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12 pages, 3680 KiB

Open AccessArticle

Elastic–Plastic Numerical Analysis of the Spinning Process of SA-372 Steel Used in High-Pressure Hydrogen Storage Cylinders (≥100 MPA)

by Ruifeng Yin, Ruidong Fu, Wenlong Wei, Jianfu Gao, Yongjiu Liu and Shuaitao Ge

Materials 2023, 16(1), 275; https://doi.org/10.3390/ma16010275 - 28 Dec 2022

Cited by 1 | Viewed by 1450

Abstract

Elastic–plastic numerical analysis of the spinning process of SA-372 steel is used in high-pressure hydrogen storage to analyze high-pressure hydrogen storage cylinders with high precision and excellent hydrogen embrittlement resistance. The spinning process of SA-372 steel used to form such a cylinder with [...] Read more.

Elastic–plastic numerical analysis of the spinning process of SA-372 steel is used in high-pressure hydrogen storage to analyze high-pressure hydrogen storage cylinders with high precision and excellent hydrogen embrittlement resistance. The spinning process of SA-372 steel used to form such a cylinder with a pressure of 100 MPa is investigated through elastic–plastic finite element analysis. The variations in the stress, strain, pressure, temperature, and wall thickness during the spinning processes are comprehensively examined, and the optimized processing parameters are determined based on the numerical analysis results. Finally, these optimal parameters are used to conduct actual spin-forming experiments. The numerical results are found to be in excellent agreement with the experimental results, which verifies the feasibility and effectiveness of the proposed elastic–plastic numerical analysis model for the optimization of spinning process parameters. Furthermore, the hydrogen embrittlement test based on ISO 11114-4:2005 method A proves that the cylinder shoulder has a good hydrogen embrittlement resistance. Full article

(This article belongs to the Special Issue Advances in Structural Analysis of Materials: Finite Element Modeling)

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18 pages, 7593 KiB

Open AccessArticle

Numerical and Experimental Investigations of the Influence of Operation on the Technical Condition of Pressure Vessels

by Przemyslaw Moczko, Michał Paduchowicz and Damian Pietrusiak

Materials 2022, 15(20), 7281; https://doi.org/10.3390/ma15207281 - 18 Oct 2022

Cited by 2 | Viewed by 1478

Abstract

The paper presents the issues related to the design and assessment of the technical condition as well as determination of the residual durability of pressure equipment. Based on a real a example, a liquid nitrogen spherical tank, we present the development and applicability [...] Read more.

The paper presents the issues related to the design and assessment of the technical condition as well as determination of the residual durability of pressure equipment. Based on a real a example, a liquid nitrogen spherical tank, we present the development and applicability of the method for assessment of the durability of the structure. In terms of the material itself, the authors analyze macroscale (structural) factors of the geometry of the real structure (by 3D scanning: material wear detection, deflections and deformations, etc.) and measured real operational loads to develop an integrated method, including material model and behavior in its operational condition, delivering a useful tool for macroscale structural analyses of the materials under complex load (mechanical, thermal, chemical, etc.). As a result, a detailed analysis of the tank is presented. The paper gives an idea of the method, its development, usefulness, and applicability of the presented approach by indication of the mutual influence of pressure vessel components (e.g., stubs, manholes) and operational loads, which may result in underestimating the strength and durability of the pressure vessels in the design process and during operation. Full article

(This article belongs to the Special Issue Advances in Structural Analysis of Materials: Finite Element Modeling)

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22 pages, 3013 KiB

Open AccessArticle

A Thermo-Mechanical Stress Based Fatigue Life Evaluation of a Mine Hoist Drum Brake System Using COMSOL Multiphysics

by Sorin Mihai Radu, Florin Dumitru Popescu, Andrei Andraș, Zoltán Virág, Ildiko Brînaș and Manuel-Ionuț Draica

Materials 2022, 15(19), 6558; https://doi.org/10.3390/ma15196558 - 21 Sep 2022

Cited by 1 | Viewed by 2279

Abstract

In this study, the fatigue usage factors for Findley and Matake stress-based criteria were determined in the case of an MK5×2 mine hoist drum brake system subjected to cyclic maneuver braking. The study was conducted for this type of brake system, because the [...] Read more.

In this study, the fatigue usage factors for Findley and Matake stress-based criteria were determined in the case of an MK5×2 mine hoist drum brake system subjected to cyclic maneuver braking. The study was conducted for this type of brake system, because the majority of mine hoists in Romanian mines are equipped with this brake type, being in operation for several decades. A geometric model of the brake was built using SolidWorks and imported in COMSOL Multiphysics to perform thermo-mechanical simulations. Based on the deformations and von Mises stresses determined by the thermomechanical simulation and, considering the calculated endurance limits of the brake system materials, Matake and Findley fatigue life evaluation simulations from COMSOL’s fatigue module were conducted. The results show that the highest fatigue is expected on the drum lining surface towards the exit point from under the brake shoe in both cases, and the values of the usage factor of 0.307 (Findley) and 0.401 (Matake) are both under the critical value 1, meaning that the stress limit has not been exceeded for the brake system components and, thus, failure is not expected. Simulations were conducted considering an estimated 1.06 × 10⁵ cycles during one year, more than both the usual service/replacement interval of the friction components of the brake, and the period of mandatory technical inspections imposed by regulations. Full article

(This article belongs to the Special Issue Advances in Structural Analysis of Materials: Finite Element Modeling)

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27 pages, 12067 KiB

Open AccessArticle

Comparative Analysis of Mine Shaft Hoisting Systems’ Brake Temperature Using Finite Element Analysis (FEA)

by Florin Dumitru Popescu, Sorin Mihai Radu, Andrei Andraș, Ildiko Brînaș, Daniela Ioana Budilică and Valentin Popescu

Materials 2022, 15(9), 3363; https://doi.org/10.3390/ma15093363 - 7 May 2022

Cited by 15 | Viewed by 4428

Abstract

This paper studies both the thermal and mechanical behavior of brake system models in the case of the emergency braking of a mine hoist model. Using a step-by-step approach inspired by studies conducted on small brake systems with high rotation speeds specific to [...] Read more.

This paper studies both the thermal and mechanical behavior of brake system models in the case of the emergency braking of a mine hoist model. Using a step-by-step approach inspired by studies conducted on small brake systems with high rotation speeds specific to road and rail vehicles, a comparative analysis using a computer simulation was performed for the two types of brakes of a mine hoist system. A Solidworks model was built for two configurations: the drum-and-shoe and the disc-and-pads, and it was imported to COMSOL Multiphysics, where the material properties and simulation parameters were defined. Simulations were performed for each configuration, first using a Heat transfer module in the solids to investigate the frictional heat. The results showed the locations of the hot points on the disc and on the drum, with the surface temperature reaching 97 °C on the disc and 115 to 159 °C on the drum. Next, simulations using a Structural Mechanics module were run to obtain the stress and deformation induced by the heat generated during braking. The von Mises stress of the drum-and-shoe brake occurred on the external surface of the drum and had a value of 2 × 10⁸ N/m². For the disc-and-pad brake, the stress occurred towards the edges of the brake pad contact and was 4 × 10⁸ N/m². Both values were under the yield stress of the passive brake element material. Regarding the deformations, for the drum-and-shoe brake, it appeared towards the outer boundary of the drum, being 0.45 mm, and for the disc-and-pad brake, it was situated at the external edge of the disc, being 0.25 mm. COMSOL Multiphysics allowed the evaluation of the thermo-mechanical behavior using noninvasive techniques since actual emergency braking testing on a working mine hoisting installation is not possible because of safety and logistic concerns. Full article

(This article belongs to the Special Issue Advances in Structural Analysis of Materials: Finite Element Modeling)

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17 pages, 5928 KiB

Open AccessArticle

Dynamic NVH Numerical Analysis of Power Steering in the Presence of Lubricant in the System

by Damian Pietrusiak, Jakub Wróbel, Mateusz Czechowski and Wiesław Fiebig

Materials 2022, 15(7), 2406; https://doi.org/10.3390/ma15072406 - 24 Mar 2022

Cited by 4 | Viewed by 2458

Abstract

The ongoing shift towards hybrid and electric vehicles has a strong impact on noise and vibration engineering. New, complex dynamic phenomena are brought to vehicle user attention due to the absence of internal combustion engines and the significant role in vehicle and drive [...] Read more.

The ongoing shift towards hybrid and electric vehicles has a strong impact on noise and vibration engineering. New, complex dynamic phenomena are brought to vehicle user attention due to the absence of internal combustion engines and the significant role in vehicle and drive feel perception. This paper presents an FEM (Finite Element Method) dynamic simulation model of an automotive Electric Power Steering assembly. Preliminary modal simulations and experiments as well as field data replication techniques were implemented to identify the phenomena and prepare and validate model components. A full dynamic model of an Electric Power Steering was presented, and fine-tuned including the presence of lubrication at the gear mesh interface. Experimental investigations were conducted alongside FEM simulations for various model setups. Linear and nonlinear contact stiffness models were implemented, as well as contact damping, and simulated at chosen assembly interfaces. The results indicated that in the case of NVH (Noise Vibration and Harshness) analysis of shock/impact originating problems, contact parameters used for static, quasi-static, and low velocity analyses were not applicable. Nonlinear and damped contact stiffness provided better results in such a case. Full article

(This article belongs to the Special Issue Advances in Structural Analysis of Materials: Finite Element Modeling)

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12 pages, 4532 KiB

Open AccessArticle

Accuracy Evaluation of Thermoelastic Stress Analysis with the Use of Experimental and Numerical Methods

by Robert Misiewicz, Przemysław Moczko and Adam Bajcar

Materials 2022, 15(5), 1961; https://doi.org/10.3390/ma15051961 - 7 Mar 2022

Cited by 1 | Viewed by 1747

Abstract

Thermoelastic Stress Analysis (TSA) is one of the very few methods allowing the determination of a continuous stress distribution on the object’s surface under variable loading conditions. Such results provide a lot of valuable information in the field of technical condition assessment and [...] Read more.

Thermoelastic Stress Analysis (TSA) is one of the very few methods allowing the determination of a continuous stress distribution on the object’s surface under variable loading conditions. Such results provide a lot of valuable information in the field of technical condition assessment and residual life prediction. In order to improve the accuracy of the TSA, the Lock-In signal processing method is implemented. This research is aimed at verifying the effectiveness of this improvement and determining the TSA stress detection threshold, as it is important information in terms of the applicability of this method in the low-stress conditions encountered in considerations of fatigue of load-carrying structures. A steel sample with a centrally located hole was subjected to cyclic loads to determine the threshold of stress detection and accuracy of TSA. As a result of the research, the relationship between the magnitude of stress excitations and the underestimation of the measured stresses was developed. Based on the conducted investigations, it was concluded that reasonable TSA results can be acquired for excitations that induce a temperature response above 10 mK (0.5 NEDT). The presented field test example proves that in industrial applications reasonable results can be acquired for thermal responses below the NEDT of the IR camera. It was concluded that it is possible to successfully implement TSA in low-stress applications (temperature response below NEDT). Full article

(This article belongs to the Special Issue Advances in Structural Analysis of Materials: Finite Element Modeling)

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15 pages, 8713 KiB

Open AccessArticle

Finite Volume Method Modeling of Heat Transfer in Acoustic Enclosure for Machinery

by Jakub Wróbel and Urszula Warzyńska

Materials 2022, 15(4), 1562; https://doi.org/10.3390/ma15041562 - 19 Feb 2022

Cited by 1 | Viewed by 1954

Abstract

This paper deals with the problem of heat accumulation in acoustic enclosures. Increased noise levels at production sites or manufacturing lines force the application of acoustic enclosures. Effective noise reduction due to enclosures often comes with the additional thermal insulation of the device, [...] Read more.

This paper deals with the problem of heat accumulation in acoustic enclosures. Increased noise levels at production sites or manufacturing lines force the application of acoustic enclosures. Effective noise reduction due to enclosures often comes with the additional thermal insulation of the device, which in many cases causes a strong increase in the device operation temperature. This paper presents the methodology of thermal phenomena numerical modeling based on the potential influence of acoustic enclosures on the increase in device operation temperature. The proposed model consists of an original acoustic enclosure concept design, and the numerical modeling is based on the computational fluid dynamics FVM (finite volume method) conducted in Ansys Fluent. The research comprised a set of simulations at different air flow rates of 52.5 m³/h, 105 m³/h, 210 m³/h and 420 m³/h at the enclosure inlet. The analysis carried out on the basis of flow paths and temperature distribution plots inside the enclosure led to the conclusion that the expected, analytically calculated minimum volumetric flow rate is not sufficient to effectively cool the investigated device to the required temperature of 26 °C, and higher air flow rates should be applied. Simulation results indicated that the numerical tools can be useful in the prediction of the heat exchange process, as well as in the selection of an appropriate source and location of cooling. Full article

(This article belongs to the Special Issue Advances in Structural Analysis of Materials: Finite Element Modeling)

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24 pages, 196458 KiB

Open AccessArticle

Prediction of Material Failure Time for a Bucket Wheel Excavator Boom Using Computer Simulation

by Andrei Andraș, Sorin Mihai Radu, Ildiko Brînaș, Florin Dumitru Popescu, Daniela Ioana Budilică and Eva Biro Korozsi

Materials 2021, 14(24), 7897; https://doi.org/10.3390/ma14247897 - 20 Dec 2021

Cited by 11 | Viewed by 3530

Abstract

Breakdown of stackers and excavators in opencast mines is possible because of operating, manufacturing and structural causes, and it produces high financial losses. These can be prevented by using various measures, including analyses and strength tests, with computerized modeling and simulation using FEA [...] Read more.

Breakdown of stackers and excavators in opencast mines is possible because of operating, manufacturing and structural causes, and it produces high financial losses. These can be prevented by using various measures, including analyses and strength tests, with computerized modeling and simulation using FEA or other techniques being implemented in the recent years. In this paper a fatigue study is conducted on the boom of a BWE. Based on a computer model of the boom previously developed in SOLIDWORKS by our author team, first the modal analysis is conducted for three positions of the boom by studying the frequency response during the excavation process. This is followed by the time response determination corresponding to the maximum displacement frequency, in order to assess the stress during the excavation process, which causes the material fatigue in the boom structure. It was found that the maximum displacements appear when the BWE boom operates in a horizontal position. The aim was to estimate the period of time to failure in order to prevent unwanted accidents, and to develop a method that is applicable to any surface mining or industrial machine with similar structure. Full article

(This article belongs to the Special Issue Advances in Structural Analysis of Materials: Finite Element Modeling)

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25 pages, 11622 KiB

Open AccessArticle

Theoretical and Experimental Analysis of Inter-Layer Stresses in Filament-Wound Cylindrical Composite Structures

by Piotr Krysiak, Aleksander Błachut and Jerzy Kaleta

Materials 2021, 14(22), 7037; https://doi.org/10.3390/ma14227037 - 20 Nov 2021

Cited by 7 | Viewed by 3311

Abstract

This paper analyses the issues relative to the modelling of tubular (cylindrical) composite structures. This paper aims to describe the design of a multi-layer structure of filament-wound composite pipes where, after loading, the hoop-stress distribution would be as uniform as possible. That would [...] Read more.

This paper analyses the issues relative to the modelling of tubular (cylindrical) composite structures. This paper aims to describe the design of a multi-layer structure of filament-wound composite pipes where, after loading, the hoop-stress distribution would be as uniform as possible. That would allow the mass of the composite to decrease while maintaining the proper mechanical strength. This publication presents the development of a calculation model dedicated to mono- and multi-layered tubular composite structures. The equations describing the stress pattern were based on the Lamé Problem, whereas to describe the modelled structures, an anisotropy coefficient was introduced and interlayer pressures values were determined. To verify the calculations, experimental studies were performed. The test specimens were fabricated by winding fibre bundles around a steel core (as rings with an internal diameter of 113 mm and a height of 30 mm). For the test, the method of pressing a conical ring into a split ring, which acts on the internal surface of the tested cylindrical sample, was selected. The operation of the test rig (test stand) was simulated using the Finite Element Method (FEM). Measurements with strain gauges were conducted during the experiments. Full article

(This article belongs to the Special Issue Advances in Structural Analysis of Materials: Finite Element Modeling)

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15 pages, 3082 KiB

Open AccessArticle

MDCT-Based Finite Element Analysis for the Prediction of Functional Spine Unit Strength—An In Vitro Study

by Nithin Manohar Rayudu, Thomas Baum, Jan S. Kirschke and Karupppasamy Subburaj

Materials 2021, 14(19), 5791; https://doi.org/10.3390/ma14195791 - 3 Oct 2021

Cited by 2 | Viewed by 2153

Abstract

(1) Objective: This study aimed to analyze the effect of ligaments on the strength of functional spine unit (FSU) assessed by finite element (FE) analysis of anatomical models developed from multi-detector computed tomography (MDCT) data. (2) Methods: MDCT scans for cadaveric specimens were [...] Read more.

(1) Objective: This study aimed to analyze the effect of ligaments on the strength of functional spine unit (FSU) assessed by finite element (FE) analysis of anatomical models developed from multi-detector computed tomography (MDCT) data. (2) Methods: MDCT scans for cadaveric specimens were acquired from 16 donors (7 males, mean age of 84.29 ± 6.06 years and 9 females, mean age of 81.00 ± 11.52 years). Two sets of FSU models (three vertebrae + two disks), one with and another without (w/o) ligaments, were generated. The vertebrae were segmented semi-automatically, intervertebral disks (IVD) were generated manually, and ligaments were modeled based on the anatomical location. FE-predicted failure loads of FSU models (with and w/o ligaments) were compared with the experimental failure loads obtained from the uniaxial biomechanical test of specimens. (3) Results: The mean and standard deviation of the experimental failure load of FSU specimens was 3513 ± 1029 N, whereas of FE-based failure loads were 2942 ± 943 N and 2537 ± 929 N for FSU models with ligaments and without ligament attachments, respectively. A good correlation (ρ = 0.79, and ρ = 0.75) was observed between the experimental and FE-based failure loads for the FSU model with and with ligaments, respectively. (4) Conclusions: The FE-based FSU model can be used to determine bone strength, and the ligaments seem to have an effect on the model accuracy for the failure load calculation; further studies are needed to understand the contribution of ligaments. Full article

(This article belongs to the Special Issue Advances in Structural Analysis of Materials: Finite Element Modeling)

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14 pages, 2052 KiB

Open AccessArticle

Sensitivity Analysis Using a Reduced Finite Element Model for Structural Damage Identification

by Qiuwei Yang and Xi Peng

Materials 2021, 14(19), 5514; https://doi.org/10.3390/ma14195514 - 23 Sep 2021

Cited by 8 | Viewed by 2001

Abstract

Sensitivity analysis is widely used in engineering fields, such as structural damage identification, model correction, and vibration control. In general, the existing sensitivity calculation formulas are derived from the complete finite element model, which requires a large amount of calculation for large-scale structures. [...] Read more.

Sensitivity analysis is widely used in engineering fields, such as structural damage identification, model correction, and vibration control. In general, the existing sensitivity calculation formulas are derived from the complete finite element model, which requires a large amount of calculation for large-scale structures. In view of this, a fast sensitivity analysis algorithm based on the reduced finite element model is proposed in this paper. The basic idea of the proposed sensitivity analysis algorithm is to use a model reduction technique to avoid the complex calculation required in solving eigenvalues and eigenvectors by the complete model. Compared with the existing sensitivity calculation formulas, the proposed approach may increase efficiency, with a small loss of accuracy of sensitivity analysis. Using the fast sensitivity analysis, the linear equations for structural damage identification can be established to solve the desired elemental damage parameters. Moreover, a feedback-generalized inverse algorithm is proposed in this work in order to improve the calculation accuracy of damage identification. The core principle of this feedback operation is to reduce the number of unknowns, step by step, according to the generalized inverse solution. Numerical and experimental examples show that the fast sensitivity analysis based on the reduced model can obtain almost the same results as those obtained by the complete model for low eigenvalues and eigenvectors. The feedback-generalized inverse algorithm can effectively overcome the ill-posed problem of the linear equations and obtain accurate results of damage identification under data noise interference. The proposed method may be a very promising tool for sensitivity analysis and damage identification based on the reduced finite element model. Full article

(This article belongs to the Special Issue Advances in Structural Analysis of Materials: Finite Element Modeling)

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23 pages, 8877 KiB

Open AccessArticle

Adaptive Finite Element Model for Simulating Crack Growth in the Presence of Holes

by Abdulnaser M. Alshoaibi and Yahya Ali Fageehi

Materials 2021, 14(18), 5224; https://doi.org/10.3390/ma14185224 - 10 Sep 2021

Cited by 5 | Viewed by 2766

Abstract

This study presents a developed finite element code written by Visual Fortran to computationally model fatigue crack growth (FCG) in arbitrary 2D structures with constant amplitude loading, using the linear elastic fracture mechanics (LEFM) concept. Accordingly, optimizing an FCG analysis, it is necessary [...] Read more.

This study presents a developed finite element code written by Visual Fortran to computationally model fatigue crack growth (FCG) in arbitrary 2D structures with constant amplitude loading, using the linear elastic fracture mechanics (LEFM) concept. Accordingly, optimizing an FCG analysis, it is necessary to describe all the characteristics of the 2D model of the cracked component, including loads, support conditions, and material characteristics. The advancing front method has been used to generate the finite element mesh. The equivalent stress intensity factor was used as the onset criteria of crack propagation, since it is the main significant parameter that must be precisely predicted. As such, a criterion premised on direction (maximum circumferential stress theory) was implemented. After pre-processing, the analysis continues with incremental analysis of the crack growth, which is discretized into short straight segments. The adaptive mesh finite element method was used to perform the stress analysis for each increment. The displacement extrapolation technique was employed at each crack extension increment to compute the SIFs, which are then assessed by the maximum circumferential stress theory to determine the direction of the crack growth and predict the fatigue life as a function of crack length using a modified form of Paris’ law. The application examples demonstrate the developed program’s capability and performance. Full article

(This article belongs to the Special Issue Advances in Structural Analysis of Materials: Finite Element Modeling)

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17 pages, 4201 KiB

Open AccessArticle

Inverse Transformation in Eddy Current Tomography with Continuous Optimization of Reference Defect Parameters

by Paweł Nowak, Roman Szewczyk and Anna Ostaszewska-Liżewska

Materials 2021, 14(17), 4778; https://doi.org/10.3390/ma14174778 - 24 Aug 2021

Cited by 1 | Viewed by 1828

Abstract

This paper presents a methodology of inverse tomography transformation in eddy current tomography with the use of continuous optimization of reference defect parameters. Ferromagnetic steel samples with rectangular air inclusion defects of known dimensions were prepared and measured using an eddy current tomography [...] Read more.

This paper presents a methodology of inverse tomography transformation in eddy current tomography with the use of continuous optimization of reference defect parameters. Ferromagnetic steel samples with rectangular air inclusion defects of known dimensions were prepared and measured using an eddy current tomography setup. FEM-based (Finite Element Method based) forward tomography transformation was developed and utilized in inverse tomography transformation. The presented method of inverse tomography transformation is based on the continuous optimization of parameters that can describe the sample, such as the diameter and dimensions of the reference defect. The obtained results of inverse tomography transformation were in high accordance with the real parameters of the samples. Additionally, the presented method had acceptable repeatability. The obtained values of the sample parameters fit within the range of expanded uncertainty when compared to the real parameters of the sample. Full article

(This article belongs to the Special Issue Advances in Structural Analysis of Materials: Finite Element Modeling)

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22 pages, 12573 KiB

Open AccessFeature PaperArticle

Investigation of Mechanical Strains in Thermal Compensation Loop of Superconducting NbTi Cable during Bending and Cyclic Operation

by Artur Iluk

Materials 2021, 14(5), 1097; https://doi.org/10.3390/ma14051097 - 26 Feb 2021

Cited by 1 | Viewed by 2256

Abstract

In the paper, the thermal compensation loops on a composite, superconducting NbTi cable were investigated. This type of cable is used in the superconducting, fast ramping magnets of the SIS100 synchrotron, part of the Facility for Antiproton and Ion Research (FAIR) under construction [...] Read more.

In the paper, the thermal compensation loops on a composite, superconducting NbTi cable were investigated. This type of cable is used in the superconducting, fast ramping magnets of the SIS100 synchrotron, part of the Facility for Antiproton and Ion Research (FAIR) under construction in Darmstadt, Germany. The influence of space restrictions and electromagnetic cross-talk on the design of the thermal compensation loop was discussed. Plastic deformation of cable components during bending was analyzed by numerical simulations and experiments. A three-dimensional numerical model of the cable was prepared with individual superconducting wires in contact with a central cooling pipe. The bending of a straight cable into a compensation loop shape was simulated, followed by cyclic operation of the cable during thermal cycles. The maximum strains in the superconducting strands and cooling tube were analyzed and discussed. Full article

(This article belongs to the Special Issue Advances in Structural Analysis of Materials: Finite Element Modeling)

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