Koiter's Perturbation Research Articles

Efficient post-buckling analysis of variable-stiffness plates using a perturbation approach

The present work discusses the development of a formulation for efficiently analyzing variable-stiffness plates operating in the post-buckling regime. The approach relies upon the combined use of a single-mode Koiter's perturbation strategy along with a mixed variational formulation expressed in terms of Airy stress function and out-of-plane displacement, where the unknowns are approximated using global trial functions based on Legendre polynomials. A highly efficient numerical tool is achieved, which allows the initial post-buckling field to be analyzed with the ease of closed-form solutions, but a much wider field of employ in terms of elastic couplings, boundary and loading conditions. The quality of the predictions is illustrated by means of a comprehensive set of comparisons against results from the literature. Possible applications of the approach are shown, where the exploration of the design space offered by curvilinear fibers requires thousands of non-linear post-buckling analyses to be run.

STOCHASTIC POST-BUCKLING OF FRAMES USING KOITER'S METHOD

The objective of this paper is to explore the impact of stochastic inputs on the buckling and post-buckling response of structural frames. In particular, we examine the impact of random member stiffness on the buckling load, and the initial slope and curvature of the post-buckling response of three example frames. A finite element implementation of Koiter's perturbation method is employed to efficiently examine the post-buckling response. Monte Carlo simulations where the member stiffness is treated as a random variable, as well as correlated and uncorrelated random fields, are completed. The efficiency of Koiter's perturbation method is the key to the feasibility of applying Monte Carlo simulation techniques, which typically requires a large number of sample simulations. In an attempt to curtail the need for multiple sample calculations, an alternative first-order perturbation expansion is proposed for approximating the mean and variance of the post-buckling behavior. However, the limitations of this first-order perturbation approximation are demonstrated to be significant. The simulations indicate that deterministic characteristics of the post-buckling response can be inadequate in the face of input randomness. In one case, a frame that is stable symmetric in the deterministic case is found to be asymmetric when randomness in the input is incorporated; therefore, this frame has real potential for imperfection sensitivity. The importance of random field models for the member stiffness as opposed to random variable models is highlighted. The simulations indicate that the post-buckling response can magnify input randomness, as variability in the post-buckling parameters can be greater than the variability in the input parameters.

A Koiter's perturbation strategy for the imperfection sensitivity analysis of thin-walled structures with residual stresses

This paper suggests a strategy for the imperfection sensitivity analysis of elastic thin-walled structures with notable residual stresses. The analysis is carried out by means of a Koiter's perturbation approach. The concept of imperfection, traditionally associated with geometric and load factors, is extended in this paper to the residual stresses. The strategy is implemented in a FEM code. A comparison of the obtained results allows a discussion on the accuracy and the influence of the different coefficients connected to the asymptotic analysis of the residual stresses.

PERTURBATION APPROACH TO ELASTIC POST-BUCKLING ANALYSIS

This paper aims to show that effective and reliable computer codes can be obtained by a suitable finite element implementation of the Koiter's perturbation method. However, careful attention has to be paid to all the implementation details in order to avoid kinematical inconsitencies that can strongly affect the results.

A nonlinear beam finite element for the post-buckling analysis of plane frames by Koiter's perturbation approach

A nonlinear finite element of plane beam oriented to Koiter's perturbation analysis of frames is presented. The locking problem arising in the calculation of the post-critical curvature is thoroughly examined and solved at the continuum level, by means of a suitable definition of the kinematic settings. The proposed strain measures are Lagrangian and rationally founded (geometrically exact). The exact solutions of the critical problem have been chosen as shape functions of the finite element, so obtaining an immediately convergent finite element in the calculation of the critical load and of the post-critical slope.