Approximate Methods
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Laís De Bortoli Lecchi ◽  
Walnório Graça Ferreira ◽  
Paulo Manuel Mendes Pinheiro da Providência e Costa ◽  
Arlene Maria Cunha Sarmanho

abstract: Current practices in structural engineering demand ever-increasing knowledge and expertise concerning stability of structures from professionals in this field. This paper implements standardized procedures for geometrically nonlinear analysis of steel and reinforced concrete structures, with the objective of comparing methodologies with one another and with a geometrically exact finite element analysis performed with Ansys 14.0. The following methods are presented in this research: Load Amplification Method, from NBR 8800:2008; the γ z coefficient method, from NBR 6118:2014; the P-Delta iterative method and the α c r coefficient method, prescribed in EN 1993-1-1:2005. A bibliographic review focused on standardized approximate methods and models for consideration of material and geometric nonlinearities is presented. Numerical examples are included, from which information is gathered to ensure a valid comparison between methodologies. In summary, the presented methods show a good correlation of results when applied within their respective recommended applicability limits, of which, Eurocode 3 seems to present the major applicability range. The treated approximate methods show to be more suitable for regular framed structures subjected to regular load distributions.

Vladilen Petrov

The article discusses ways to improve the accuracy of solving problems of nonlinear structural mechanics. It is shown that the combination of the method of sequential loading and the Newton-Kantorovich method can improve the accuracy of the solution and reduce the complexity of obtaining results. The solution of the given linear equations can be obtained by numerical and approximate methods known in the literature.

2021 ◽  
pp. 165-179
Kenneth Derucher ◽  
Chandrasekhar Putcha ◽  
Uksun Kim ◽  
Hota V.S. GangaRao

Dang Quoc Huu

The Multi-Skill Resource-Constrained Project Scheduling Problem (MS-RCPSP) is a combinational optimization problem with many applications in science and practical areas. This problem aims to find out the feasible schedule for the completion of projects and workflows that is minimal duration or cost (or both of them - multi objectives). The researches show that MS-RCPSP is classified into NP-Hard classification, which could not get the optimal solution in polynomial time. Therefore, we usually use approximate methods to carry out the feasible schedule. There are many publication results for that problem based on evolutionary methods such as GA, Greedy, Ant, etc. However, the evolutionary algorithms usually have a limitation that is fallen into local extremes after a number of generations. This paper will study a new method to solve the MS-RCPSP problem based on the Particle Swarm Optimization (PSO) algorithm that is called R-PSO. The new improvement of R-PSO is re-assigning the resource to execute solution tasks. To evaluate the new algorithm's effectiveness, the paper conducts experiments on iMOPSE datasets. Experimental results on simulated data show that the proposed algorithm finds a better schedule than related works.

Vincent Graves ◽  
Bridgette Cooper ◽  
Jonathan Tennyson

Abstract There are many measurements and calculations of total electron impact ionisation cross sections. However, many applications, particularly in plasma physics, also require fragmentation patterns. Approximate methods of deducing partial cross sections are tested based on the use of total cross section computed within the well-used Binary Encounter Bethe (BEB) approximation. Partial ionisation cross sections for three series of molecules including CH$_4$, CF$_4$ and CCl$_4$; SiH$_4$ and SiCl$_4$; NH$_3$ and PH$_3$, were estimated using two methods. Method one is semi-empirical and uses mass spectroscopy data to fix the partial cross sections at a single electron energy. The second is a a fully computational method proposed by Huber {\it et al.} (2019, J. Chem. Phys., 150, 024306). Comparisons with experimental results suggest that the mass spectroscopy method is more accurate. However, as Huber's method requires no experimental input, this method could be used as a first approximation when no experimental data is available. As mass spectroscopy sometimes provides incomplete datasets, a hybrid method based on the use of both methods is also explored.

2021 ◽  
pp. 096228022110510
Stefan Wellek

More often than not, clinical trials and even nonclinical medical experiments have to be run with observational units sampled from populations to be assumed heterogeneous with respect to covariates associated with the outcome. Relevant covariates which are known prior to randomization are usually categorical in type, and the corresponding subpopulations are called strata. In contrast to randomization which in most cases is performed in a way ensuring approximately constant sample size ratios across the strata, sample size planning is rarely done taking stratification into account. This holds true although the statistical literature provides a reasonably rich repertoire of testing procedures for stratified comparisons between two treatments in a parallel group design. For all of them, at least approximate methods of power calculation are available from which algorithms or even closed-form formulae for required sample sizes can be derived. The objective of this tutorial is to give a systematic review of the most frequently applicable of these methods and to compare them in terms of their efficiency under standard settings. Based on the results, recommendations for the sample size planning of stratified two-arm trials are given.

Т.П. Кныш ◽  
М.В. Сухотерин ◽  
С.О. Барышников

Задача изгиба прямоугольной панели обшивки от действия распределенной по оси симметрии поперечной нагрузки не имеет точного решения в конечном виде в виду сложности краевых условий и вида нагрузки. Использование другими авторами различных приближенных методов оставляет открытым вопрос о точности полученных результатов. Целью исследования является получение точного решения с помощью гиперболо-тригонометрических рядов по двум координатам. Для этого используется метод бесконечной суперпозиции указанных рядов, которые в отдельности удовлетворят лишь части граничных условий. Порождаемые ими невязки взаимно компенсируются в ходе итерационного процесса и стремятся к нулю. Частное решения представлено двойным рядом Фурье. Точное решение достигается увеличением количества членов в рядах и числа итераций. При достижении заданной точности процесс прекращается. Получены численные результаты для прогибов и изгибающих моментов для квадратной пластины при различной длине загруженной части оси пластины. Представлены 3D-формы изогнутой поверхности пластины и эпюры изгибающих моментов. The problem of bending a rectangular skin panel from the action of a transverse load distributed along the axis of symmetry does not have an exact solution in the final form due to the complexity of the boundary conditions and the type of load. The use of various approximate methods by other authors leaves open the question of the accuracy of the results obtained. The aim of the study is to obtain an exact solution using hyperbolo-trigonometric series in two coordinates. To do this, we use the method of infinite superposition of these series, which individually satisfy only part of the boundary conditions. The residuals generated by them are mutually compensated during the iterative process and tend to zero. The quotient of the solution is represented by a double Fourier series. The exact solution is achieved by increasing the number of terms in the series and the number of iterations. When the specified accuracy is reached, the process stops. Numerical results are obtained for deflections and bending moments for a square plate with different lengths of the loaded part of the plate axis. 3D shapes of the curved surface of the plate and diagrams of bending moments are presented.

2021 ◽  
Vol 2131 (3) ◽  
pp. 032083
S A Rukhlenko

Abstract Normal impact of a massive body on a uniformly stretched plate lying on the base is investigated. A hinged round or rectangular plate on an elastic base, or an infinite plate on the surface of an ideal incompressible fluid is considered. The solution to the elastoplastic impact is in good agreement with numerical calculations and experimental data. With a small parameter of elastic collapse, that is, with the developed local plastic deformations, a solution to the problem of impact with rigid-plastic local collapse can be used. Approximate formulas for calculating the main characteristics of rigid-plastic impact are set up.

2021 ◽  
Vol 2131 (2) ◽  
pp. 022029
Yu P Manshin ◽  
E Yu Manshina

Abstract Sufficient safety of the parts, which determines the safety of the system specified by the technical assignment, is the necessary quality of the project, the subject of the design engineer’s attention and the customer’s requirement. An extensive task is the collection of data for iterative refinement of the resource for project details in a probabilistic aspect. It can be significantly reduced when using approximate methods for estimating the resource at intermediate stages of refining the project to the required resource with a calculated probability of failure-free operation. Thus, by the analysis of dimensionless relations of parameters of models of fatigue damage development, it is possible to obtain tools of numerical estimation of technological and constructive techniques of increase of a resource of details and their rational combination. The paper deals with the numerical measures of various directions of upgrading the fatigue life of the parts, derived from the dimensionless relations of the parameters of fatigue damage development models.

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