Nonlinear Calculation Methods Research Articles

Razvoj računalnog programa za proračun pojačanja stupova FRP-a: studija slučaja

This manuscript delineates an extensive inquiry into a structure in Ankara, Turkey, specifically focusing on its existing state, retrofitting initiative, and concomitant software development. The evaluation of the building’s current state, earthquake loads, and anticipated structural stresses was conducted per the Turkish Seismic Code of 2018. The structural model was analysed, incorporating data derived from on-site inspections, surveys, and samples from the building’s concrete core and reinforcement elements by employing non-linear calculation methods. Remedial measures were undertaken after recognising deficiencies in the structure’s performance, including strengthening columns and selecting slabs by applying Fibre-Reinforced Polymer (FRP) composites. Subsequently, the authors engineered the FRP Composite Column Strengthening software. This software facilitates the computation of axial compression strength, shear strength, and ductility enhancements for columns after the retrofitting process.

Calculation and Analysis of Unbalanced Magnetic Pull of Rotor under Motor Air Gap Eccentricity Fault

Due to various factors such as manufacturing, assembly and operation, the motor air gap will be uneven in the circumferential direction, resulting in the air gap eccentricity having a longer air gap on one side and a shorter air gap on the other side, which affects the normal operation and service life of the motor. This paper analyzed and compared the applicability of linear and nonlinear calculation methods of unbalanced magnetic pull. Based on the method of finite element analysis, the unbalanced magnetic pull of motor rotor under static eccentricity, dynamic eccentricity and compound eccentricity faults were calculated, and the influence of eccentricity on unbalanced magnetic pull was compared, respectively. The results showed that when the motor has static eccentricity, the main components of unbalanced magnetic pull on the rotor are zero frequency and twice the electrical frequency. When the motor has dynamic eccentricity, the unbalanced magnetic tension component of the rotor is mainly frequency conversion. When the motor has two faults at the same time, the unbalanced magnetic pull has zero frequency, rotating frequency and double electric frequency components at the same time. With the increase in the relative eccentricity, the frequency components of the unbalanced magnetic pull under the three faults increase. An air gap eccentricity fault widely exists in motor equipment. When the unbalanced magnetic pull increases to a certain extent, the rotor will be pulled towards the stator, causing the occurrence of rub-impact phenomenon, and seriously threatening the safe operation of the system. In this paper, the numerical analysis method and finite meta-computing method were used for the first time to analyze and compare the unbalanced magnetic pull on the rotor of permanent magnet synchronous motor under three kinds of air gap eccentricity faults. The results showed that the characteristic frequency amplitude of the unbalanced magnetic pull calculated by the two methods is relatively close. Therefore, it is of great significance to carry out calculation and analysis of the unbalanced magnetic pull force under the air gap eccentric fault of the motor.

Non-linear displacement and deformation damage limits of reinforced concrete circular columns by analytical observations according to TBSC 2018

In the study, based on the non-linear calculation methods used to determine the seismic performance of structures in TBSC 2018, the stress-strain, moment-curvature, displacement capacity, plastic rotation limits, and deformation-based damage limit values of the reinforced concrete circular cross-section columns were calculated and compared according to different design parameters. The studied effects of the design parameters on the non-linear relation of reinforced concrete columns were also evaluated in terms of strength, curvature, and displacement ductility of the sections. All design parameters affecting the non-linear behavior and deformation limits of the reinforced concrete circular cross-section columns were taken into account. Deformation demands for reinforced concrete structural members are essential for detecting element damage. Based on TBSC (2018), non-linear relationships of reinforced concrete columns were obtained in order to calculate plastic hinge properties and deformation limits. For the Limited Damage, Controlled Damage, and Collapse Prevention performance levels defined for the structural elements in TBSC 2018, plastic rotation and deformation limit values were obtained according to the characteristic values calculated from the non-linear analyzes of reinforced concrete circular columns. For column models, damage limits and damage zones calculated based on TBSC 2018 were shown on the visually obtained moment-curvature relationships. Depending on the upper deformation limit values derived, cross-sectional deformation damage levels were determined and evaluated using the moment-curvature relationships. The variation of the non-linear behavior of column models by design parameters and deformation-based damage limits were examined both analytically and visually. The deformation limits remain in a safer direction as a result of increasing longitudinal and spiral reinforcement ratios for the reinforced concrete circular columns.

Latest findings on the behaviour factor q for the seismic design of URM buildings

Recent earthquakes as the 2012 Emilia earthquake sequence showed that recently built unreinforced masonry (URM) buildings behaved much better than expected and sustained, despite the maximum PGA values ranged between 0.20–0.30 g, either minor damage or structural damage that is deemed repairable. Especially low-rise residential and commercial masonry buildings with a code-conforming seismic design and detailing behaved in general very well without substantial damages. The low damage grades of modern masonry buildings that was observed during this earthquake series highlighted again that codified design procedures based on linear analysis can be rather conservative. Although advances in simulation tools make nonlinear calculation methods more readily accessible to designers, linear analyses will still be the standard design method for years to come. The present paper aims to improve the linear seismic design method by providing a proper definition of the q-factor of URM buildings. These q-factors are derived for low-rise URM buildings with rigid diaphragms which represent recent construction practise in low to moderate seismic areas of Italy and Germany. The behaviour factor components for deformation and energy dissipation capacity and for overstrength due to the redistribution of forces are derived by means of pushover analyses. Furthermore, considerations on the behaviour factor component due to other sources of overstrength in masonry buildings are presented. As a result of the investigations, rationally based values of the behaviour factor q to be used in linear analyses in the range of 2.0–3.0 are proposed.

Obtaining and Comparison of Nonlinear Calculation Methods and Performance Analysis of Curtain Frame Systems According to TBDY 2018 and ASCE 41-17

Bu çalışmada, ASCE 41-17’de tanımlanan ve TBDY 2018’e göre kullanıcı tarafından hesaplanan doğrusal olmayan elemanların plastik mafsal özellikleri ve hasar sınırları ele alınarak itme analizi gerçekleştirilmiştir. Bu çalışmada dört açıklıklı üç, beş ve yedi katlı perdeli çerçeveli bina ele alınarak analiz sonuçları karşılaştırılmıştır. Betonarme elemanların plastik mafsal özelliklerinin etkili parametreleri plastik mafsal uzunluğu ve enine donatı mesafesidir. Bu çalışmada artımsal eşdeğer deprem yükü ile itme analizi yöntemiyle BKTS-1, 2 ve 3 betonarme binaların analizleri ETABS 19-0.2 programı ile gerçekleştirilmiştir. Gerçekleştirilen analizlerin sonucunda iki farklı yönetmeliğe göre kapasite eğrileri elde edilmiştir. TBDY 2018’e göre elde edilen kapasite eğrilerinin sonucunda performans noktalarında elde edilen taban kesme kuvvetlerinin miktarı ve tepe yerdeğiştirme miktarı ASCE 41-17’ye göre daha fazla elde edilmiştir. İki farklı yönetmeliğe göre elde edilen sonuçlarında etkilenen faktörler; yapıya etkiyen düşey yük miktarı, betonarme elemanların efektif rijitliği ve plastik mafsal özellikleridir.

Performance Analysis of Reinforced Concrete Structural Systems with Nonlinear Calculation Methods according to TBDY 2018

Yapısal elemanların deprem performansının belirlenmesi için TBDY (2018)’de betonarme elemanlar için öngörülen şekildeğiştirme esaslı hasar sınırları incelenmiştir. Bu çalışmada ilk olarak; kesit geometrisinin, malzeme modelinin ve eksenel yük seviyesinin betonarme taşıyıcı elemanların davranışı üzerindeki etkisi analitik olarak hesaplanmıştır. Taşıyıcı sistem elemanların davranışı, malzemelerin doğrusal olmayan davranışı dikkate alınarak moment-eğrilik ilişkisinden değerlendirilmiştir. Yer değiştirme taleplerine karşılık gelen eleman hasarları elde edilerek hasar sınırları değerlendirilmiştir. Farklı performans düzeyleri için elemanların plastik mafsal bölgeleri için akma ve plastik dönme değerleri hesaplanmıştır. Yapısal elemanlar için farklı performans düzeylerine göre şekildeğiştirme taleplerine karşılık gelen hasar sınırları elde edilerek değerlendirilmiştir. Analitik çalışma sonuçlarından elde edilen şekildeğiştirme üst sınır değerlerine bağlı olarak tasarlanan betonarme yapıların doğrusal olmayan (itme) analizleri yapılarak detaylı bir çalışma yapılmıştır. Performans değerlendirmesi için tasarlanan modellerin tasarım depremi ve en büyük deprem yükü etkisi altındaki yapısal performansı incelenmiştir. Gerçekleştirilen artımsal itme analizleri sonucu farklı tip betonarme taşıyıcı sistemler için elde edilen kapasite eğrileri ve performans noktalarındaki deprem istemleri (taban kesme kuvvetleri- tepe yer değiştirmeleri, kat kesme kuvvetleri ve göreli kat ötelemeleri) karşılaştırılmıştır. Bu karşılaştırmalar şekil ve çizelgelerde detaylı olarak incelenerek irdelenmiştir.

Interaction of screw piles with the base

The article presents the results of the practical applications of screw piles foundations for block quick-assembly buildings and buildings made of a metal frame. The results of experimental and theoretical studies of foundations in various ground conditions are presented. A method for estimating the stress-strain state of screw pile foundations using nonlinear calculation methods is proposed. The influence of pile length and blade diameter on the change in displacements and load-bearing capacity in cohesive and non-cohesive soils on the effect of pushing and anchor loads is revealed. The nature of the distribution of stresses and deformations at the base of foundations made of screw piles is revealed. The article is useful for engineers, specialists and researchers in the field of soil mechanics, foundation engineering and geotechnics.

Experimental and theoretical studies of the interaction of slotted foundations with the basis

The article presents the results of experimental and numerical modelling of slotted foundations. Model and large-scale experimental studies were conducted. The influence of the number, thickness, and depth of sinking of the slotted foundation walls on the distribution of stresses and deformations in the basis is established. The results of numerical studies show the distribution of stress and strain components at the base of slotted foundations, taking into account the elastic-plastic properties of the soil. For the estimation of slotted foundations based on the maximum permissible precipitation using solutions of nonlinear soil mechanics, the factors affecting the precipitation are identified and the corresponding approximate dependencies are obtained. The use of non-linear calculation methods makes it possible to design slotted foundations based on the ultimate deformations. These studies are confirmed by the results of experiments of various authors. Designs of slotted foundations are implemented in the construction of buildings and structures, which reduce the cost of the zero cycle, reduce the material consumption in comparison with standard solutions. The article is of interest to specialists in the field of soil mechanics, geotechnics, and foundation engineering.

Mevcut Betonarme Bir Binanın 2007 ve 2018 Deprem Yönetmeliklerine Göre Deprem Yükleri Altındaki Taşıyıcı Sistem Perfomansının Değerlendirilmesi

Son yıllarda, mevcut binaların deprem etkisi altındaki taşıyıcı sistem performanslarının belirlenmesi için kuvvet esaslı yöntemlerin yerine, şekildeğiştirme ve yerdeğiştirme esaslı doğrusal olmayan yöntemler kullanılmaya başlanmıştır. Türkiye Bina Deprem Yönetmeliği (TBDY-2018) ve Deprem Bölgelerinde Yapılacak Binalar Hakkında Yönetmelik’te (DBYBHY-2007) mevcut binaların performanslarının belirlenmesi için doğrusal ve doğrusal olmayan hesap yöntemlerine yer verilmiştir. TBDY-2018’de doğrusal olmayan hesap için önerilen yöntemler, Tek Modlu İtme Yöntemi, Çok Modlu İtme Yöntemi ve Zaman Tanım Alanında hesap yöntemidir. DBYBHY-2007’de doğrusal olmayan hesap için önerilen yöntemler, Artımsal Eşdeğer Deprem Yükü Yöntemi, Artımsal Mod Birleştirme Yöntemi ve Zaman Tanım Alanında hesap yöntemidir. TBDY-2018 ve DBYBHY-2007 arasındaki en büyük fark, betonarme kesitlerin etkin kesit rijitlikleri ve hasar sınırı tarifleridir. Bu çalışmada, mevcut 5 katlı betonarme konut yapısının DBYBHY-2007 ve TBDY-2018’e göre Doğrusal Olmayan Artımsal İtme Analizi yöntemiyle deprem yükleri altında bina taşıyıcı sisteminin performans analizi yapılmış ve sonuçlar karşılaştırılarak irdelenmiştir.

Optimal design of foundations by means of nonlinear calculation methods

This paper proposes using the defining equations from the theory of adaptive evolution of mechanical systems (which is based on the variational principles of nonlinear structural mechanics) to design the shape and size of foundations. It presents an expression for finding the potential energy of a system and the deformation energy density, as well as the variational Lagrange equation. The paper formulates a nonlinear boundary problem solved by finite-element analysis. The solution imposes a constraint on the modulus of elasticity to take into account the physico-mechanical properties of the materials. A calculation algorithm and an ADPL program are written for ANSYS. The paper also presents a solution to the problem of finding the rational foundation shaped for the case of plain strain. The solution-derived rational foundation shape is shown. The authors plot the stresses and energy densities as a function of evolution at the onset and finish of iterative processes. Note that the resulting foundation shape is more stable, more accurately positioned in the soil, and can carry a greater load compared to more conventional shapes.

Nonlinear calculation of reinforced concrete structures to the impact of the air shock wave

Introduction. Researched methods of accounting for the nonlinear operation of reinforced concrete structures on the example of an industrial structure, when exposed to an air shock wave using modern software systems based on the finite element method. The calculation of reinforced concrete construction to the impact of an air shock wave, if no increased requirements for tightness are presented to it, in accordance with current regulatory documents, must be carried out taking into account the elastic-plastic work, crack opening in the stretched zone of concrete and plastic deformations of reinforcement are allowed. Reviewed by new coupling approach to determining the dynamic loads of a shock wave, implemented in the LS-DYNA software package, which allows to take into account the effects of a long-range explosion and wave-wrapping around a structure. Materials and methods. The study of the stress-strain state of the structures was carried out using numerical simulation. For the nonlinear equivalent-static method, a step-by-step calculation algorithm is used, with gradual accumulation and distribution of stresses, implemented in the LIRA-SAPR software package. For the nonlinear dynamic method, the Lagrangian-Eulerian formulation is used using the methods of gas dynamics in the LS-DYNA software package. Results. As a result of numerical simulation, the following was done analysis of existing methods of nonlinear calculations; analysis of the existing loads during the flow of shock waves around the structure; analysis of the forces and movements in the bearing elements, as well as pictures of the destruction of concrete and reinforcement. Conclusions. According to the results of the comparison of the two approaches, conclusions are drawn about the advantages and disadvantages of the methods. Advantages of nonlinear dynamic calculation methods are noted compared to the equivalent-static ones. Use of the combined approach to the description of the shock wave front gives a reduction in time and allows us to describe the interaction of the wave with the structure with sufficient accuracy. The findings indicate the relevance of the study and provide an opportunity to move to more reasonable computational models.

Comparison of the calculation results of structures for specified accelerograms by nonlinear static and nonlinear dynamic methods

Relevance. Modern national standards for the design of buildings and structures for seismic impacts suggest the calculation of structures in a nonlinear setting. Only linear-spectral method, which has been used and is still used, is not enough for calculation. This is due to the fact that it does not allow directly taking into account the nonlinear work of the structures. To solve the problem, nonlinear dynamic methods of calculation in the time domain can be used. At the moment, such methods are implemented only in specialized software complexes, and in most cases cannot be used by ordinary designers. Thus, it became necessary to apply simpler nonlinear calculation methods. In foreign standards for calculation of seismic resistance of buildings and structures, nonlinear static methods, or pushover analysis, have long been used. But in the national design practice until recently, these methods have not received due attention. Thus, the relevance of the study of the possibility of using these methods in engineering practice is beyond doubt. The aim of work. The purpose of this article is to estimate the accuracy of a nonlinear static method in comparison with a nonlinear dynamic method when calculating structures for given accelerograms. Solution technique. In the article three steel frames are considered: one-, threeand seven-story. The selection of sections was made in accordance with the requirements of the national standards on earthquake-resistant construction for seismic loads of the basic safety earthquake (BSE) level. Next, frames are designed for the seismic loads of the maximum considered earthquake (MCE) level on a set of accelerograms of different frequency composition. The calculation was performed by a nonlinear dynamic method in the LS-DYNA software package and a nonlinear static method in the LIRA 10.6 and MATLAB software complexes. Results. Calculations showed that in all the cases considered, except for one, a nonlinear static method showed a conservative estimate of the response of the system, in comparison with the nonlinear dynamic method. But in some cases the reaction was greatly overestimated.

Effect of chamber enclosure time on soil respiration flux: A comparison of linear and non-linear flux calculation methods

One of the shortcomings of closed chamber methods for soil respiration (SR) measurements is the decreased CO2 diffusion rate from soil to chamber headspace that may occur due to increased chamber CO2 concentrations. This feedback on diffusion rate may lead to underestimation of pre-deployment fluxes by linear regression techniques. Thus, usually the cumulative flux curve becomes downward concave due to the decreased gas diffusion rate. Non-linear models based on biophysical theory usually fit to such curvatures and may reduce the underestimation of fluxes. In this study, we examined the effect of increasing chamber enclosure time on SR flux rates calculated using a linear, an exponential and a revised Hutchinson and Mosier model (HMR). Soil respiration rates were measured with a closed chamber in combination with an infrared gas analyzer. During SR flux measurements the chamber was placed on fixed collars, and CO2 concentration in the chamber headspace were recorded at 1-s intervals for 45 min. Fluxes were measured in different soil types (sandy, sandy loam and organic soils), and for various manipulations (tillage, rain and drought) and soil conditions (temperature and moisture) to obtain a range of fluxes with different shapes of flux curves. The linear method provided more stable flux results during short enclosure times (few min) but underestimated initial fluxes by 15–300% after 45 min deployment time. Non-linear models reduced the underestimation as average underestimation was only about 10% after 45 min for regular flux curves. For irregular flux curves with a rapid increase in CO2 concentration immediately after chamber deployment it was shown that short enclosure times were prone to overestimation of pre-deployment fluxes, but this was mitigated by longer enclosure times (>10–15 min).

Comparison of Nonlinear Static and Dynamic Analyses on a R/C Building

In recent years, nonlinear calculation methods can be easily carried out by means of developing computer technologies. In this way, comparisons of the nonlinear methods have started to increase rapidly and more studies are carried out on regular and irregular buildings. However, it is most important to compare consistency of the methods on buildings. In this study, most common nonlinear static (pushover) and nonlinear dynamic analysis (time history analysis) methods were compared on an asymmetric planned reinforced concrete (R/C) building. Building having horizontal and vertical irregularities was 5-story. Analyses were carried out by using SAP2000 program. The results are discussed in terms of base shear, lateral displacements and top displacement ratios.

J-estimation formulas for nonlinear crack problems

Application of nonlinear fracture mechanics criteria and calculation methods requires the availability of solutions to elastic-plastic crack problems that relate J-integral to load (or nominal stresses) and crack geometry. Such solutions depend on details of deformation behaviour of materials. Numerical methods have been used successfully for solving certain problems [1], but these numerical solutions are difficult to transfer from one configuration or material to another. Nonlinear or fully plastic solutions have been obtained for several simple crack configurations. These are discussed in [2-4]. Solutions include a dimensionless function of the hardening exponent and of dimensionless groups of geometric parameters. For most cases the function must be computed numerically and that could be connected with some difficulties. Therefore, a working out of approximate and universal enough analytical solutions is an actual problem. Approximate solutions have been obtained for some basic nonlinear crack problems using the method in [5,6]. Here a new simple solution will be considered on the basis of stress concentration analysis near a notch-crack tip. A notch of length 2a with the curvature radius p at the tip has flat surfaces parallel to the x axis (Fig. 1). For the stress and strain concentration analysis near the notch tip in loading solids we shall use the Cherepanov-Rice contour energy integral. We indicate the integration path in the arc F t which is the rounded part of the notch. The notch surfaces are freed of stresses. Then the J-integral can be represented by the following expression

A Model of W Virginis with RV Tauri Characteristics

Nonlinear calculation methods for model representing W virginis, noting rapid amplitude growth and luminosity-to-mass ratio