A nanoscale beam model containing defect under the piezoelectricity considering the surface effects and flexoelectricity is established on the framework of Euler-Bernoulli theory. The governing equations of motion and related boundary conditions are derived by using Hamilton’s principle. The imperfect nanobeam is modeled by dividing the beam into two separate parts that are connected by a rotational and a longitude spring at the defect location. Analytical results on the free vibration response of the imperfect piezoelectric nanobeam exhibit that the flexoelectricity and the surface effects are sensitive to the boundary conditions, defect position, and geometry of the nanobeam. Numerical results are provided to predict the mechanical behavior of a weakened piezoelectric nanobeam considering the flexoelectric and surface effects. It is also revealed that the voltage, defect severity, and piezoelectric material have a critical role on the resonance frequency. The work is envisaged to underline the influence of surface effects and flexoelectricity on the free vibration of a cracked piezoelectric nanobeam for diverse boundary conditions. It should be mentioned, despite our R. Sourkiprevious works, an important class of piezoelectric materials used nowadays and called piezoelectric ceramics is considered in the current study.
Influence of geometric imperfections of mast shaft in form of initial mast span curvatures both on internal forces status in the structure elements as well as on those elements effort, which is particularly important at the design stage, was analysed based on an example of certain specific mast. The calculations were performed taking into account L/1000 imperfections equal to the permissible assembly deviations as per [1], and L/500 equal to initial imperfections as for uniform built-up columns according to [2]. Remarks and final conclusions have practical meaning and can be useful in design practice.
The approach to numerical analyses was changed by the introduction of Eurocodes . The EN 1993-1-6 standard allows taking into account imperfections on the shape of a buckling form from a linear elastic bifurcation analysis. The article analyses the first ten forms of imperfection from a linear elastic bifurcation analysis on the reduction of the capacity of a cylindrical shell. Calculations were made using finite element methods.
Probabilistic analysis of a space truss is presented in the paper. Reliability of such a structure is sensitive to geometrical and material imperfections. The objective of this paper is to present a variant of the point estimate method (PEM) to determine mean values and standard deviations of limit loads of engineering structures. The main advantage presented by this method is the small number of sample calculations required to obtain estimators of investigated parameters. Thus the method is straightforward, requiring only preliminaries of probability theory. This approach is illustrated by limit state analysis of a space truss, considering geometric and material imperfections. The calculations were performed for different random models, so the influence of random parameters on the limit load of the truss can be determined. A realistic snow load was imposed.
Assessment of the flexural buckling resistance of bisymmetrical I-section beam-columns using FEM is widely discussed in the paper with regard to their imperfect model. The concept of equivalent geometric imperfections is applied in compliance with the so-called Eurocode’s general method. Various imperfection profiles are considered. The global effect of imperfections on the real compression members behaviour is illustrated by the comparison of imperfect beam-columns resistance and the resistance of their perfect counterparts. Numerous FEM simulations with regard to the stability behaviour of laterally and torsionally restrained steel structural elements of hot-rolled wide flange HEB section subjected to both compression and bending about the major or minor principal axes were performed. Geometrically and materially nonlinear analyses, GMNA for perfect structural elements and GMNIA for imperfect ones, preceded by LBA for the initial curvature evaluation of imperfect member configuration prior to loading were carried out. Numerical modelling and simulations were conducted with use of ABAQUS/Standard program. FEM results are compared with those obtained using the Eurocode’s interaction criteria of Method 1 and 2. Concluding remarks with regard to a necessity of equivalent imperfection profiles inclusion in modelling of the in-plane resistance of compression members are presented.
This paper concerns load testing of typical bridge structures performed prior to operation. In-situ tests of a twospan post-tensioned bridge loaded with three vehicles of 38-ton mass each formed the input of this study. On the basis of the results of these measurements an advanced FEM model of the structure was developed for which the sensitivity analysis was performed for chosen uncertainty sources. Three uncorrelated random variables representing material uncertainties, imperfections of positioning and total mass of loading vehicles were indicated. Afterwards, two alternative FE models were created based on a fully parametrised geometry of the bridge, differing by a chosen global parameter – the skew angle of the structure. All three solid models were subjected to probabilistic analyses with the use of second-order Response Surface Method in order to define the features of structural response of the models. It was observed that both the ranges of expected deflections and their corresponding mean values decreased with an increase of the skewness of the bridge models. Meanwhile, the coefficient of variation and relative difference between the mean value and boundary quantiles of the ranges remain insensitive to the changes in the skew angle. Owing to this, a procedure was formulated to simplify the process of load testing design of typical bridges differing by a chosen global parameter. The procedure allows - if certain conditions are fulfilled - to perform probabilistic calculations only once and use the indicated probabilistic parameters in the design of other bridges for which calculations can be performed deterministically.
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