Combined effects of in-plane boundary conditions and stiffening on buckling of eccentrically stringer-stiffened cylindrical panels

Donnel type stability equations for buckling of stringer stiffened cylindrical panels under combined axial compression and hydrostatic pressure are solved by the displacement approach of [6], The solution is employed for a parametric study over a wide range of panel and stringer geometries to evaluate the combined influence of panel configurations and boundary conditions along the straight edges on the buckling behavior of the panel relative to a complete “counter” cylinder (i.e. a cylinder with identical skin and stiffener parameters).

The parametric studies reveal a “sensitivity” to the “weak in shear”, N_x = N_xφ = 0, along the straight edges, SS1 boundary conditions type where the panel buckling loads are always smaller than those predicted for a complete “counter” cylinder. In the case of “classical”, SS3 B.Cs., there always exist values of panel width, 2φ₀, for which ρ = 1, i.e. the panel buckling load equals that of the complete “counter” cylinder. For SS2 and SS4 B.Cs. types, the nature by which the panel critical load approaches that of the complete cylinder appears to be panel configuration dependent.

Utilization of panels for the experimental determination of a complete cylinder buckling load is found to be satisfactory for relatively very lightly and heavily stiffened panels, as well as for short panels, (L/R) = 0.2 and 0.5. Panels of moderate length and stiffening have to be debarred, since they lead to nonconservative buckling load predictions.     

Elastic buckling of rectangular mindlin plate with mixed boundary conditions

An approximate method for analyzing the elastic buckling of Mindlin plates is proposed. The solutions of the differential equations of buckling of Mindlin plate are obtained in discrete forms by applying numerical integration. The discrete solutions give the transverse shear forces, twisting moment, bending moments, rotations and deflection at the all discrete points which are the intersections of the vertical and horizontal equally dividing lines on the plate. In order to confirm the convergency and accuracy of numerical solutions, the buckling loads of simply supported square Mindlin plates are calculated, and the results are compared with other published finite element solutions. As an application, the buckling loads and buckling modes of Mindlin plates with various types of mixed boundaries are calculated.     

Large amplitude vibrations of circular plates with mixed boundary conditions

In this paper, a method of analysing large amplitude vibrations of circular plates with mixed boundary conditions is explained and is illustrated with an example where part of the boundary is clamped and the remaining simply-supported     

Elastic buckling of tapered circular plates

This paper is concerned with the elastic buckling of tapered circular plates. The study is prompted by the fact that results hitherto available are restricted to a narrow range of taper parameters and are somewhat different from each other. For the buckling analysis, a simple and yet accurate numerical method is presented. It is based on the shooting method and the Rayleigh-Ritz approach. Comprehensive generic buckling results of circular plates with linearly and parabolically varying thicknesses are generated. Comparison studies of the buckling results showed that some of the existing results were erroneous. Optimal values of taper parameters for such tapered plates are also given.     

Nonlinear torsional buckling and postbuckling analysis of cylindrical silicon nanoshells incorporating surface free energy effects

In the present study, a size-dependent shell model is developed which can afford to describe the nonlinear torsional buckling and postbuckling characteristics of cylindrical nanoshells in the presence of surface stress effects. To accomplish this purpose, the Gurtin–Murdoch theory of elasticity together with the von Karman geometric nonlinearity is implemented into the first-order shear deformation shell theory. A linear variation through the thickness is considered for the normal stress component of the bulk to satisfy the balance conditions on the free surfaces of the nanoshell. By means of the virtual work principle, the non-classical governing differential equations are constructed in which the transverse displacement and Airy stress function are considered as independent variables. Thereafter, a boundary layer theory is employed including the effect of surface stress in conjunction with the nonlinear prebuckling deformations and the large postbuckling deflections. Subsequently, an efficient solution methodology based on an improved perturbation technique is put to use to obtain the size-dependent critical torsional buckling loads and the associated postbuckling equilibrium paths. It is observed that the torsional load exhibits a significant increase after reaching the minimum postbuckling load. Also, it is revealed that the effect of surface stress becomes negligible at high values of the deflection.

     

Effect of boundary conditions on natural frequencies for rotating composite cylindrical shells with orthogonal stiffeners

The effect of the boundary conditions on the natural frequencies for rotating composite cylindrical shells with the orthogonal stiffeners is investigated using Love’s shell theory and the discrete stiffener theory. The frequency equation is derived using the Rayleigh–Ritz procedure based on the energy method. The considered boundary conditions are four sets, namely: (1) clamped–clamped; (2) clamped–simply supported; (3) clamped–sliding; and (4) clamped–free. The beam modal function is used for the axial vibration mode and the trigonometric functions are used for the circumferential vibration mode. The composite shells are stiffened with uniform intervals and the stiffeners have the same material. By comparison with the previously published analytical results for the rotating composite shell without stiffeners and the orthogonally stiffened isotropic cylindrical shells, it is shown that natural frequencies can be determined with adequate precision.     

Local artificial boundary conditions for Schrödinger and heat equations by using high-order azimuth derivatives on circular artificial boundary

The aim of the paper is to design high-order artificial boundary conditions for the Schrödinger equation on unbounded domains in parallel with a treatment of the heat equation. We first introduce a circular artificial boundary to divide the unbounded definition domain into a bounded computational domain and an unbounded exterior domain. On the exterior domain, the Laplace transformation in time and Fourier series in space are applied to achieve the relation of special functions. Then the rational functions are used to approximate the relation of the special functions. Applying the inverse Laplace transformation to a series of simple rational function, we finally obtain the corresponding high-order artificial boundary conditions, where a sequence of auxiliary variables are utilized to avoid the high-order derivatives in respect to time and space. Furthermore, the finite difference method is formulated to discretize the reduced initial–boundary value problem with high-order artificial boundary conditions on a bounded computational domain. Numerical experiments are presented to illustrate the performance of our method.     

Vibration and buckling analysis of axisymmetric polar orthotropic circular plates

The vibration and stability analysis of polar orthotropic circular plates using the finite element method is discussed. In order to formulate the eigenvalue problems associated with the vibration and stability analyses, the clement stiffness, mass, and stability coefficient matrices are presented. By assuming the static displacement function, which is an exact solution of the polar orthotropic circular plate equation, approximates the vibration and buckling modes, the mass and stability coefficient matrices are readily derived from the given displacement function. Results showing the effects of orthotropy on natural frequencies and buckling loads are compared with their isotropic counterpart.     

功能梯度材料圆板的非线性热振动及屈曲

采用弹性理论建立了功能梯度材料板的静力平衡方程,利用静力平衡方程确定了功能梯度材料板的中性面位置,在此基础上推导出了功能梯度材料板在均匀温度场中的非线性振动及屈曲微分方程组,求得了功能梯度材料圆板的非线性振动及屈曲的近似解,讨论分析了中性面位置、梯度指数、温度等因素对功能梯度材料圆板非线性振动及屈曲的影响.把该方法计算结果与有限元计算结果进行了比较,验证了该方法的计算结果是可靠的.算例分析表明,中性面位置对均匀温度场中功能梯度材料圆板的非线性振动及屈曲有一定影响.     

Free vibration analysis of circular cylindrical shells

Determination of the vibrational characteristics of circular cylindrical shells often requires significant computational effort. This paper presents the results of a comprehensive, computer based, numerical investigation of the free vibration of circular cylindrical shells. An analytical procedure which accurately predicts the natural frequencies and radial mode shapes (corresponding to axial wave number and circumferential wave number both equal to one) for a wide range of circular cylindrical shells is developed. The procedure is applicable to shells either with or without a top closure. Several numerical examples are presented which illustrate application of the procedure and verify its accuracy.     

轴向载荷作用下圆柱壳的屈曲仿真

本文采用非线性有限元方法，在经典刚塑性理论的基础上，考虑了材料非线性、大变形效应对材料的影响，利用大型通用程序LS—DYNA对圆柱壳轴向冲击屈曲过程进行了计算机仿真分析。分析表明，利用非线性有限元数值仿真方法，可以对圆柱壳屈曲这一复杂的力学过程进行真实有效的模拟再现。     

Thermal buckling of circular plates with localized axisymmetric damages

Thermal buckling analysis of circular plates with localized axisymmetric damages has been carried out using the finite element method. The damages are characterized as degradation in material properties locally. Thermal buckling load parameters are evaluated for both simply supported and clamped circular plates with varying locations, magnitudes and lengths of damage. Numerical results are presented for different cases, and trends in variations of load parameters are discussed.     

Axisymmetric snap buckling of imperfect, tapered circular plates

The application of the Dynamic Relaxation method to the analysis of the axisymmetric snap buckling behaviour of uniformly loaded, imperfect, tapered circular plates is briefly described. It is then used to carry out a limited study of the effects of: (1) imperfection magnitude, (2) thickness taper ratio and (3) support conditions on the plate response. Two types of response are distinguished: (a) “snap-through” and (b) “smooth-transition”. The former type of response is found to occur only when the imperfection amplitude is sufficiently large. Furthermore, the results of the study show that decreasing the taper ratio and clamping the plate boundary both serve to raise the snap buckling load and that the latter measure is relatively more efficient in this respect.     

Dynamic buckling of functionally graded multilayer graphene nanocomposite annular plate under different boundary conditions in thermal environment

This paper deals with dynamic stability of functionally graded (FG) nanocomposite annular plate reinforced with graphene platelets (GPLs) subjected to a periodic radial compressive load in thermal environment. On the basis of modified Halpin–Tsai micromechanics model, the effective elastic modulus of structure is estimated. Taking into consideration of the first-order shear deformation theory, the governing motion equations are obtained via the Hamilton’s principle. Afterward, the partial differential motion equations are discretized into a system of Mathieu–Hill equations by utilizing generalized differential quadrature method. Furthermore, the Bolotin’s technique is applied to determine the principle unstable zone of functionally graded graphene platelet reinforced composite (FG-GPLRC) annular plate. The accuracy and validity of current study are examined by comparing the fundamental natural frequencies of structure with those published in available literature. Eventually, to investigate the influences of number of layers, GPLs patterns and their geometric, boundary conditions, geometrical parameters of structure, static load factor, and temperature change on the DIRs of FG-GPLRC multilayer annular plate, different parametric studies are performed.

     

Elasto-plastic shear buckling of square plates with circular holes

With in-plane stresses calculated by finite element analysis, critical loads are obtained by the Rayleigh-Ritz method for a square plate subjected to uniform edge shear stress and containing centrally located circular holes. Elastic and elasto-plastic buckling is examined for clamped and simply supported plates, and results are compared with previous analyses and experiments for various sized holes. The range of hole sizes considered is extended to include larger holes than previously examined, and for small holes, the results suggest that the critical stress is higher than previously thought. For elasto-plastic buckling, critical shear stresses are given for the full range of appropriate slenderness. Experimental results for the cases of simply supported plates support the analytical results, whereas verification for clamped plates remains inconclusive on account of limited reliable test data.     

On load interaction in the non linear buckling analysis of cylindrical shells

The elastic stability of shells or shell-like structures under two independent load parameters is considered. One of the loads is associated to a limit point form of buckling, whereas the second is a bifurcation. A simple one degree of freedom mechanical system is first investigated, for which an analytical solution is possible. Next, a cylindrical shell under the combined action of axial load and localised lateral pressure is studied via a non linear, two-dimensional, finite element discretization. It is shown that both problems display the same general behaviour, with a stability boundary in the load space which is convex towards the region of stability. The results show the need of performing a full non-linear analysis to evaluate the stability boundary for the class of interaction problems considered.     

Combined effects of working environmental conditions in VDT work

The combined effects of city noise and luminance of the computer display were evaluated from the changes in lymphocytes and mental activities of participants. Healthy male students were tested under the following four experimental conditions: (1) a calculating task on a video display terminal (VDT) with luminance of 90 cd m^-2 without city noise; (2) a calculating task on a VDT with luminance of 20 cd m^-2 without city noise; (3) a calculating task on a VDT with luminance of 90 cd m^-2 with city noise of 70 dB(A); and (4) a calculating task on a VDT with luminance of 20 cd m^-2 with city noise of 70 dB(A). A visual reaction test (VRT) was performed, and critical flicker fusion frequency (CFF), heart rate (HR), numbers of circulating white blood cells (WBCs), lymphocyte subsets and subjective symptoms of fatigue were measured (1) before; (2) just after; and (3) 30 min after each 60 min test. Subjective symptoms of fatigue significantly increased just after experiments conducted under the two noisy conditions. VRT and CFF showed significant changes in the case of the highluminance display with noise. WBCs and neutrophils showed significant increases in the two quiet conditions. These results suggested that high luminance with noise had the most effect on subjective fatigue and mental activities.     

DQM in-plane free vibration of laminated moderately thick circular deep arches

A differential quadrature (DQ) solution for moderately thick laminated circular arches with general boundary conditions is presented. The governing equations are based on the Reissner–Naghdi type shell theory, which include the effects of transverse shear deformation and rotary inertia. Explicit discrete forms of the equations of motion and the boundary conditions are presented. It is shown that using only few grid points, accurate results are obtained which demonstrate the efficiency and convenience of the DQ method (DQM) for the problem under consideration. The effects of different types of boundary conditions, opening angle, thickness-to-length and orthotropy ratios on the frequencies of antisymmetric cross-ply laminated arches are studied.     

Combined effects of working environmental conditions in VDT work

The combined effects of city noise and luminance of the computer display were evaluated from the changes in lymphocytes and mental activities of participants. Healthy male students were tested under the following four experimental conditions: (1) a calculating task on a video display terminal (VDT) with luminance of 90 cd m(-2) without city noise; (2) a calculating task on a VDT with luminance of 20 cd m(-2) without city noise; (3) a calculating task on a VDT with luminance of 90 cd m(-2) with city noise of 70 dB(A); and (4) a calculating task on a VDT with luminance of 20 cd m(-2) with city noise of 70 dB(A). A visual reaction test (VRT) was performed, and critical flicker fusion frequency (CFF), heart rate (HR), numbers of circulating white blood cells (WBCs), lymphocyte subsets and subjective symptoms of fatigue were measured (1) before; (2) just after; and (3) 30 min after each 60 min test. Subjective symptoms of fatigue significantly increased just after experiments conducted under the two noisy conditions. VRT and CFF showed significant changes in the case of the high-luminance display with noise. WBCs and neutrophils showed significant increases in the two quiet conditions. These results suggested that high luminance with noise had the most effect on subjective fatigue and mental activities.