受轴压黏弹性层合圆柱壳的极值点蠕变失稳

基于Donnell薄壳理论, 采用准弹性方法, 分析了含初始几何缺陷黏弹性层合圆柱壳极值点形式的延迟失稳特征。由轴向缩短量的突然增加定义失稳临界时间, 对玻璃纤维/环氧树脂层合圆柱壳进行了数值计算。结果表明: 圆柱壳存在临界时间趋于无穷的持久临界荷载; 表征延迟失稳程度的瞬时弹性临界荷载与持久临界荷载之差值随着初始几何缺陷的增加而减小; 边界条件、 铺设方式对延迟失稳的影响机制可通过对应弹性层合圆柱壳的缺陷敏感性分析来考察。      

On the imperfection sensitivity of complete spherical shells

The imperfection sensitivity of elastic complete spherical shells under external pressure is studied for axisymmetric deformations and qualitatively different types of imperfections by means of a numerical analysis of the Reissner shell equations. It is shown that strong reductions of the critical load are obtained for small deviations of the middle surface of the shell from the perfect spherical configuration whereas imperfections of the shell thickness do not have a substantial influence on the critical load.     

Singular perturbations for sensitivity analysis in symmetric bifurcation buckling

A direct procedure for the evaluation of imperfection‐sensitivity in bifurcation problems is presented. The problems arise in the context of the general theory of elastic stability (Koiter's theory) for discrete structural systems, in which the total potential energy is employed together with a stability criterion based on energy derivatives. The imperfection sensitivity of critical states, such as bifurcations and trifurcations, is usually represented as a plot of the critical load versus the amplitude ε of the imperfection considered. However, such plots have a singularity at the point with ε=0, so that a regular perturbation expansion of the solution is not possible. In this work, we describe a direct procedure to obtain the sensitivity of the critical load (eigenvalue of the bifurcation problem) and the sensitivity of the critical direction (eigenvector of the bifurcation problem) using singular perturbation analysis. The perturbation expansions are constructed as a power series in terms of the imperfection amplitude, in which the exponents and the coefficients are the unknowns of the problem. The solution of the exponents is obtained by means of trial and error using a least degenerate criterion, or by geometrical considerations. To compute the coefficients a detailed formulation is presented, which employs the conditions of equilibrium and stability at the critical state and their contracted forms. The formulation is applied to symmetric bifurcations, and the coefficients are solved up to third‐order terms in the expansion. The algorithmis illustrated by means of a simple example (a beam on an elastic foundation under axial load) for which the coefficients are computed and the imperfection‐sensitivity is plotted. Copyright © 2001 John Wiley & Sons, Ltd.     

SENSITIVITY ANALYSIS OF BIFURCATION LOAD OF FINITE-DIMENSIONAL SYMMETRIC SYSTEMS

Three methods are presented for sensitivity analysis of bifurcation load factor of finite-dimensional conservative symmetric systems subjected to a set of symmetric proportional loads. In the first method, a conventional method with diagonalization is utilized to derive an explicit formula of sensitivity coefficients corresponding to a minor imperfection. Next, a new concept is introduced to find the sensitivity coefficients of the load factor, displacements and the eigenmodes under fixed lowest eigenvalue of the tangent stiffness matrix. Based on this concept, a method is presented for finding approximate sensitivity coefficients of the buckling load factor. Finally, a direct method is presented to find the accurate sensitivity coefficients of the bifurcation load factor, displacements at buckling and the buckling mode of a symmetric system. Note that different formula should be used for sensitivity analysis of a limit point load factor. In the examples, the proposed three methods are compared in view of accuracy of the results and simplicity in coding.     

电除尘器壳体墙板立柱结构体系缺陷敏感性研究

电除尘器是用于消除大气烟尘的重要环保设备,壳体是其中最重要的工艺部分。壳体墙板为加劲钢板,与立柱连续焊接连接,组成共同承载的结构体系。壳体承受的横向荷载为负压与风荷载,作用在墙板上,壳体承受的竖向荷载主要作用在立柱上。墙板的初始缺陷会影响立柱的承载能力。该文通过非线性有限元方法,研究不同缺陷幅值时,完善结构极值点变形缺陷模态、完善结构非线性分岔点变形缺陷模态、特征值屈曲缺陷模态、墙板正弦波形缺陷模态以及墙板安装过程中的焊接收缩残余变形与残余应力对立柱承载力的影响。当缺陷幅值一定时,各种初始几何缺陷形式中,以完善结构的极值点变形缺陷模态为最不利。墙板安装过程中的焊接收缩引起的残余应力对于立柱承载是有利的,但是提高承载力很小。随着焊接收缩量的增大,残余应力值增大,同时考虑残余应力和残余变形影响得到的立柱承载力比仅考虑残余变形得到的承载力的增加量变大。     

Thermal Postbuckling Analysis of Imperfect Reissner-Mindlin Plates on Softening Nonlinear Elastic Foundations

A thermal postbuckling analysis is presented for a simply supported, moderately thick rectangular plate subjected to uniform or nonuniform tent-like temperature loading and resting on a softening nonlinear elastic foundation. The initial geometrical imperfection of the plate is taken into account. The formulations are based on the Reissner-Mindlin plate theory considering the first-order shear-deformation effect, and including plate-foundation interaction and thermal effects. The analysis uses a deflection-type perturbation technique to determine the thermal buckling loads and postbuckling equilibrium paths. Numerical examples are presented that relate to the performances of perfect and imperfect, moderately thick plates resting on softening nonlinear elastic foundations. The effects played by foundation stiffness, transverse shear deformation, plate aspect ratio, thermal load ratio and initial geometrical imperfections are studied. Typical results are presented in dimensionless graphical form and exhibit interesting imperfection sensitivity.     

Accurate and efficient a posteriori account of geometrical imperfections in Koiter finite element analysis

The Koiter method recovers the equilibrium path of an elastic structure using a reduced model, obtained by means of a quadratic asymptotic expansion of the finite element model. Its main feature is the possibility of efficiently performing sensitivity analysis by including a posteriori the effects of the imperfections in the reduced nonlinear equations. The state‐of‐art treatment of geometrical imperfections is accurate only for small imperfection amplitudes and linear pre‐critical behaviour. This work enlarges the validity of the method to a wider range of practical problems through a new approach, which accurately takes into account the imperfection without losing the benefits of the a posteriori treatment. A mixed solid‐shell finite element is used to build the discrete model. A large number of numerical tests, regarding nonlinear buckling problems, modal interaction, unstable post‐critical and imperfection sensitive structures, validates the proposal. Copyright © 2017 John Wiley & Sons, Ltd.     

具有初始几何缺陷加劲板的动态屈曲

针对工程中常用的加劲板,研究了动态屈曲的求解方法。将加劲板分为母板与加劲肋两个部分考虑,其中母板按经典薄板理论计算,加劲肋视为Euler梁。假定加劲板的位移,利用Hamilton原理结合系统能量和振型叠加法建立了加劲板的动态屈曲特征方程。最后,选择四边简支加劲板进行数值分析,分析中考虑初始几何缺陷的影响,并讨论了初始几何缺陷、加劲肋的数量及其刚度的变化对动态屈曲临界荷载的影响。结果表明：一阶模态的初始几何缺陷对加劲板的临界荷载影响很大,而增加加劲肋的数量及其刚度可以提高加劲板的抗动态屈曲能力。研究结果也为加劲板的结构设计方法提供一定的参考。     

Probabilistic analysis of delamination onset in linear anisotropic elastic and viscoelastic composite columns

Previously developed deterministic and stochastic combined load invariant failure criteria are used to determine the onset of delamination in elastic and viscoelastic columns. The analysis includes the effects of initial imperfections as well as offset column loads and transverse shear contributions. The delamination predictions are found to be sensitive to the magnitude of applied loads and of initial imperfections. Illustrative numerical examples are presented for elastic and viscoelastic columns with random combined failure stresses in bending, shear, compression and with normal interlaminar stresses. Probabilities of delamination onset are established for various axial loads and initial imperfections and in the viscoelastic columns additionally as a function of lifetime. Since the failure theories consider the combined effects of bending, shear, compression and normal interlaminar stresses, delamination onset is predicted at smaller axial loads than the critical buckling loads in the elastic case and at shorter viscoelastic lifetimes compared to equivalent columns with no delamination effects.     

Dynamic buckling of FGM truncated conical shells subjected to non-uniform normal impact load

Dynamic buckling of functionally graded materials truncated conical shells subjected to normal impact loads is discussed in this paper. In the analysis, the material properties of functionally graded materials shells 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. Geometrically nonlinear large deformation and the initial imperfections are taken into account. Galerkin procedure and Runge–Kutta integration scheme are used to solve nonlinear governing equations numerically. From the characteristics of dynamic response obtain critical loads of the shell according to B-R criterion. From the research results it can be found that gradient properties of the materials have significant effects on the critical buckling loads of FGM shells.     

The dynamic elastic buckling of a circular arch with finite displacements and initial imperfections

The equilibrium equations for elastic circular arches are established using the principle of virtual work. The nonlinear partial differential equations of motion are solved using a finite difference method (Park's method for time difference). The dynamic stability of a hinged and a clamped elastic circular arch with a uniform step load is analysed with finite deformations and initial geometric imperfections. Results show that the buckling mode varies with the value of the arch half angle, θ₀. The boundary condition and initial imperfection amplitude also effect the buckling mode. A nearly perfect arch usually buckling with a “direct” buckling form, while an imperfect arch with an “indirect” buckling form. The effect of θ₀ on the ratio p_d/p_s (p_d is the dynamic critical load and p_s the static critical load) is shown for different initial imperfections and different boundary conditions.     

Local Buckling Delamination of a Rectangular Sandwich Plate Containing Interface Embedded Rectangular Cracks and Made From Elastic and Viscoelastic Materials

A three-dimensional buckling delamination problem for a rectangular sandwich plate made from elastic and viscoelastic materials is studied. It is supposed that the plate contains interface embedded rectangular cracks and that the edge-surfaces of these cracks have initial infinitesimal imperfections. The evolution of these initial imperfections with an external bi-axial compressed force (for the case where the materials of the layers of the plate are elastic) or with duration of time (for the case where the materials of the layers of the plate are viscoelastic) is investigated. The corresponding boundary value problem is formulated within the framework of the piecewise homogeneous body model with the use of three-dimensional geometrically nonlinear field equations of the theory of viscoelastic bodies. This problem is solved by employing boundary form perturbation techniques, Laplace transform and FEM. According to the initial imperfection criterion, the values of the critical parameters are determined. Numerical results on the critical force and critical time are presented and discussed. In particular, it is established that the values of the critical forces obtained for the buckling delamination around the rectangular embedded interface cracks are significantly greater than those obtained for the corresponding edge and band cracks.     

Postbuckling of functionally graded cylindrical shells with tangential edge restraints and temperature-dependent properties

This paper presents an analytical approach to investigate the buckling and postbuckling behavior of functionally graded cylindrical shells subjected to thermal and axial compressive loads. Material properties are assumed to be temperature dependent and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of constituents. The governing equations are established within the framework of classical thin shallow shell theory taking both geometrical nonlinearity in von Kármán–Donnell sense and initial imperfection into consideration. Thermal stability analysis also incorporates the effects of tangential edge constraints. A Galerkin procedure is applied to derive expressions of load-deflection relations from which the thermal buckling loads and postbuckling curves of the shells are obtained by an iteration. Effects played by material and geometrical properties, tangential stiffness, imperfection and buckling modes are discussed.     

Imperfection sensitivity in the nonlinear vibration of initially stresses functionally graded plates

In this paper, the nonlinear partial differential equations of nonlinear vibration for an imperfect functionally graded plate (FGP) in a general state of arbitrary initial stresses are presented. The derived equations include the effects of initial stresses and initial imperfections size. The material properties of a FGP are graded continuously in the direction of thickness. The variation of the properties follows a simple power-law distribution in terms of the volume fractions of the constituents. Using these derived governing equations, the nonlinear vibration of initially stressed FGPs with geometric imperfection was studied. The present approach employed a perturbation technique, the Galerkin method and the Runge–Kutta method. The perturbation technique was used to derive the nonlinear governing equations. The motion of imperfect FGPs was obtained by performing the Galerkin method and then solved by the Runge–Kutta method. Numerical solutions are presented for the performances of perfect and imperfect FGPs. The nonlinear vibration of a simply supported ceramic/metal FGP was solved. It is found that the initial stress, geometric imperfection and volume fraction index greatly change the behavior of nonlinear vibration.     

Optimization method for the determination of the most unfavorable imperfection of structures

The paper presents an optimization method for direct determination of the most unfavorable imperfection of structures by means of ultimate limit states. When analyzing imperfection sensitive structures it turns out that the choice of the shape and size of initial imperfections has a major influence on the response of the structure and its ultimate state. Within the optimization algorithm the objective function is constructed by means of a fully nonlinear direct and first order sensitivity analysis. The method is not limited to small imperfections and also allows the imposition of “technological” constraints on the shape of the imperfection, thus making it possible to avoid unrealistically low ultimate loads. When carefully constructed, the objective function and constraints remain linear enabling the use of numerically efficient and readily available linear programming algorithms. Imperfection analyses are shown for thin-walled girders and a cylinder to demonstrate the applicability and efficiency of the proposed method.     

Instabilities in torispheres and toroids under suddenly applied external pressure

An elastic analysis of geometrically perfect and imperfect torispheres and perfect closed toroids under suddenly applied external pressure of infinite duration is presented in this paper. It is found that under suddenly applied pressure, a geometrically perfect torisphere fails by indirect axisymmetric snapping and that the critical pressure at which snapping occurs is smaller than the static bifurcation buckling pressure. The critical pressure depends on the rate at which load is applied. Analysis of geometrically imperfect torispheres is also considered. Imperfections in the form of localised flat patch and imperfections with affinity to the buckling eigenmode shape are used. For larger amplitudes of shape deviations the dynamic load bearing capacity of imperfect domes is greater than in the corresponding static cases. A reverse situation exists for the smaller amplitudes of imperfections. The geometrically perfect closed toroids of circular and elliptical cross-section fail at step pressures which are almost the same as the static bifurcation loads.     

Thermal Postbuckling of Imperfect Shear-Deformable Laminated Plates on Two-Parameter Elastic Foundations

Thermal postbuckling analysis is presented for a simply supported, shear-deformable composite laminated plate subjected to uniform or nonuniform parabolic temperature loading and resting on a two-parameter (Pasternak-type) elastic foundation. The initial geometric imperfection of the plate is taken into account. Reddy's third-order shear-deformation plate theory with von Karman nonlinearity is used. The governing equations also include the plate-foundation interaction and thermal effects. The analysis uses a mixed Galerkin-perturbation technique to determine thermal buckling loads and postbuckling equilibrium paths. Numerical examples are presented that relate to the performances of perfect and imperfect, symmetric cross-ply laminated plates resting on Pasternak-type elastic foundations from which results for Winkler elastic foundations are obtained as a limiting case. The influence played by a number of effects, among them foundation stiffness, transverse shear deformation, plate aspect ratio, fiber orientation, thermal load ratio, and initial geometric imperfections, is studied. Typical results are presented in dimensionless graphical form.     

Inperfection sensitivity of laminated cylindrical shells in torsion and axial compression

The imperfection sensitivity of thin cylindrical shells, made out of fiberreinforced composite material and subjected to either uniform axial compression or torsion, and the effects upon it of certain parameters, are investigated. The sensitivity is established through plots of critical loads (limit point loads) versus imperfection amplitude. The larger the drop in critical load value with increasing amplitude, the greater the sensitivity. Results are presented for four- and six-ply laminates with simply supported boundaries and various stacking sequences. These sequences lead to symmetric, antisymmetric and asymmetric configurations with respect to the laminate midsurface. The material for all configurations is boron/epoxy. The parametric studies include primarily the effect of lamina stacking and length-to-radius ratio on the critical loads. Among the important findings are that (a) laminated cylindrical shells are more imperfection sensitive under axial compression than under torsion, (b) the imperfection sensitivity decreases as the length-to-radius ratio increases and (c) lamina stacking has a pronounced effect on the imperfection sensitivity of the laminated shell.     

Optimization of geometrically non‐linear symmetric systems with coincident critical points

A new formulation is presented for optimum design of an elastic symmetric structure for specified non‐linear buckling load factor. It is shown that the method of sensitivity analysis of bifurcation load factor developed in Ohsaki and Vetani (Int. J. Numer. Methods Engng. 1996; 39 : 1707–1720) can also be applied for the case where the structure reaches coincident critical points including a limit point. Based on the method of sensitivity analysis, an algorithm is presented for finding optimum designs for specified coincident critical points. The well‐known danger of designing a structure that exhibits coincident buckling is discussed in detail. It is shown in the examples of trusses that the structural volume may be successfully reduced as a result of optimization even if the reduction of the maximum load factor due to possible asymmetric initial imperfection is considered. Copyright © 2000 John Wiley & Sons, Ltd.     

Mechanical and thermal postbuckling of higher order shear deformable functionally graded plates on elastic foundations

This paper presents an analytical investigation on the buckling and postbuckling behaviors of thick functionally graded plates resting on elastic foundations and subjected to in-plane compressive, thermal and thermomechanical loads. Material properties are assumed to be temperature independent, and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of constituents. The formulations are based on higher order shear deformation plate theory taking into account Von Karman nonlinearity, initial geometrical imperfection and Pasternak type elastic foundation. By applying Galerkin method, closed-form relations of buckling loads and postbuckling equilibrium paths for simply supported plates are determined. Analysis is carried out to show the effects of material and geometrical properties, in-plane boundary restraint, foundation stiffness and imperfection on the buckling and postbuckling loading capacity of the plates.