计算结果．计算结果表明，弹性板的固结位移随饱和土的排水泊松比的减少而增加，而弹性板的初始位移随饱和土的不排水泊松比的减少而增加．     

空间引力波望远镜主镜组件结构设计及热稳定性分析

针对空间引力波探测对望远镜系统提出的皮米级稳定性和λ/30波前误差的应用需求,提出了一种光机集成分析与优化方法。首先开展了主镜侧支撑点位置分析和支撑结构拓扑优化;然后基于并联Bipod连杆支撑的柔度矩阵,建立了各结构参数的评价函数,并通过Matlab分析初步确定柔性支撑尺寸参数取值范围;最后,搭建了光机集成仿真平台对结构进一步优化。结果表明,系统一阶频率为392.43 Hz,重力和温度载荷下主镜面形变化优于λ/60;在10 μK/Hz^1/2的空间热扰动下,主镜组件尺寸稳定性在10 pm/Hz^1/2水平。

     

大口径反射镜侧支撑结构力学分析

从理论上论述了在真空望远镜主反射镜的几种侧支撑结构,并运用有限元法对之分别进行了分析计算,得到使用了不同侧支撑结构的真空望远镜主镜在不同观测角度时的表面变形结果,通过比较变形结果,得到使用新配方粘接剂的粘接侧支撑机构支撑效果更好.在已确定使用Grubb十八点底支撑结构后,分析了使用粘接剂的侧支撑结构主反射镜变形与应力情况.通过有限元分析结果,得出变形结果符合整个光学系统的公差要求,同时证明了使用改性粘接剂的侧支撑系统可有效减少光学件表面变形量.     

天文学自适应光学成像望远镜的模拟

为分析天文学自适应光学(AO)望远镜中AO系统的校正性能,利用Matlab仿真其成像过程。采用正交基为Zernike多项式的自相关法产生符合大气统计特性的大气相位屏,仿真平行光通过大气后的瞬时畸变波前相位;采用快速傅里叶变换仿真哈特曼-夏克波前传感器的成像光斑,根据实际成像与参考平面波成像的质心坐标之差,计算波前传感器子孔径内的平均波前斜率。模拟比较了1.2m望远镜两种AO系统布局的校正性能,结果表明,子孔径为正六边形AO系统的校正性能略优于子孔径为正方形AO系统的校正性能,两种AO系统的SR比(StrechlRatio)分别为0.872和0.859。     

Nonlinear response of a shear deformable S-FGM shallow spherical shell with ceramic-metal-ceramic layers resting on an elastic foundation in a thermal environment

This article presents an analytical approach to investigate the nonlinear stability of thick, functionally graded material (FGM) shallow spherical shells resting on elastic foundations, subjected to uniform external pressure and exposed to thermal environments. Material properties are assumed to be temperature dependent and graded in the thickness direction according to a Sigmoid power law distribution (S-FGM) in terms of the volume fractions of constituents. Using the first-order shear deformation theory and the Galerkin method, the effects of materials, geometry, elastic foundation parameters, and temperature on the nonlinear response of the thick S-FGM shells are analyzed and discussed in detail.     

弹性地基上四边自由矩形薄板的自由振动

将弹性地基用Winkler模型来代替。首先把弹性地基上矩形薄板的动力学方程表示成为Hamilton正则方程，然后采用辛几何方法对全状态相变量进行分离变量，并利用得到的共扼辛正交归一关系，求出弹性地基上四边自由矩形薄板的固有频率和振型的解析解表达式。由于在求解过程中不需要事先人为的选取挠度函数，而是从弹性地基上矩形薄板的动力学基本方程出发，直接利用数学的方法求出可以满足四边自由边界条件的固有频率和振型的解析解表达式，使得问题的求解更加合理化。文中的最后还给出了计算实例来验证本文所采用的方法以及所推导出公式的正确性。     

Delamination of layered structures on elastic foundation

This study presents an interface fracture mechanics analysis of delamination of a layered beam resting on a Winkler elastic foundation subject to general mechanical loads. A crack tip element on elastic foundation model is established first, through which, two concentrated forces existing at the crack tip are determined in closed-form. Then total energy release rate of the crack can be expressed in term of these two forces. By using available numerical results in the literature, the phase angle of the total energy release rate is also obtained. To verify the validity and accuracy of the solutions, debonding of a bonded overlay from the base structure resting on a Winkler elastic foundation is analyzed using the present solution. Comparisons with the baseline results obtained by finite element analysis suggest that the present analytical solution provides an excellent estimation of the total energy release rate and its phase angle for interface cracks in layered structure on elastic foundation. This study provides an approximated analysis of the debonding of a thin overlay debonding from the concrete pavement, where the effect of the base structure is simplified by a Winkler elastic foundation. This solution can also be used to analyze other similar delamination problems, such as local delamination in laminated composites, and face sheet delimitation in sandwich beams.     

望远镜光学结构对自适应光学校正能力的影响分析

自适应光学系统在高分辨力成像望远镜中发挥了重要作用。自适应光学系统对于望远镜系统中的低阶像差几乎可以完全校正,但是会牺牲变形镜的校正行程量;对于中高阶像差,自适应光学系统不能完全校正,如何减小高阶残余误差是望远镜系统设计需要考虑的问题之一。本文首先分析了望远镜光学结构中的主镜结构、次镜遮拦、次镜支撑筋、主次镜装调和光学加工等静态和准静态像差情况,然后分析了这些因素如何影响自适应光学校正能力,最后给出了对望远镜光学结构的要求。     

The interaction of a curved crack with a circular elastic inclusion

The solution to a curved matrix crack interacting with a circular elastic inclusion is presented. The problem is formulated using the Kolosov–Muskhelishvili complex stress potential technique where the crack is represented by an unknown distribution of dislocations. After an appropriate parameterization, the resulting singular integral equations are solved with the Lobatto-Chebyshev quadrature technique. The accuracy of the current solution is shown by comparing these results to previously published results. A preliminary investigation is conducted to study the effects of crack curvature and inclusion stiffness on the stress intensity factors and it is shown that in certain instances, the effect of the crack curvature and the inclusion stiffness are competing influences.     

Edge crack in an elastic layer resting on Winkler foundation

The paper deals with the stress analysis near a crack tip in an elastic layer resting on Winkler foundation. The edge crack is assumed to be normal to the lower boundary plane. The upper surface of the layer is loaded by given forces normal to the boundary. The considered problem is solved by using the method of Fourier transforms and dual integral equations, which are reduced to a Fredholm integral equation of the second kind. The stress intensity factor is given in the term of solution of the Fredholm integral equation and some numerical results are presented.     

Static and dynamic analysis of an FGM doubly curved panel resting on the Pasternak-type elastic foundation

The static, dynamic, and free vibration analysis of a functionally graded material (FGM) doubly curved panel are investigated analytically in the present paper. The FGM Panel is originated from a rectangular planform and its principle curvatures are considered to be constant. All mechanical properties of the FGM panel are assumed to vary continuously through the thickness according to a power law formulation except Poisson’s ratio, which is kept constant. A Pasternak-type elastic foundation containing damping effects is considered to be in contact with the panel during deformation. The elastic foundation reacts in both compression and tension. Equations of motion are established based on the first order shear deformation and the modified Sanders shell theories. Following the Navier type solution, the established equations are reduced to time-dependent ordinary differential equations. Using the Laplace transform, the time-dependency of the problem is eliminated. The solutions are obtained analytically in the Laplace domain and then are inverted to the time domain following an analytical procedure. Finally, the analytical results are verified with those reported in the literature.     

空间望远镜层合材料镜片展开过程非线性动力学行为分析

为了研究空间望远镜柔性子镜展开过程对镜片型面精度和望远镜系统的扰动问题,以花瓣式可展开空间望远镜抛物层合镜片为研究对象,基于绝对节点坐标法,采用考虑初始形态曲率的曲壳单元对镜片的形变位移进行描述,表征了层合镜片几何非线性关系与材料非线性关系下的应变和应力关系。利用虚功原理推导了傍瓣子镜展开过程的耦合动力学方程,考虑了镜片弹性变形与大范围运动的耦合作用。针对使用的曲壳单元和传统建模方式,分别对镜片展开过程进行仿真分析,结果表明使用绝对节点坐标法更有利于描述柔性体大变形与大范围运动的耦合,壳单元在描述曲壳结构时更加精确。铰链驱动力矩能够激发镜片的振荡,特别是在多镜片同时展开时,多柔体的耦合作用会严重影响镜面的型面精度,进而扰动卫星本体的姿态。结论对空间望远镜的镜面精度和姿态精度的分析与控制具有理论价值和工程实际意义。     

Buckling analysis of orthotropic rectangular plate resting on Pasternak elastic foundation under biaxial in-plane loading

In this study, buckling of rectangular orthotropic plates resting on a Pasternak elastic foundation under biaxial in-plane loading by the power series method (the method of Frobenius) was analyzed. Similar to many studies, two opposite edges of loading are simply supported and two other edges are assumed clamped. In order to extract the characteristic equations of orthotropic rectangular plate under in-plane loading resting on a Pasternak elastic foundation, the classical plate theory, by considering the interaction between plate and foundation, is used. The results showed that in the aspect ratio of less than 2, the existing Pasternak foundation caused the buckling load to increase severely, but by increasing the aspect ratio, the effect of the foundation is negligible. Applying the in-plane load in the y-direction caused the buckling load to decrease, but by increasing the aspect ratios the effect of the load is negligible.     

Longitudinal varying elastic foundation effects on vibration behavior of axially graded nanobeams via nonlocal strain gradient elasticity theory

In this research, vibration characteristics of axially functionally graded nanobeams resting on variable elastic foundation are investigated based on nonlocal strain gradient theory. This nonclassical nanobeam model contains a length scale parameter to explore the influence of strain gradients and also a nonlocal parameter to study the long-range interactions between the particles. The present model can degenerate into the classical models if the material length scale parameter and the nonlocal stress field parameter are both taken to be zero. Elastic foundation consists of two layers: a Winkler layer with variable stiffness and a Pasternak layer with constant stiffness. Linear, parabolic and sinusoidal variations of Winkler foundation in longitudinal direction are considered. Material properties are graded axially via a power-law distribution scheme. Hamilton's principle is employed to derive the governing equations that are solved applying a Galerkin-based solution for different boundary edges. Comparison study is also performed to verify the present formulation with those of previous papers. Results are presented to investigate the influences of the nonlocal and length scale parameters, various material compositions, elastic foundation parameters, type of foundation and various boundary conditions on the vibration frequencies of AFG nanobeams in detail.     

基于弹性基础梁理论的复合材料薄壁圆柱壳屈曲承载力模型

提出一种复合材料薄壁圆柱壳轴压局部屈曲承载力计算模型。在梁弯曲变形平截面假定和小变形假定的基础上,提出复合材料层合梁抗弯刚度的计算方法;根据轴压下圆柱壳的几何对称性及受力对称性,将圆柱壳局部屈曲问题转化为轴向和环向壳带的弯曲变形问题。依据薄壳稳定理论,建立弹性基础上纵向壳带局部屈曲模型,得到了复合材料圆柱壳屈曲承载力解析公式。理论计算公式与经验工程计算公式相比,具有形式上的相似性,且得到的计算系数可直接求出,而非经验范围选取。对三种铺层的复合材料薄壁圆柱壳进行了轴压试验,结合文献试验数据对比,试验结果与理论预测值基本一致,满足工程精度要求,验证了模型的正确性。     

Temperature-dependent discrete layer-differential quadrature bending analysis of the multi-layered functionally graded annular plates rested on a two-parameter elastic foundation

A discrete layer approach coupled with the differential quadrature method (DQM) is employed to temperature dependent analyze the laminated functionally graded (FG) annular plates under mechanical loading in a thermal environment. The formulations are derived based on the elasticity theory, which includes the effects of the initial thermal stresses and two-parameter elastic foundation. The material properties are assumed to be temperature-dependent and graded in the thickness direction. In order to accurately evaluate the effect of the thermal environment, the initial thermal stresses are obtained by solving the thermoelastic equilibrium equation. Comparison studies with the available solutions in the literature for FG plates are performed. Then, as an application, three common types of FG sandwich plates, namely, the sandwich with homogeneous face sheets and FG core and the sandwich with FG face sheets and homogeneous metal (soft) and ceramic (hard) core are analyzed. The influences of temperature rise, temperature-dependence of material properties, layers lay-out, foundation stiffness parameters, material graded index, and geometrical parameters on the solution are carried out. The new results can be used as benchmark solutions for future researches.     

Winkler地基上修正Timoshenko梁振动分析

利用Bernoulli-Euler梁理论建立的弹性地基梁模型应用广泛,但其在高阶频率及深梁计算中误差较大,利用修正的Timoshenko梁理论建立新的弹性地基梁振动微分方程,由于其在Timoshenko梁的基础上考虑了剪切变形所引起的转动惯量,因而具有更好的精确度。利用ANAYS beam54梁单元进行振动模态的有限元计算,所求结果与理论基本无误差,从而验证了该理论的正确性。基于修正Timoshenko梁振动理论推导出了弹性地基梁双端自由-自由、简支-简支、简支-自由、固支-固支等多种边界条件下的频率超越方程及模态函数。分析了弹性地基梁在不同理论下不同约束条件及不同高跨比情况下的计算结果,从而论证了该理论计算弹性地基梁的适用性。分析了不同弹性地基梁理论下波速、群速度与波数的关系。得到了约束条件和梁长对振动模态及地基刚度对振动频率有重要影响等结论。