Random Initial Imperfections Research Articles

Nonlinear buckling of a structure with random imperfection and random axial compression by a conditional simulation technique

This investigation deals with the buckling problem of a column with random geometric imperfection, resting on a nonlinear elastic foundation. In contrast to most of the earlier studies, it is assumed that the column is subjected to a random axial compression. The random initial imperfection is expressed in terms of buckling modes with coefficients obeying the truncated normal distribution. The external load is modeled as a random variable with the extreme-value distribution. An improved simulation technique with high computational efficiency is employed to obtain the probability of failure of the structure. Statistical analysis of the simulation data is proposed, and the final result is given in the form of confidence interval, which can be used directly in engineering design.

Collapse of axially compressed cylindrical shells with random imperfections

The establishment of an International Imperfection Data Bank is discussed. Characteristic initial imperfection distributions associated with different fabrication techniques are shown. Using a first-order, second-moment analysis, a stochastic method is presented, whereby the stability of isotropic, orthotropic and anisotropic nominally circular cylindrical shells under axial compression, external pressure and/or torsion possessing general nonsymmetric random initial imperfections can be evaluated. Results of measurements of initial imperfections are represented in Fourier series and the Fourier coefficients are used to construct the second-order statistical properties needed. The computation of the buckling loads is done with standard computer codes and includes a rigorous satisfaction of the specified boundary conditions. It is shown that the proposed stochastic approach provides a means to combine the latest theoretical findings with the practical experiences spanning about 75 years in an optimal manner via the advanced computational facilities currently available.

Random fields in the limit analysis of elastic-plastic shell structures

The purpose of this work is to analyse the problem: what is the effect of the assumed types and intensities of random initial geometrical imperfections on the equilibrium paths and the limit loads? To this end a new method of simulation of nonhomogeneous two-dimensional random fields on regular nets has been developed. The method is based on two concepts: an envelope of the random field and local covariance matrices classified according to the symmetry groups. The numerical examples deal with post-buckling responses of FEM models of shallow shells with different types of imperfections (whitenoise, Wiener and degenerated fields) using a Monte Carlo approach.

On Random Imperfections for Structures of Regular-Polygonal Symmetry

A theoretical study is made on the effect of random initial imperfections on the load-bearing capacities of structures of regular-polygonal symmetry. The group-theoretic method is employed to implement the symmetry in the formulation. In view of the concept of critical initial imperfection, the explicit form of probability density function of the load-bearing capacity of structures is derived for random initial imperfections. In particular, tight bounds on the range of load-bearing capacity are presented for various types of simple and double critical points. The theoretical and empirical probability distribution functions are compared for simple truss structures to show the validity and effectiveness of the present method.

Elastic Buckling Analysis of Rigidly Jointed Single Layer Reticulated Domes with Random Initial Imperfection

In the present paper, the effect of imperfection on the elastic buckling load and mode shapes of externally-loaded single layer reticulated domes is investigated. The types of buckling concerned here are the general buckling, the local (dimple) buckling and the buckling of a member. As to the geometric parameter of a dome, the slenderness factor S is adopted which represents the openness and slenderness of the dome. The maximum value of the imperfection is assumed to be the normal random variable. The buckling loads are computed by the linear and the nonlinear buckling analysis using the finite element method. The statistical values are calculated by the three-points estimates method. The main points of interest are the influence of the shape and the extent of an imperfection on the buckling load.

Buckling failure probability of imperfect elastic frames

Probabilistic buckling failure of random imperfect frames is studied via the stochastic finite element method. The statistics of buckling strengths of elastic frames with random initial imperfections, uncertain sectional and material properties are inferred from the statistics of the basic system parameters through the utilization of the stochastic finite element method. The effects of variations in geometric imperfections, sectional and material properties on variation in buckling strength are investigated. The failure probability of imperfect frames consisting of random system parameters subject to random loads is computed in load space. Factors affecting the reliability of the frames are identified and discussed. It was found that sectional properties, the shape of geometric imperfection, and the magnitude of imperfection may have important effects on frame reliability.

Buckling analysis of imperfect frames using a stochastic finite element method

A stochastic finite element method is developed for the buckling analysis of frames with random initial imperfections, uncertain sectional and material properties. The random geometrical imperfections of the frames are described by member initial crookednesses which are modeled as given initial displacement functions with amplitudes treated as random variables. The effects of the random initial geometric imperfections are formulated as a set of equivalent random nodal coordinates in the finite element discretization of the members. The mean-centered second-order perturbation technique is used to formulate the stochastic finite element method for the buckling analysis of the imperfect frames. Use of the present method is illustrated by several examples of buckling analysis of random frames. Results derived from the Monte Carlo method are also obtained for comparison.

Collapse of axially compressed cylindrical shells with random imperfections

Using the first-order, second-moment analysis, a stochastic method is presented, whereby the stability of isotropic, orthotropic, and anisotropic nominally circular cylindrical shells under axial compression, external pressure, and/or torsion possessing general nonsymmetric random initial imperfections can be evaluated

Random initial imperfections of structures

This paper is a theoretical study on random initial imperfections of structures. The explicit form of probability density function of the load-bearing capacity (critical load) of structures is derived for random initial imperfections based on a decomposition of the space of imperfection vectors into two orthogonal subspaces: the subspace that asymptotically affects the load-bearing capacity and the other that does not. Tight bounds on the range of load-bearing capacity are presented for various types of simple critical points. By means of the asymptotic theory of statistics, we show the inefficiency of a conventional random method that approximates the minimum loadhearing capacity by the minimum load for a number of random initial imperfections. The theoretical and empirical probability distribution functions for simple truss structures are compared to show the validity and effectiveness of the present method.

Monte Carlo analysis of nonlinear vibration of rectangular plates with random geometric imperfections

The effect of random initial geometric imperfections on the vibration behavior of rectangular plates is investigated in this paper using a statistical method. The random initial geometric imperfections of plates are described by Gaussian random fields and simulated numerically using Elishakoff's method. Lindstedt-Poincaré's perturbation technique is employed to solve Duffing's Equation with an additional quadratic spring term derived in the vibration analysis of imperfect rectangular plates. A Monte Carlo analysis for simply supported plates is carried out in detail to illustrate the proposed approach. It is shown that the effect of random geometric imperfections on the vibration behavior of the plates can be described quantitatively in terms of the frequency reliability function and the hardening type probability.

The stiffness and strength requirements for platform-beams in an industrial hall

Multiple storeys of platform-beams are used to reduce the effective length of columns in some types of industrial building where the storey height is very great. This paper reports on a study of the stiffness and strength requirements which should be imposed on the platform-beams to brace the columns effectively. Closed forms solutions and simple-to-use formulae are provided in which the effect of the random column initial imperfection has been considered.

Reliability of Randomly Imperfect Beam‐Columns

A stochastic finite element method is developed for reliability studies of problems such as beam‐columns under axial loading with random geometric imperfections, uncertain material properties, and uncertain moduli of elastic foundations. The random geometric imperfections are described by an explicit form of autocorrelation function or a given initial displacement function with amplitude described as a random variable. The effects of random initial geometric imperfections are treated as a set of equivalent random initial forces. This concept enables the direct employment of existing stochastic finite element methods developed for treating random forces. This formulation can be straightforwardly used to study the reliability of practical beam‐column problems with complex loadings, realistic boundary conditions, arbitrary geometries, and imperfections, for which analytical solutions are difficult to obtain. To establish the validity of the present formulation, a series of examples including random loadings and uncertain material properties were solved. Since existing alternative solutions are limited, analytical solutions are also obtained for comparison. The last of the series of examples is a simply supported beam‐column with four simultaneous uncertain parameters: geometric imperfection, modulus of elasticity, moment of inertia, and modulus of elastic foundation. All the four parameters cover ranges of values with practical significance.

Axial Impact Buckling of a Column With Random Initial Imperfections

Axial impact buckling of perfectly elastic bars with initial imperfections is considered in a probabilistic setting. It is assumed that the initial imperfection function involved a single parameter, which in turn is a continuous random variable with given probability distribution function. The structure is said to buckle if the absolute value of the total displacement exceeds a prescribed value. The probabilistic nature of the random, critical time when such a failure occurs for the first time, is studied.

General random imperfections in the buckling of axially loaded cylindrical shells

Mean values as well as confidence intervals for the critical load of axially loaded cylindrical shells containing general random initial imperfections are obtained. The results display trends that have been observed experimentally and provide insight into previously proposed design criteria. It has been determined that nonaxisymmetric initial imperfections play a vital role in the determination of the critical load statistics and that this role varies with the shell radius-to-thickness ratio. The work should provide a sound theoretical basis for the design of randomly imperfect cylindrical shells.

Probability analysis of the stability and minimization of the mass of cylindrical shells made of a composite material having random initial imperfections

Probability analysis of the stability and minimization of the mass of cylindrical shells made of a composite material having random initial imperfections

鋼圧縮材の座屈強度の確率論的方法による研究 : ランダムな残留応力, 降伏応力, 初期たわみを有する H 形鋼の弱軸まわりの座屈

This paper intends to obtain the reference data in order to make better column formulas, considering the scatter of buckling load in compressive members. In consideration of the scatter of the buckling load, we investigate the effect of random initial imperfections, which are random residual stress, random yield stress and random initial deflection thought most important, with probabilistic methods. In the first, the probability distribution of buckling loads about weak axis for rolled H-section members are made with the Monte-Carlo simulation procedure mainly. Next, we statistically deal with the result of the simulation and obtain the probability distribution function, mean value, standard deviation and coefficient of variation of the buckling load. And we considered them carefully. After all, some properties connected with the variation of buckling load in compressive members are represented definitely. Furthermore, reffering to the allowable compressive stress in Steel Structural Design Specification (A. I. J.), we point out that the factor of safety in column formula is doubtful about critical slenderness ratio.

Closure to “Discussion of ‘Buckling of a Long, Axially Compressed, Thin Cylindrical Shell With Random Initial Imperfections’” (1973, ASME J. Appl. Mech., 40, pp. 634–635)

Closure to “Discussion of ‘Buckling of a Long, Axially Compressed, Thin Cylindrical Shell With Random Initial Imperfections’” (1973, ASME J. Appl. Mech., 40, pp. 634–635)

Buckling of a Long, Axially Compressed, Thin Cylindrical Shell With Random Initial Imperfections

The effect of random geometric imperfections on the maximum load-carrying capacity of an axially compressed thin cylindrical shell is studied. Following a perturbation approach, equations are derived which relate the first and second-order statistics of the maximum load to the statistics of the initial imperfections. Assuming that the imperfections are represented by Gaussian stationary and ergodic random processes, it is shown that the mean maximum load is expressible in quadrature forms involving the power spectral density of the initial imperfection. Furthermore, the maximum load is seen to be equal to its mean value with probability one. A simple asymptotic formula for the maximum load is derived assuming the variance of the initial imperfection is small. In this case the critical load depends only upon the imperfection variance and the power spectral density at a given wave number. For the types of imperfections considered, it is found that random axisymmetric imperfections reduce the load-carrying capacity of the cylindrical shell more than nonaxisymmetric imperfections.