Classical and nonlinear buckling analyses of spherical sandwich shells

The buckling and initial postbuckling behavior of clamped shallow spherical sandwich shells with dissimilar face sheets under a uniform pressure is studied. The numerical results show that the buckling and initial post-buckling behavior of clamped shallow spherical sandwich shells with dissimilar face sheets is similar to that of the corresponding homogeneous shell.     

A NEW STATE SPACE SOLUTION FOR RECTANGULAR THICK LAMINATES WITH CLAMPED EDGES Hu Wenfeng Liu Yihua

通过把固支边上的边界位移函数作为状态变量引入状态方程,得到了含固支边矩形单层与叠层厚板的精确解. 在求解过程中,将非齐次状态方程的求解变为齐次状态方程的求解,省略了求解待定常数的中间过程,使求解过程变得简单. 所得到的解能够严格满足固支边界条件,在同一材料层内不需作分层处理,因而更加精确. 此外,对固支边的应力提出了新的计算方法,能够得到更精确的边界应力. 算例表明,本文解比现有精确解收敛快,与有限元解吻合的更好,尤其是在固支边处体现得更加明显.     

Generalization of Seide’s problem by the regulated stochastic linearization technique

In this paper, the nonlinear random vibration of a uniform beam clamped at both of its ends is investigated by the regulated stochastic linearization technique. A closed system of nonlinear algebraic equations for linearization coefficients is obtained using the frequency–response function matrix. Root mean-square response of maximum deflection of the beam that is obtained from the present technique is subsequently compared with that furnished by the conventional linearization. The numerical results show that the regulated stochastic linearization technique constitutes an excellent alternative to the classical linearization scheme for analyzing responses of the clamped–clamped beam.     

悬臂半无限大板弯曲的边界积分公式

根据双调和方程边值问题的边界积分公式,求得了一般载荷作用下悬臂半无限大板的弯曲解,在此基础上求解了不同边界条件下几种半无限大板的弯曲问题.其解式收敛速度快、计算精度高,计算过程相对简单,并与相应有限元解进行了对比分析.     

Bending of a uniformly loaded clamped sector plate

The paper involves the expansion of the biharmonic deflection function in a series of non-orthogonal functions satisfying the condition of clamped edges. Each of these non-orthogonal functions is expanded in a series of orthogonal functions which satisfy a certain fourth order differential equation and the boundary conditions implied by the fact that the edges are clamped. This reduces the bending of a uniformly loaded clamped sector plate to the solution of a linear algebraic system of equations. Numerical results for the deflection of the central line are obtained when the semi-sector angle is 15 degrees.     

Active and passive magnetic constrained damping treatment

This paper has presented a new class of active and passive magnetic constrained layer damping (APMCLD) treatment for controlling vibration of three-layer clamped–clamped beams. Firstly, optimal placement strategies of discrete patches are investigated. The predictions of model are validated experimentally using three-layer clamped–clamped beams treated with fully or segmented passive magnetic constrained layer damping (MCLD) treatments. The results indicate that full MCLD treatment induces less improvement of damping characteristics. Also, the obtained results illustrate that, the improvement of damping performance using two-patched MCLD treatment becomes more apparent at the first mode compared to the corresponding performance using a single-patched MCLD treatment when the total length of damping layer is from 0.3L to 0.65L under considered magnetic force. Further, damping performances of APMCLD using several control strategies including simple PD controllers are investigated. The analytical results show that it induces less improvement of damping characteristics for higher modes using simple positive proportional feedback controllers whereas higher modes can been suppressed effectively using negative derivative feedback controllers. For broad band control of structural vibration, it is more effective using APMCLD treatments with combined proportional and derivative controllers. Moreover, the MCLD treatment still plays an important role in damping out structural vibrations even though active control systems fail.     

Behavior of microconcrete hyperbolic-paraboloid shell

The paper presents the results of an experimental as well as analytical investigation on the behavior of square hyperbolic-paraboloid (hypar) shell, subjected to uniformly distributed load and clamped all along the boundaries. The experimental investigation involves casting and testing of a microconcrete model of size 1000 mm×1000 mm, rise 222 mm and shell thickness 15 mm, clamped along all the four edges. The experimental results within elastic limit are compared with the results of a finite-element analysis using a doubly curved triangular shell element. The model was tested to destruction to study the behavior of the shell at ultimate load stage.     

Bending of uniformly loaded rectangular plates with two adjacent edges clamped, one edge simply supported and the other edge free

ＩｎｔｒｏｄｕｃｔｉｏｎＤｕｒｉｎｇｔｈｅｌａｔｅｓｅｖｅｎｔｉｅｓ,ＺｈａｎｇＦｕｆａｎｏｂｔａｉｎｅｄｔｈｅｅｘａｃｔｓｏｌｕｔｉｏｎｓｔｏｔｈｅｂｅｎｄｉｎｇｐｒｏｂｌｅｍｏｆｒｅｃｔａｎｇｕｌａｒｃａｎｔｉｌｅｖｅｒｐｌａｔｅｓａｎｄｒｅｃｔ...     

Explicit frequency equations of free vibration of a nonlocal Timoshenko beam with surface effects

Considerations of nonlocal elasticity and surface effects in micro-and nanoscale beams are both important for the accurate prediction of natural frequency. In this study, the governing equation of a nonlocal Timoshenko beam with surface effects is established by taking into account three types of boundary conditions: hinged–hinged, clamped–clamped and clamped–hinged ends. For a hinged–hinged beam, an exact and explicit natural frequency equation is obtained. However, for clamped–clamped and clamped–hinged beams, the solutions of corresponding frequency equations must be determined numerically due to their transcendental nature. Hence, the Fredholm integral equation approach coupled with a curve fitting method is employed to derive the approximate fundamental frequency equations, which can predict the frequency values with high accuracy. In short,explicit frequency equations of the Timoshenko beam for three types of boundary conditions are proposed to exhibit directly the dependence of the natural frequency on the nonlocal elasticity, surface elasticity, residual surface stress, shear deformation and rotatory inertia, avoiding the complicated numerical computation.     

Secondary buckling of a flat plate under uniaxial compression: Part 2. Analysis of clamped plate by F.E.M. and comparison with experiments

In Part 1, a theoretical analysis was used to study the secondary buckling of a simply supported plate. In Part 2, a clamped plate is analysed by the finite element method. The stability criterion for a non-linear post-buckling equilibrium state is evaluated by the sign of the determinant of the stiffness matrix. It should be noted that the secondary buckling loads of clamped plates are unexpectedly smaller than those of simply supported plates and are only one and a half times the primary buckling loads. In previous analyses, only a quarter segment of the plate was considered by assuming a stable equilibrium state with symmetrical mode. However, instability can also be predicted by considering the unsymmetrical mode over the whole plate. Results of experimental analysis of secondary instability of clamped square plates under uniaxial compression agreed with the numerical results.     

矩形板屈曲问题的一个小波解

利用Wavelet-Galerkin法分析了四边固支与四边简支矩形板的屈曲问题.以小波作为基函数表示板的挠度,推导出屈曲系数及屈曲模态的计算过程.数值计算给出了不同边长比的矩形板的屈曲系数及屈曲半波数.与传统的三角函数作基函数的Galerkin法及有限元法结果比较,结果表明在一定条件下小波可以作为试函数解决结构力学的屈...     

Experiments on the stability of spherical and paraboloidal shells

This paper presents the experimental part of a study of the elastic stability of clamped and hinged spherical and paraboloidal shell caps subjected to external uniform pressure loading. Ninety-six poly-vinyl-chloride (PVC) shells of 15-in. base diameter and formed by thermovacuum process, were tested and their critical loads recorded. The effects of geometry, clamped and hinged boundary conditions, height/span and radius of curvature/thickness ratios on the critical pressure were investigated. The results are compared, where possible, with experimental data obtained by previous investigators.     

Thin plate spline radial basis functions for vibration analysis of clamped laminated composite plates

A meshless method based on thin plate spline radial basis functions and higher-order shear deformation theory are presented to analyze the free vibration of clamped laminated composite plates. The singularity of thin plate spline radial basis functions is eliminated by adding infinitesimal to the zero distance. Convergence characteristics of the present thin plate spline radial basis functions for the vibration analysis of the clamped laminated plates are investigated. The frequencies computed by the present method agree well with the available published results.     

TENSION OF A CLAMPED RECTANGULAR PLATE CONTAINING A CENTRAL CRACK

Using the fundamental solution of a single crack and the Fourier transform solution of an infinite strip, the tension problem of a clamped rectangular plate containing a central crack is reduced to solve a system of singular integral equations. Then, the normal stress on clamped side and the stress intensity factars of the central cruck are carried out by means of Gauss-Jacobi integration formulas. The comparison of numerical results is shown in the "table of stress intensity factars".     

均布载荷作用下带边缘大波纹膜片的非线性弯曲

采用轴对称旋转壳体的简化Reissner方程，研究了在均布载荷作用下具有硬中心的带边缘大波纹膜片的非线性弯曲问题．应用积分方程方法，获得了具有夹紧固定和滑动固定两种外边界的膜片的特征关系，即荷载-中心挠度曲线．作为算例，给出了夹紧固定膜片中的应力分布．     

Dynamic behavior of inelastic cylindrical shells at finite deformation

Numerical approaches based on a minimum principle in dynamic finite plasticity are developed to study the dynamic behavior of inelastic cylindrical thin shells and rectangular plates at finite deformation. The minimum principle, which is based on the concept of finite variations in accelerations, is expressed in terms of Lagrangian strains and Kirchhoff stresses. The responses of a clamped cylindrical shell panel and a clamped rectangular plate to impulsive loadings are analyzed by using an incremental finite-difference method. An incremental Kantorovich method is employed to study the dynamic behavior of a complete cylindrical shell of finite length and loaded impulsively on its inner surface. The motions are simulated through a timewise step-by-step integration scheme. The results obtained in this analysis compare favorably with the theoretical and experimental results available in the literature.     

Elasticity solution of clamped-simply supported beams with variable thickness

This paper studies the stress and displacement distributions of continuously varying thickness beams with one end clamped and the other end simply supported under static loads. By introducing the unit pulse functions and Dirac functions, the clamped edge can be made equivalent to the simply supported one by adding the unknown horizontal reactions. According to the governing equations of the plane stress problem, the general expressions of displacements, which satisfy the governing differefitial equations and the boundary conditions attwo ends of the beam, can be deduced. The unknown coefficients in the general expressions are then determined by using Fourier sinusoidal series expansion along the upper and lower boundaries of the beams and using the condition of zero displacements at the clamped edge. The solution obtained has excellent convergence properties. Comparing the numerical results to those obtained from the commercial software ANSYS, excellent accuracy of the present method is demonstrated.     

Determination of the microscale stress–strain curve and strain gradient effect from the micro-bend of ultra-thin beams

A simple method is established to determine the microscale uniaxial stress–strain curve from the load and deflection data for a doubly clamped beam. The method is based on the fact that, for beam deflection much larger than the beam thickness, the axial stretching dominates the deformation in the doubly clamped beam and the doubly clamped beam behaves like a simple plastic hinge. The microscale uniaxial stress–strain curve, together with the cantilever beam experiments, is used to determine the strain gradient effect in Au thin beams. The effect of finite rotation is also discussed.     

Study of the effect of thermal gradient on free vibration of clamped visco-elastic rectangular plates with linearly thickness variation in both directions

The effect of thermal gradient on the free vibration of clamped visco-elastic rectangular plate with linearly thickness variations in both the directions has been studied here. The governing differential equation has been solved using Rayleigh-Ritz technique. The frequency equation is derived for the clamped boundary condition on all the four edges. The effect of linear temperature variation has been considered. Deflection and time period corresponding to the first two modes of vibrations of a clamped plate have been computed for various values of aspect ratio, thermal constants, and taper constants.     

Tension of a clamped rectangular plate containing a central crack

Using the fundamental solution of a single crack and the Fourier transform solution of an infinite strip, the tension problem of a clamped rectangular plate containing a central crack is reduced to solve a system of singular integral equations. Then, the normal stress on clamped side and the stress intensity factors of the central crack are carried out by means of Gauss-Jacobi integration formulas. The comparison of numerical results is shown in the “table of stress intensity factors”. This work was supported by the Science Fund of the Academy of Sciences of China.