Optimization of geometrically imperfect stiffened cylindrical shells under axial compression

A procedure is outlined for optimizing stiffened, thin, circular, cylindrical shells under uniform axial compression against general instability, in the presence of initial geometric imperfection. The procedure consists of two parts (a) optimization on the basis of a linear buckling analysis and perfect geometry, and (b) parametric studies on a reasonable region in the design space surrounding the optimum point (as obtained from part (a)) to assess the effect of initial geometric imperfections. This procedure is demonstrated through two design examples, for which it is concluded, that the presence of initial geometric imperfections does not alter the optimum weight and the corresponding design variables appreciably.     

A posteriori initial imperfection identification in shell buckling problems

The current research seeks to demonstrate that an inverse solution approach, leveraging nonlinear finite element analysis with a divide and conquer type stochastic search algorithm, can identify the presence of localized denting imperfections in cylindrical shell structures. This imperfection field identification is achieved using rather sparse displacement measurements taken at safe, service loading conditions. Both the existence and nature of the imperfection field present in a given shell structure instance are determined. These inferred imperfections are subsequently used to make reasonably accurate predictions regarding the actual shell structure strength at ultimate loading.     

Sensitivity of buckling loads of anisotropic shells of revolution to geometric imperfections and design changes

Buckling load sensitivity calculations in the shell-of-revolution program FASOR are discussed. This development is based on Koiter's initial postbuckling theory, which has been generalized to include the effect of stiffness changes, as well as geometric imperfections. The implementation in FASOR is valid for anisotropic, as well as orthotropic, shells. Examples are presented for cylindrical panels under axial compression, complete cylindrical shells in torsion, and antisymmetric angle-ply cylindrical panels under edge shear.     

含几何缺陷的均质材料悬臂薄板的自由振动

以TC4钛合金均质材料悬臂薄板为研究对象.基于经典板壳理论,通过Rayleigh-Ritz法,根据悬臂板边界条件预设模态函数,求得包括全局、局部的函数型几何缺陷的悬臂板的前四阶固有频率.探究了悬臂板的缺陷类型、尺寸、位置等多种因素对自由振动的影响.     

Fast procedure for Non-uniform optimum design of stiffened shells under buckling constraint

For tailoring the non-uniform axial compression, each sub-panel of stiffened shells should be designed separately to achieve a high load-carrying efficiency. Motivated by the challenge caused by numerous variables and high computational cost, a fast procedure for the minimum weight design of non-uniform stiffened shells under buckling constraint is proposed, which decomposes a hyper multi-dimensional problem into a hierarchical optimization with two levels. To facilitate the post-buckling optimization, an efficient equivalent analysis model of stiffened shells is developed based on the Numerical Implementation of Asymptotic Homogenization Method. In particular, the effects of non-uniform load, internal pressure and geometric imperfections are taken into account during the optimization. Finally, a typical fuel tank of launch vehicle is utilized to demonstrate the effectiveness of the proposed procedure, and detailed comparison with other optimization methodologies is made.

     

On post-buckling analysis and experimental correlation of cylindrical composite shells with Reissner-Mindlin-Von Kármán type facet model

In this paper post-buckling analysis of carbon fibre reinforced plastic cylindrical shells under axial compression is considered. Reissner-Mindlin-Von Kármán type shell facet model is used in the computations. The effect of geometric imperfection shape and amplitude on nonlinear analysis results is discussed. Numerical-experimental correlation is performed using the results of experimental buckling tests found in the literature. Results show that bringing the diamond shape geometric imperfection in the model significantly improves the correlation and gives good accuracy in simulating cylindrical shell post-buckling behaviour.     

Nonlinear dynamic buckling of spherical caps with initial imperfections

A finite difference method is developed for the large deformation elastic-plastic dynamic buckling analysis of axisymmetric spherical caps with initial imperfections. The problem formulation is based on governing differential equations of motion, treating the plastic deformation as an effective plastic load. Both perfectly plastic and strain hardening behavior are implemented in the program. Strain hardening is incorporated through use of the Prager-Ziegler kinematic hardening rule, so that the Bauschinger effect is accounted for. The solution for the large deformation elastic-plastic dynamic response of a spherical cap is compared very favorably with other findings. Two spherical cap models are selected to study the title problem. Results obtained indicate that both plastic yielding and initial imperfection play significant roles in reducing the load carrying capacity of these shell structures. Both increase their influence as the thickness to radius ratio and the imperfection magnitude increase, respectively. It is also found that dynamic effect has the influence of lowering load carrying capacity of perfect spherical caps; however, its influence on imperfect spherical caps depends on the magnitude of initial imperfections.     

Some computational aspects of a group theoretic finite element approach to the buckling and postbuckling analyses of plates and shells-of-revolution

Progress in the application of group theoretic methods to the nonlinear bifurcation analysis of symmetric structures has provided new hope in understanding the global postbuckling behavior of symmetric thin shell structures. However, what is still lacking in the computational mechanics community is a general purpose FE code with a group theoretic capability designed to take ‘optimal’ advantage of existing symmetry. This paper addresses some of the important issues associated with developing such a code—the long term goal being to provide structural analysts with new numerical tools for doing careful global analyses of imperfection sensitive structures which may eventually lead to more accurate predictions of the maximum load-carrying capacity of thin imperfection sensitive shell structures.     

Finite element analysis of buckling and post-buckling behaviors of arches with geometric imperfections

The buckling and post-buckling behavior of arches is very sensitive to their geometric imperfections. The purpose of this paper is to develop a refined curved finite element that might accurately represent the actual geometry of arches so that the imperfection effects on their buckling behavior could be properly investigated. For an arch with known geometric imperfections, the element stiffness matrix is precisely formulated in terms of Lagrangian variables for a perfect arch from a general incremental variational principle. In general, the element stiffness matrix contains Lagrangian strain, first and second order incremental strain and imperfection terms. For any general planar imperfect arch with a variable curvature, the element stiffness matrix is evaluated by numerical integration; however, for a nominally circular arch, it can be represented in closed form. Numerical results in terms of load-deformation curves are presented for a number of circular arches with and without imperfections and compared with existing solutions.     

Optimization of inelastic conical shells with cracks

Inelastic conical shells loaded by the central rigid boss with vertical load are studied. The thickness of the conical part of the structure is piecewise constant. The connection between the shell and the boss is weakened with a stable crack. The designs with the maximal load-carrying capacity are established under a given material consumption of the shell. Material of the shell wall obeys the von Mises yield condition.     

Imperfection for realistic image synthesis

Creating objects with surface imperfections is accomplished through texture specification and generation techniques. Based on fractal subdivision techniques and relatively simple distribution models, a wide class of surface imperfections may be generated, combined and rendered. The surface effects include scratches, splotches, smudges, corrosion, mould, stains and rust. A rule-based system is used to position the various surface imperfections on the texture map, and a simple natural language interface is used to specify the kinds of imperfections and their generative parameters through adverbs and prepositional phrases. Results along some of the imperfection dimensions are illustrated.     

Large deformation elastic-plastic buckling analysis of spherical caps with initial imperfections

Large deformation elastic-plastic buckling loads are obtained for axisymmetric spherical caps with initial imperfections. The problem formulation is based on equilibrium equations in which the plastic deformation is taken as an effective plastic load. Both perfectly plastic and strain hardening behavior are considered. Strain hardening is represented by the Prager-Ziegler kinematic hardening theory, so that the Bauschinger effect is accounted for. Solutions of elastic-plastic circular plates and spherical caps are in good agreement with previous results. For the spherical cap it was determined that both initial imperfection and plastic deformation have the same effect of reducing buckling capacity; as the magnitude of the imperfection increases, the influence of plastic deformation becomes less important. It is also found that the geometric parameter λ, which is used as an important factor in elastic response, becomes meaningless for the elastic-plastic buckling analysis of spherical caps.     

The accuracy of Donnell''s equations for axially-loaded, imperfect orthotropic cylinders

The accuracy of Donnell's equations for the buckling analysis of imperfect (limit point instability), circular, cylindrical, thin orthotropic shells under axial compression is investigated. This is accomplished by comparing critical loads obtained by employing Donnell-type kinematic equations with those based on the more accurate Sanders-type. For this purpose, a solution methodology is developed and described in the body of the paper. This methodology is then employed to generate critical loads for several orthotropic geometries, which cover a wide but practical range of parameters. These include cylinder length to radius ratios, radius to thickness ratios, two positions of the strong direction relative to the cylinder axis (θ=0 and 90°) and two shapes of the initial geometric imperfection, axisymmetric and symmetric. Classical simply supported boundaries are used for all configurations for which results are generated.     

Determination of the patch loading resistance of girders with corrugated webs using nonlinear finite element analysis

The corrugated steel plate is a widely used structural element in many fields because of its many favourable properties. This structural layout has spread in the field of bridges, too, especially for steel and composite bridges. Against of the numerous applications there are no standard design formulas for the patch loading resistance of girders with trapezoidally corrugated steel webs. The focus of the current paper is the determination of its design value with nonlinear finite element analysis. Experimental research is conducted on 12 test specimens. Failure mode, load carrying capacity and post ultimate behaviour are analysed. Based on the executed experiments numerical model is developed, and the patch loading resistance is determined by nonlinear analysis using geometrical and material nonlinear analysis and imperfections. The applied imperfection shape and scaling factor used for the nonlinear analysis are investigated and its influence on the structural behaviour is determined. Based on the experiments and numerical investigations, recommendations are formulated for possible equivalent geometric imperfection shape and scaling factor for girders with corrugated webs.     

Stochastic inverse identification of geometric imperfections in shell structures

It is now widely known that the presence of geometric imperfections in shell structures constitutes an important contribution to the discrepancy between theoretical and experimentally realizable ultimate loads governed by buckling. The present paper describes a method by which an actual initial imperfection field may be estimated using the service load response of a shell structure. The approach requires solving a stochastic inverse problem wherein uncertainty regarding initial imperfection predictions is expressed within the context of a Bayesian posterior distribution. The proposed approach could be applied to condition assessment and performance evaluation activities in practice.     

圆柱壳在热载荷及微扰外压作用下的分岔

在考虑温度对圆柱壳材料性能影响的基础上,建立了圆柱壳在扰动外压作用下的几何非线性动力控制方程.并采用伽辽金原理及 Melnikov 法研究了圆柱壳在热载荷及微扰外压作用下的分岔,进一步讨论分析了温度、Batdorf 参数等因素对圆柱壳发生混沌运动区域的影响,得出了随温度、Batdorf 参数的增大,混沌运动区域将越来越大的结论.     

\begin{document}$H_\infty$\end{document} Consensus Control of Discrete-Time Multi-Agent Systems Under Network Imperfections and External Disturbance

This paper presents a distributed control protocol for consensus control of multi-agent systems (MASs) under external disturbances and network imperfections, including communication delay and random packet dropout. To comply with the discrete nature of networked systems, in contrast to most of the existing work for MASs under network imperfections, the agents are modeled by discrete-time dynamics. The communication network is considered to be undirected, its delay is considered to be time-varying but bounded, and its packet dropout is modeled by a Bernoulli distributed white sequence. Sufficient conditions in terms of linear matrix inequalities (LMIs) for asymptotic mean-square consensus stability are derived under network imperfections without considering external disturbances. A desired disturbance attenuation level in the presence of both external disturbances and network imperfections is also provided. A simulation example is given to verify the effectiveness of the proposed approach in coping with network imperfection and disturbances.      

The effect of material and thickness variability on the buckling load of shells with random initial imperfections

The effect of material and thickness imperfections on the buckling load of isotropic shells is investigated in this paper. For this purpose, the concept of an initial ‘imperfect’ structure is introduced involving not only geometric deviations of the shell structure from its perfect geometry but also a spatial variability of the modulus of elasticity as well as the thickness of the shell. The initial geometric imperfections are described as a two-dimensional uni-variate (2D-1V) stochastic field with statistical properties that are either based on an available data bank of measured initial imperfections or assumed, in cases where no experimental data is available. In order to describe the non-homogeneous characteristics of the initial imperfections, the spectral representation method is used in conjunction with an autoregressive moving average model with evolutionary power spectra based on a statistical analysis of the experimentally measured imperfections. In cases where no experimental results is available, the initial imperfections are assumed to be homogeneous and their impact on the buckling load is investigated on the basis of ‘worst’-case scenarios with respect to the correlation length parameters of the stochastic fields. The elastic modulus and the shell thickness are described as 2D-1V non-correlated homogeneous stochastic fields, while the stochastic stiffness matrix of the shell elements is formulated using the local average method. The Monte Carlo Simulation method is used to calculate the variability of the buckling load, while for the determination of the limit load of the shell, a stochastic formulation of the elastoplastic and geometrically non-linear TRIC facet triangular shell element is implemented.     

An alternative approach to optimization of structures prone to instability

The paper addresses the problem of the optimization of the structures that, when perfect, are apt to lose stability by bifurcation and have symmetric bifurcation points.Unlike the typical treatment of the problem, the paper suggests an optimization approach that takes into account the sensitivity of the structure to imperfections.Two different ways of accounting for imperfection sensitivity are presented. In the first one, the structure is treated as perfect and the objective function (load factor subjected to maximization) in formed on the basis of post-buckling analysis. In the second formulation, the structure is considered as impaired by imperfections and the objective function is established on the basis of a nonlinear static analysis of the structure.Both formulations are illustrated by simple examples.