Olexandr Yevkin

Software for Structures · R&D

The advantages and disadvantages of application of Pad� e approxim-ants to regression analysis with two independent covariates are discussed. The main difficulty of using Pad� e function is nonlinearity of data fitting. Possible approaches to overcoming the problem are discussed. New formulation of residuals is suggested in the method of least squa...

The simple analytical model of spherical shell buckling suggested in the previous publication in the TWS journal is applied to studying the response of the structure to different perturbations given as random variables. Among them probing radial force, energy barrier and geometrical imperfections are considered as factors decreasing uniform bucklin...

An important property of localization in buckling of spherical shells under external pressure is discussed. It is shown that the localization is possible for structures with nonlinear softening. An analytical model of local buckling of spherical shell is developed. Rayleigh-Ritz method is used at small and moderate deflections. At large deflections...

This is a sequel to the work published by the authors in RAMS-2017, where they discussed regularization techniques for recurrent failure prediction using Kijima models. The main practical goal of such modeling is to predict the expected number of events (failures) in time, based on the underlying failure time distribution, which in turn, governs th...

The advantages and difficulties of application of Padé approximants to two-dimensional regression analysis are discussed. New formulation of residuals is suggested in the method of least squares. It leads to a system of linear equations in case of rational functions. The possibility of using Tikhonov regularization technique to avoid overfitting is...

Buckling of unstiffened axially compressed cylindrical shells under different types of local perturbations has been studied in many theoretical and experimental researches in the last decade. Software packages based on the finite element method were used for analysis of structure behavior. Different approaches, based on these studies, were suggeste...

The results of unique experimental studies of buckling of dented axially compressed unstiffened cylindrical shells are provided in the suggested paper. The dimple-like geometrical imperfections of different shape, size, deflection amplitude, and number of dents were created on cylindrical shells before axial loading. The initial deflection amplitud...

Energy barrier as a measure of metastability of axially compressed cylindrical shell is developed in the case of elasto-plastic material of the structure. The concept of local shell buckling is used for estimation of design buckling load. It does not require measuring initial geometrical shell imperfections which is challenging or sometimes impossi...

According to the concept of local buckling of compressed isotropic cylindrical shells, the buckling process begins with appearance of one or several dimple-like buckles. Then, depending on the load level, it leads to local or general shell buckling. The latter causes the loss of structure bearing capacity and catastrophic consequences. Therefore th...

There is a variety of models available for repairable systems with general repairs. Most popular are the Kijima models (reflecting the generalized renewal process of recurrent failures) and the Lam model (reflecting the geometric process). The Kijima models relating system's real and virtual ages can be thought of as the time shift transformation,...

The asymptotic method for spherical shells at large deflections was developed in the case of composite shell subject to external pressure. Reissner’s equations describing axially symmetric deformation of deep shells with arbitrary deflections and rotation angles were considered as initial ones. They were significantly simplified and asymptotic form...

The energy barrier concept is developed for the case of dynamic loading of spherical shells. Simple semi-analytical formulae were obtained for the energy barrier for perfect shells and structures with geometrical imperfections. They were applied to the case of spatial step pressure to estimate dynamic buckling load of geometrically imperfect shells...

The concept of local buckling of compressed isotropic cylindrical shells is developed in this paper. Buckling of axially compressed cylindrical shells under different types of local perturbations has been studied in many theoretical and experimental researches. Different methodologies, based on these studies, were suggested for design buckling load...

The important role of local dimple-like equilibrium states in the buckling mechanism of compressed cylindrical shell has been revealed in many experiments. In the present paper a mathematical model describing features of local buckling of the shells is suggested. It is based on Pogorelov’s geometrical method. Derived simple analytical solution allo...

A simple formula for buckling load was derived from the asymptotic analysis of nonlinear behavior of a thin spherical shell. Firstly, two asymptotic cases were studied: the initial post-buckling regime of a perfect structure with small (compared to shell thickness) deflections and equilibrium states with large deflections. Two asymptotic formulae w...

The suggested before energy barrier criterion for design buckling pressure is extended to the case of clamped shallow spherical caps. It is developed for shells with geometrical imperfections and a new adjusted formula is obtained for design buckling load of imperfect structures. The method is applied to shells with elastic-perfectly plastic materi...

Energy perturbation is applied as a measure in the stability analysis of a spherical shell subjected to uniform external pressure. The energy barrier (buckling energy) is calculated using asymptotic method, which allows to estimate sensitivity of the structure to the perturbation. It is possible to define the level of external pressure separating a...

The problem of recurrent failure prediction arises in forecasting warranty repairs/cost, maintenance optimization and evaluation of repair quality. The most comprehensive prediction model is the g–renewal process proposed by Kijima, which allows for modelling of both perfect and imperfect repairs through the use of the so–called restoration factor....

The problem of recurrent failure prediction arises in forecasting warranty repairs/cost, maintenance optimization and evaluation of repair quality. The most comprehensive prediction model is the g-renewal process proposed by Kijima [1], which allows for modelling of both perfect and imperfect repairs through the use of the so-called restoration fac...

Consider a set of the so-called sibling components in a multi-socket repairable system. In the case of an automobile, for example, these siblings would be spark plugs, light bulbs, tires, that is, identical components that are coded with the same part number. When field data are analyzed, a dilemma arises as to how to interpret a recurrent replacem...

An asymptotic solution is suggested for a thin isotropic spherical shell subject to uniform external pressure and concentrated load. The pressure is the main load and a concentrated lateral load is considered as a perturbation that decreases buckling pressure. First, the post-buckling solution of the shell under uniform pressure is constructed. A k...

Approximate Markov chain method for dynamic fault tree analysis is suggested for both reparable and non-reparable systems. The approximation is based on truncation, aggregation and elimination of Markov chain states during the process of dynamic fault tree transformation to corresponding Markov chain. The method is valid for small probabilities. Fo...

The purpose of this paper is to share some practical applications of advanced probabilistic models in reliability data analysis. In particular, we will focus on reliability models with fixed and time−dependent covariates. While these models are popular in biological and medical studies, their application in engineering reliability data analysis is...

Markov Chain method for Dynamic Fault Tree with reparable components is discussed. The complexity of the problem and definition of dynamic gates is considered. Significant simplification of the method is suggested based on joining and truncation of Markov Chain states. The accuracy of approximation is based on assumption that Mean Time to Repair is...

Statistical estimation of G-renewal process parameters is an important estimation problem, which has been considered by many authors. We view this problem from the standpoint of a mathematically ill-posed, inverse problem (the solution is not unique and/or is sensitive to statistical error) and propose a regularization approach specifically suited...

Various replacement policies under Kijima's general repair model with the underlying Weibull distribution function are studied via two efficient methods. The first one is based on our previously derived approximate formula for the g-renewal function; the second is an improved Monte Carlo method. These methods enable an in-depth, comparative analysi...

An important characteristic of the g–renewal process, of great practical interest, is the g–renewal equation, which represents the expected cumulative number of recurrent events as a function of time. Just like in an ordinary renewal process, the problem is that the g–renewal equation does not have a closed form solution, unless the underlying even...

Several models have been developed for imperfect repairs that assume that component is "better than old but worse than new" after repair. One of the most popular is the g-renewal process introduced by Kijima & Sumita [1]. They established an effectiveness parameter q, defining a virtual age of the system component at a given time after several repa...

A Monte Carlo approach is developed for calculation of availability characteristics of a reparable unit described by g-renewal process. The analysis of availability parameters is provided in details in the case when the underlying failure distribution function is Weibull. Data represented in tables and graphs can be useful for deriving approximate...

Modularization technique allows efficient simplification of Dynamic and Static Fault Tree (FT). Each independent sub-tree (module) in static FT can be calculated separately and substituted by a basic event with obtained probability of failure. However, there is a significant restriction of this procedure in Dynamic FT, if it is converted to a Marko...

The Monte Carlo (MC) method is one of the most general ones in system reliability analysis, because it reflects the statistical nature of the problem. It is not restricted by type of failure models of system components, allows to capture the dynamic relationship between events and estimate the accuracy of obtained results by calculating standard er...

The esary proschan (EP) method and other approximations, based on minimal cut sets (MCSs) calculation, are commonly used in reliability system analysis. However, it is time consuming and even impossible to calculate all MCSs of large systems. Cut off by order or by probability is applied to find the most important MCSs. In this paper we discuss the...

Nonlinear behavior of deep orthotropic spherical shells under inward radial concentrated load is studied. The singular perturbation method is developed and applied to Reissner’s equations describing axially symmetric large deflections of thin shells of revolution. A small parameter proportional to the ratio of shell thickness to the sphere radius i...

An energy absorber, which contains an elastic thin shell of revolution, is considered. An asymptotic method is suggested for the investigation of non‐linear behaviour of the structure. An analytical solution, which is valuable for sthe design of energy absorber, has been obtained. The influence of the geometrical and stiffness parameters of the str...

The singular perturbation method is applied in combination with the variational method to the general Reissner's equations describing axially symmetric large deflections of thin composite shells of revolution with varying material and geometrical parameters in meridian direction. The obtained asymptotic nonlinear boundary value problem is significa...

The behavior of composite shells of revolution with large deflections (load–displacement diagrams and stress states) is studied. The nonlinear boundary value problems for composite shells of revolution, which have been obtained in Part 1 of the present study by means of the asymptotic approximation of Reissner's equations, are analyzed. The numeric...

Asymmetric and axisymmetric equilibrium configurations of edge-clamped shells were studied for different levels of external pressure. The transit to these forms was reached by additional kinematics local perturbations periodically sited along some parallels. The shell became more sensible to perturbations which related to asymmetric buckling config...

Toroidal shell strong bending is considered by numerical and asymptotic methods. Numerical calculation is realized by implicit algorithm of continuous solution method by parameter. Modified orthogonal method for cyclic boundary conditions is suggested for calculation of boundary conditions. Equation resolution form convenient for calculation and an...

Geometrical methods are extended to the asymptotic analysis of a version of an equation for nonshallow shells of revolution for describing the stress-strain state in the case of strong bending. Calculations are carried out using different algorithms, and the numerical results are compared. An important result of the study, which is relevant to the...

A procedure on estimation of the critical state of real thin- walled cylinders under external pressure is reported. The procedure is based on the analysis of the behaviour of an imperfect shell at precritical and postcritical stages of deformation. A problem on the postcritical deformation is solved by the asymptotic method. Perturbation proportion...

A method is proposed for the asymptotic integration of the non-linear equations of shallow elastic shell theory on the basis of a new definition of the small parameter that is selected to be proportional to the ratio between the shell thickness and the amplitude of its deflection. This parameter is actually small if the shell is in the post-critica...

A method is proposed for the asymptotic integration of the non-linear equations of shallow elastic shell theory on the basis of a new definition of the small parameter that is selected to be proportional to the ratio between the shell thickness and the amplitude of its deflection. This parameter is actually small if the shell is in the post-critica...