Search results for: continuous finite elements

Authors: Xuan Sun, Mingbo Tong

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To understand the factors which affect impact damage on composite structures, particularly the effects of impact position and ribs. In this paper, a finite element model (FEM) of low-velocity impact damage on the composite structure was established via the nonlinear finite element method, combined with the user-defined materials subroutine (VUMAT) of the ABAQUS software. The structural elements chosen for the investigation comprised a series of stiffened composite panels, representative of real aircraft structure. By impacting the panels at different positions relative to the ribs, the effect of relative position of ribs was found out. Then the simulation results and the experiments data were compared. Finally, the factors which affect impact damage on the structures were discussed. The paper was helpful for the design of stiffened composite structures.

Keywords: stiffened, low-velocity impact, Abaqus, impact energy

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Authors: A. Gherbi, L. Dahmani, A. Boudjemia

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This paper presents the Finite Element Method (FEM) for analyzing the failure pattern of rectangular slab with various edge conditions. Non-Linear static analysis is carried out using ANSYS 15 Software. Using SOLID65 solid elements, the compressive crushing of concrete is facilitated using plasticity algorithm, while the concrete cracking in tension zone is accommodated by the nonlinear material model. Smeared reinforcement is used and introduced as a percentage of steel embedded in concrete slab. The behavior of the analyzed concrete slab has been observed in terms of the crack pattern and displacement for various loading and boundary conditions. The finite element results are also compared with the experimental data. One of the other objectives of the present study is to show how similar the crack path found by ANSYS program to those observed for the yield line analysis. The smeared reinforcement method is found to be more practical especially for the layered elements like concrete slabs. The value of this method is that it does not require explicit modeling of the rebar, and thus a much coarser mesh can be defined.

Keywords: ANSYS, cracking pattern, displacements, reinforced concrete slab, smeared reinforcements

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Authors: I.J. Kim, B.C. Kim, J.H. Kim, C.-Y. Yi

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Heat transfer in a graphite calorimeter is analyzed by using the finite elements method. The calorimeter is modeled in 3D geometry. Quasi-adiabatic mode operation is realized in the simulation and the temperature rise by different sources of the ionizing radiation and electric heaters is compared, directly. The temperature distribution caused by the electric power was much different from that by the ionizing radiation because of its point-like localized heating. However, the temperature rise which was finally read by sensing thermistors agreed well to each other within 0.02 %.

Keywords: graphite calorimeter, finite element analysis, heat transfer, quasi-adiabatic mode

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Authors: Alberto Hananel

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The aim of this work is to modelize the occlusion of a person with temporomandibular disorders as an evolutionary equation and approach its solution by the construction and characterizing of discrete variational splines. To formulate the problem, certain boundary conditions have been considered. After showing the existence and the uniqueness of the solution of such a problem, a convergence result of a discrete variational evolutionary spline is shown. A stress analysis of the occlusion of a human jaw with temporomandibular disorders by finite elements is carried out in FreeFem++ in order to prove the validity of the presented method.

Keywords: approximation, evolutionary PDE, Finite Element Method, temporomandibular disorders, variational spline

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Authors: Wenbo Duan, Hossein Habibi, Vassilios Kappatos, Cem Selcuk, Tat-Hean Gan

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Ultrasonic guided waves are often used to remove ice or fouling in different structures, such as ship hulls, wind turbine blades and so on. To achieve maximum sound power output, it is important that multiple transducers are arranged in a particular way so that a desired mode can be excited. The objective of this paper is thus to provide a theoretical basis for generating a particular mode in a finite width rectangular plate which can be used for removing potential ice or fouling on the plate. The number of transducers and their locations with respect to a particular mode will be investigated, and the link between dispersion curves and practical applications will be explored. To achieve this, a semi-analytical finite element (SAFE) method is used to study the dispersion characteristics of all the modes in the ultrasonic frequency range. The detailed modal shapes will be revealed, and from the modal analysis, the particular mode with the strongest yet continuous transverse and axial displacements on the surfaces of the plate will be chosen for the purpose of removing potential ice or fouling on the plate. The modal analysis is followed by providing information on the number, location and amplitude of transducers needed to excite this particular mode. Modal excitation is then implemented in a standard finite element commercial package, namely COMSOL Multiphysics. Wave motion is visualized in COMSOL, and the mode shapes generated in SAFE is found to be consistent with the mode shapes generated in COMSOL.

Keywords: dispersion analysis, finite width plate, guided wave, modal excitation

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Authors: Alexandre Marin, Alexandra Bac, Laurent Astart

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New numerical methods for PDE resolution (such as Finite Volumes (FV) or Virtual Elements Method (VEM)) open new needs in terms of meshing of domains of interest, and in particular, polyhedral meshes have many advantages. One way to build such meshes consists of constructing Restricted Voronoi Diagrams (RVDs) whose boundaries respect the domain of interest. By minimizing a function defined for RVDs, the shapes of cells can be controlled, e.g., elongated according to user-defined directions or adjusted to comply with given aspect ratios (anisotropy) and density variations. In this paper, our contribution is threefold: First, we introduce a new gradient formula for the Voronoi tessellation energy under a continuous anisotropy field. Second, we describe a meshing algorithm based on the optimisation of this function that we validate against state-of-the-art approaches. Finally, we propose a hierarchical approach to speed up our meshing algorithm.

Keywords: anisotropic Voronoi diagrams, meshes for numerical simulations, optimisation, volumic polyhedral meshing

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Authors: Edip Kemal, Sheshov Vlatko, Bojadjieva Julijana, Bogdanovic ALeksandra, Gjorgjeska Irena

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The wave propagation phenomenon in porous domains is of great importance in the field of geotechnical earthquake engineering. In these kinds of problems, the elastic waves propagate from the interior to the exterior domain and require special treatment at the computational level since apart from displacement in the solid-state there is a p-wave that takes place in the pore water phase. In this paper, a study on the implementation of multiphase finite elements is presented. The proposed algorithm is implemented in the ANSYS finite element software and tested on one-dimensional wave propagation considering both pore pressure wave propagation and displacement fields. In the simulation of porous media such as soils, the behavior is governed largely by the interaction of the solid skeleton with water and/or air in the pores. Therefore, coupled problems of fluid flow and deformation of the solid skeleton are considered in a detailed way.

Keywords: wave propagation, multiphase model, numerical methods, finite element method

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Authors: Pholosho M. Kgopa, Phatu W. Mashela

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Due to high incidents of marginal land in Limpopo Province, South Africa, and increasing demand for arable land, small-holder farmers tend to continuously cultivate the same fields and at the same time, applying fertilisers to improve yields for meeting local food security. These practices might have an impact on the distribution of trace and essential elements. Therefore, the objective of this investigation was to assess the distribution of essential elements and trace metals in a continuously cultivated and fertilised field, at the University of Limpopo Experimental Farm. Three fields, 3 ha each were identified as continuously cultivated (CC), moderately cultivated (MC) and virgin fields (VF). Each field was divided into 12 equal grids of 50 m × 50 m for sampling. A soil profile was opened in each grid, where soil samples were collected from 0-20; 20-40 and 40-60; 60-80 and 80-100 cm depths for analysis. Samples were analysed for soil texture, pH, electrical conductivity, organic matter content, selected essential elements (Ca, P and Mg), Na and trace elements (Cu, Fe, Ni, and Zn). Results suggested that most of the variables were vertically different, with high concentrations of the test elements except for magnesium. Soil pH in depth 0-20 cm was high (6.44) in CC when compared to that in VF (5.29), but lower than that of MC (7.84). There were no distinctive vertical trends of the variables, except for Mg, Na, and K which displayed a declining trend at 40-60 cm depth when compared to the 0-20 cm depth. Concentrations of Fe, Cu, Zn, and Ni were generally low which might be due to their indirect relationship with soil pH. Continuous cultivation and fertilisation altered soil chemical properties; which could explain the unproductivity of such fields.

Keywords: over-cultivation, soil chemical properties, vertical distribution, spatial distribution

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Authors: Prabhakar Sathujoda

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Vibration analysis of a misaligned rotor coupling bearing system has been carried out while decelerating through its critical speed. The finite element method (FEM) is used to model the rotor system and simulate flexural vibrations. A flexible coupling with a frictionless joint is considered in the present work. The continuous wavelet transform is used to extract the misalignment features from the simulated time response. Subcritical speeds at one-half, one-third, and one-fourth the critical speed have appeared in the wavelet transformed vibration response of a misaligned rotor coupling bearing system. These features are also verified through a parametric study.

Keywords: Continuous Wavelet Transform, Flexible Coupling, Rotor System, Sub Critical Speed

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Authors: Guilherme Gorgulho, Carlos Roberto Camello Lima

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Critical success factors (CSF) are used to design the practice of project management that can lead directly or indirectly to the success of the project. This management includes many elements that have to be synchronized in order to ensure the project on-time delivery, quality and the lowest possible cost. The objective of this work is to develop a proposal for evaluation of the FCS in lean manufacturing projects, and apply the evaluation in a pilot project. The results show that the use of continuous improvement programs in organizations brings benefits as the process cost reduction and improve productivity.

Keywords: continuous improvement, critical success factors (csf), lean thinking, project management

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Authors: A. P. Puvanasvaran, Suresh A. L. Vasu, N. Norazlin

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The Lean Environmental Management Integration System (LEMIS) framework development is integration between lean core element and ISO 14001. The curiosity on the relationship between continuous improvement and sustainability of lean implementation has influenced this study toward LEMIS. Characteristic of ISO 14001 standard clauses and core elements of lean principles are explored from past studies and literature reviews. Survey was carried out on ISO 14001 certified companies to examine continual improvement by implementing the ISO 14001 standard. The study found that there is a significant and positive relationship between Lean Principles: value, value stream, flow, pull and perfection with the ISO 14001 requirements. LEMIS is significant to support the continuous improvement and sustainability. The integration system can be implemented to any manufacturing company. It gives awareness on the importance on why organizations need to sustain its Environmental management system. At the meanwhile, the lean principle can be adapted in order to streamline daily activities of the company. Throughout the study, it had proven that there is no sacrifice or trade-off between lean principles with ISO 14001 requirements. The framework developed in the study can be further simplified in the future, especially the method of crossing each sub requirements of ISO 14001 standard with the core elements of Lean principles in this study.

Keywords: LEMIS, ISO 14001, integration, framework

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Authors: Avaneesh Vaishwar, Badam Singh Kushvah, Devi Prasad Mishra

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We studied the variation in orbital elements of Mars and Jupiter for a time span of 200 thousand years by using secular theory. Here we took Sun oblateness into account and considered the first two zonal gravity constants (J2 and J4) for showing the effect of Sun oblateness on the orbital elements of Mars and Jupiter. We found that in both cases (with and without Sun oblateness) the variation in orbital elements of Mars and Jupiter is periodic moreover in case of the Sun oblateness, the period of variation in orbital elements is decreasing for both the planets.

Keywords: lagrange's planetary equation, orbital elements, planetary system, secular theory

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Authors: Nishant Shrivastava, D. K. Sehgal

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In Finite Element Technique nodal stresses are calculated through displacement as nodes. In this process, the displacement calculated at nodes is sufficiently good enough but stresses calculated at nodes are not sufficiently accurate. Therefore, the accuracy in the stress computation in FEM models based on the displacement technique is obviously matter of concern for computational time in shape optimization of engineering problems. In the present work same is focused to find out unique points within the element as well as the boundary of the element so, that good accuracy in stress computation can be achieved. Generally, major optimal stress points are located in domain of the element some points have been also located at boundary of the element where stresses are fairly accurate as compared to nodal values. Then, it is subsequently concluded that there is an existence of unique points within the element, where stresses have higher accuracy than other points in the elements. Therefore, it is main aim is to evolve a generalized procedure for the determination of the optimal stress location inside the element as well as at the boundaries of the element and verify the same with results from numerical experimentation. The results of quadratic 9 noded serendipity elements are presented and the location of distinct optimal stress points is determined inside the element, as well as at the boundaries. The theoretical results indicate various optimal stress locations are in local coordinates at origin and at a distance of 0.577 in both directions from origin. Also, at the boundaries optimal stress locations are at the midpoints of the element boundary and the locations are at a distance of 0.577 from the origin in both directions. The above findings were verified through experimentation and findings were authenticated. For numerical experimentation five engineering problems were identified and the numerical results of 9-noded element were compared to those obtained by using the same order of 25-noded quadratic Lagrangian elements, which are considered as standard. Then root mean square errors are plotted with respect to various locations within the elements as well as the boundaries and conclusions were drawn. After numerical verification it is noted that in a 9-noded element, origin and locations at a distance of 0.577 from origin in both directions are the best sampling points for the stresses. It was also noted that stresses calculated within line at boundary enclosed by 0.577 midpoints are also very good and the error found is very less. When sampling points move away from these points, then it causes line zone error to increase rapidly. Thus, it is established that there are unique points at boundary of element where stresses are accurate, which can be utilized in solving various engineering problems and are also useful in shape optimizations.

Keywords: finite elements, Lagrangian, optimal stress location, serendipity

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Authors: Waheed Ahmad Safi, Shunichi Nakamura

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Concrete filled steel I-girder (CFIG) bridge was proposed and the bending and shear strength was confirmed by experiments. The area surrounded by the upper and lower flanges and the web is filled with concrete in CFIG, which is used to the intermediate support of a continuous girder. Three-dimensional finite element models were established to simulate the bending and shear behaviors of CFIG and to clarify the load transfer mechanism. Steel plates and filled concrete were modeled as a three-dimensional 8-node solid element and steel reinforcement bars as a three-dimensional 2-node truss element. The elements were mostly divided into the 50 x 50 mm mesh size. The non-linear stress-strain relation is assumed for concrete in compression including the softening effect after the peak, and the stress increases linearly for concrete in tension until concrete cracking but then decreases due to tension stiffening effect. The stress-strain relation for steel plates was tri-linear and that for reinforcements was bi-linear. The concrete and the steel plates were rigidly connected. The developed FEM model was applied to simulate and analysis the bending behaviors of the CFIG specimens. The vertical displacements and the strains of steel plates and the filled concrete obtained by FEM agreed very well with the test results until the yield load. The specimens collapsed when the upper flange buckled or the concrete spalled off. These phenomena cannot be properly analyzed by FEM, which produces a small discrepancy at the ultimate states. The FEM model was also applied to simulate and analysis the shear tests of the CFIG specimens. The vertical displacements and strains of steel and concrete calculated by FEM model agreed well with the test results. A truss action was confirmed by the FEM and the experiment, clarifying that shear forces were mainly resisted by the tension strut of the steel plate and the compression strut of the filled concrete acting in the diagonal direction. A trail design with the CFIG was carried out for a four-span continuous highway bridge and the design method was established. Construction cost was estimated about 12% lower than that of a conventional steel I-section girder.

Keywords: concrete filled steel I-girder, bending strength, FEM, limit states design, steel I-girder, shear strength

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Authors: Abdulmajid Mukhtar Afat

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This paper aims at introducing finite automata theory, the different ways to describe regular languages and create a program to implement the subset construction algorithms to convert nondeterministic finite automata (NFA) to deterministic finite automata (DFA). This program is written in c++ programming language. The program reads FA 5tuples from text file and then classifies it into either DFA or NFA. For DFA, the program will read the string w and decide whether it is acceptable or not. If accepted, the program will save the tracking path and point it out. On the other hand, when the automation is NFA, the program will change the Automation to DFA so that it is easy to track and it can decide whether the w exists in the regular language or not.

Keywords: finite automata, subset construction, DFA, NFA

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Authors: Luis A. Paipa-Galeano, Yavar Jarrah-Nezhad, César A. Bernal-Torres

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This paper presents a case study of four companies in an emerging economy to identify the key success factors and barriers to sustaining continuous improvement practices. The study analyzes the empirical evidence and compares it to the literature review to provide insights for companies looking to increase their maturity level in this area. The five success factors identified are the availability of resources, commitment and support from management, participation of employees in identifying tasks to improve, clear and realistic objectives for continuous improvement, and the existence of a leader or responsible for continuous improvement. The major barriers to success are a lack of alignment between the organization’s strategic objectives and continuous improvement objectives, a lack of motivation in the team, and resistance to change. The paper concludes with recommendations for companies to reduce the risk of improvement failure and increase their maturity level in continuous improvement.

Keywords: emerging economies, Kaizen, continuous improvement sustainability, maturity model

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Authors: A. Armin, R. Fotouhi, W. Szyszkowski

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In this paper a 3-D finite element (FE) investigation of soil-blade interaction is described. The effects of blade’s shape and rake angle are examined both numerically and experimentally. The soil is considered as an elastic-plastic granular material with non-associated Drucker-Prager material model. Contact elements with different properties are used to mimic soil-blade sliding and soil-soil cutting phenomena. A separation criterion is presented and a procedure to evaluate the forces acting on the blade is given and discussed in detail. Experimental results were derived from tests using soil bin facility and instruments at the University of Saskatchewan. During motion of the blade, load cells collect data and send them to a computer. The measured forces using load cells had noisy signals which are needed to be filtered. The FE results are compared with experimental results for verification. This technique can be used in blade shape optimization and design of more complicated blade’s shape.

Keywords: finite element analysis, experimental results, blade force, soil-blade contact modeling

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Authors: Melusi Khumalo, Anastacia Dlamini

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In this paper, we consider a numerical solution for nonlinear Fredholm integral equations of the second kind. We work with uniform mesh and use the Lagrange polynomials together with the Galerkin finite element method, where the weight function is chosen in such a way that it takes the form of the approximate solution but with arbitrary coefficients. We implement the finite element method to the nonlinear Fredholm integral equations of the second kind. We consider the error analysis of the method. Furthermore, we look at a specific example to illustrate the implementation of the finite element method.

Keywords: finite element method, Galerkin approach, Fredholm integral equations, nonlinear integral equations

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Authors: Meysam Naeimi, Zili Li, Rolf Dollevoet

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A new small–scale test rig developed for rolling contact fatigue (RCF) investigations in wheel–rail material. This paper presents the scaling strategy of the rig based on dimensional analysis and mechanical modelling. The new experimental rig is indeed a spinning frame structure with multiple wheel components over a fixed rail-track ring, capable of simulating continuous wheel-rail contact in a laboratory scale. This paper describes the dimensional design of the rig, to derive its overall scaling strategy and to determine the key elements’ specifications. Finite element (FE) modelling is used to simulate the mechanical behavior of the rig with two sample scale factors of 1/5 and 1/7. The results of FE models are compared with the actual railway system to observe the effectiveness of the chosen scales. The mechanical properties of the components and variables of the system are finally determined through the design process.

Keywords: new test rig, rolling contact fatigue, rail, small scale

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Authors: Mohanad Talal Alfach

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This paper concerns the seismic behaviour of soil-piles-bridge reinforced by additional micropiles. The analysis carried out by three-dimensional finite element modelling using the FE software ABAQUS. The soil behaviour is assumed to be elastic with Rayleigh damping, while the micropiles are modeled as 3D elastic beam elements. The bridge deck slab was represented by a concentrated mass at the top of the pier column. The interaction between the added micropiles and the existing piles as well as the performance of the retrofitted soil-pile-superstructure system were investigated for different configurations of additional micropiles (number, position, inclination). Numerical simulation results show that additional micropiles constitute an efficient retrofitting solution. Analysis of results also shows that spacing between existing piles and retrofitting micropiles has little effect; while it is observed a substantial improvement (in case of weak piles/micropiles - soil interface) with reducing the inclination angle of retrofitting micropiles.

Keywords: retrofitting, seismic, finite element, micropiles, elastic

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Authors: Sina Fadaie, Seyed Abolhassan Naeini

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Coastal embankments play an important role in coastal structures by reducing the effect of the wave forces and controlling the movement of sediments. Many coastal areas are underlain by weak and compressible soils. Estimation of during construction settlement of coastal embankments is highly important in design and safety control of embankments and appurtenant structures. Accordingly, selecting and establishing of an appropriate model with a reasonable level of complication is one of the challenges for engineers. Although there are advanced models in the literature regarding design of embankments, there is not enough information on the prediction of their associated settlement, particularly in coastal areas having considerable soft soils. Marine engineering study in Iran is important due to the existence of two important coastal areas located in the northern and southern parts of the country. In the present study, the validity of Terzaghi’s consolidation theory has been investigated. In addition, the settlement of these coastal embankments during construction is predicted by using special methods in PLAXIS software by the help of appropriate boundary conditions and soil layers. The results indicate that, for the existing soil condition at the site, some parameters are important to be considered in analysis. Consequently, a model is introduced to estimate the settlement of the embankments in such geotechnical conditions.

Keywords: consolidation, settlement, coastal embankments, numerical methods, finite elements method

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Authors: Xiaofei Hu, Zhiyu Cai, Weian Yao

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V-notch problem under dynamic loading condition is considered in this paper. In the time domain, the precise time domain expanding algorithm is employed, in which a self-adaptive technique is carried out to improve computing accuracy. By expanding variables in each time interval, the recursive finite element formulas are derived. In the space domain, a Symplectic Analytical Singular Element (SASE) for V-notch problem is constructed addressing the stress singularity of the notch tip. Combining with the conventional finite elements, the proposed SASE can be used to solve the dynamic stress intensity factors (DSIFs) in a simple way. Numerical results show that the proposed SASE for V-notch problem subjected to dynamic loading condition is effective and efficient.

Keywords: V-notch, dynamic stress intensity factor, finite element method, precise time domain expanding algorithm

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Authors: Ali Osman Güney, Bahattin Kanber

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In this work, the effect of material type, diameter, orientation and closeness of fibers on the general performance of reinforced vulcanized rubbers are investigated using finite element method with experimental verification. Various fiber materials such as hemp, nylon, polyester are used for different fiber diameters, orientations and closeness. 3D finite element models are developed by considering bonded contact elements between fiber and rubber sheet interfaces. The fibers are assumed as linear elastic, while vulcanized rubber is considered as hyper-elastic. After an experimental verification of finite element results, the developed models are analyzed under prescribed displacement that causes tension. The normal stresses in fibers and shear stresses between fibers and rubber sheet are investigated in all models. Large deformation of reinforced rubber sheet also represented with various fiber conditions under incremental loading. A general assessment is achieved about best fiber properties of reinforced rubber sheets for tension-load conditions.

Keywords: reinforced vulcanized rubbers, fiber properties, out of plane loading, finite element method

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Authors: Esmaeil Asadzadeh, Mehtab Alam

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Well documented records of the past failures of the structures reveals that the progressive collapse of structures is one of the major reasons for dramatic human loss and economical consequences. Progressive collapse is the failure mechanism in which the structure fails gradually due to the sudden removal of the structural elements. The sudden removal of some structural elements results in the excessive redistributed loads on the others. This sudden removal may be caused by any sudden loading resulted from local explosion, impact loading and terrorist attacks. Hyperbolic thin walled concrete shell structures being an important part of nuclear and thermal power plants are always prone to such terrorist attacks. In concrete structures, the gradual failure would take place by generation of initial cracks and its propagation in the supporting columns along with the tower shell leading to the collapse of the entire structure. In this study the mechanism of progressive collapse for such high raised towers would be simulated employing the finite element method. The aim of this study would be providing clear conceptual step-by-step descriptions of various procedures for progressive collapse analysis using commercially available finite element structural analysis software’s, with the aim that the explanations would be clear enough that they will be readily understandable and will be used by practicing engineers. The study would be carried out in the following procedures: 1. Provide explanations of modeling, simulation and analysis procedures including input screen snapshots; 2. Interpretation of the results and discussions; 3. Conclusions and recommendations.

Keywords: progressive collapse, cooling towers, finite element analysis, crack generation, reinforced concrete

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Authors: Ibtisam Masmali, Edwin Beggs

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In this paper, we take example of differential calculi, on the finite group A4. Then, we apply methods of non-commutative of non-commutative differential geometry to this example, and see how similar the results are to those of classical differential geometry.

Keywords: differential calculi, finite group A4, Christoffel symbols, covariant derivative, torsion compatible

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Authors: Pyung Soo Kim, Eung Hyuk Lee, Mun Suck Jang

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In the current paper, a residual generation filter with finite memory structure is proposed for fault detection. The proposed finite memory residual generation filter provides the residual by real-time filtering of fault vector using only the most recent finite observations and inputs on the window. It is shown that the residual given by the proposed residual generation filter provides the exact fault for noise-free systems. Finally, to illustrate the capability of the proposed residual generation filter, numerical examples are performed for the discretized DC motor system having the multiple sensor faults.

Keywords: residual generation filter, finite memory structure, kalman filter, fast detection

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Authors: Gelacio JuáRez-Luna, Daniel Enrique GonzáLez-RamíRez, Enrique Tenorio-Montero

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Frame elements coupled with springs elements are used for modelling the development of hinges in segmented tunnels, the spring elements modelled the rotational, transversal and axial failure. These spring elements are equipped with constitutive models to include independently the moment, shear force and axial force, respectively. These constitutive models are formulated based on damage mechanics and experimental test reported in the literature review. The mesh of the segmented tunnels was discretized in the software GID, and the nonlinear analyses were carried out in the finite element software ANSYS. These analyses provide the capacity curve of the primary and secondary lining of a segmented tunnel. Two numerical examples of segmented tunnels show the capability of the spring elements to release energy by the development of hinges. The first example is a segmental concrete lining discretized with frame elements loaded until hinges occurred in the lining. The second example is a tunnel with primary and secondary lining, discretized with a double ring frame model. The outer ring simulates the segmental concrete lining and the inner ring simulates the secondary cast-in-place concrete lining. Spring elements also modelled the joints between the segments in the circumferential direction and the ring joints, which connect parallel adjacent rings. The computed load vs displacement curves are congruent with numerical and experimental results reported in the literature review. It is shown that the modelling of a tunnel with primary and secondary lining with frame elements and springs provides reasonable results and save computational cost, comparing with 2D or 3D models equipped with smeared crack models.

Keywords: damage, hinges, lining, tunnel

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Authors: Karim Mohamed Fawzy Ghuiba, Alaa Aldeen Abd Al Hakeem Balbaa, Shams Elbaz

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Objectives: To compare between the effects continuous and pulsed ultrasound on pain and function in patient with knee osteoarthritis. Design: Randomized-Single blinded Study. Participants: 6 patients with knee osteoarthritis with mean age 53.66±3.61years, Altman Grade II or III. Interventions: Subjects were randomly assigned into two groups; Group A received continuous ultrasound and Group B received pulsed ultrasound. Outcome measures: Effects of pulsed and continuous ultrasound were evaluated by pain threshold assessed by visual analogue scale (VAS) scores and function assessed by the Western Ontario and McMaster Universities osteoarthritis index (WOMAC) scores. Results: There was no significant decrease in VAS and WOMAC scores in patients treated with pulsed or continuous ultrasound; and there were no significant differences between both groups. Conclusion: there is no difference between the effects of pulsed and continuous ultrasound in pain relief or functional outcome in patients with knee osteoarthritis.

Keywords: knee osteoarthritis, pulsed ultrasound, ultrasound therapy, continuous ultrasound

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Authors: Ying Yi Wu

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The study of finite groups is a central topic in algebraic structures, and one of the most fundamental questions in this field is the classification of finite groups up to isomorphism. In this paper, we investigate the cyclic property of groups of prime order, which is a crucial result in the classification of finite abelian groups. We prove the following statement: If p is a prime, then every group G of order p is cyclic. Our proof utilizes the properties of group actions and the class equation, which provide a powerful tool for studying the structure of finite groups. In particular, we first show that any non-identity element of G generates a cyclic subgroup of G. Then, we establish the existence of an element of order p, which implies that G is generated by a single element. Finally, we demonstrate that any two generators of G are conjugate, which shows that G is a cyclic group. Our result has significant implications in the classification of finite groups, as it implies that any group of prime order is isomorphic to the cyclic group of the same order. Moreover, it provides a useful tool for understanding the structure of more complicated finite groups, as any finite abelian group can be decomposed into a direct product of cyclic groups. Our proof technique can also be extended to other areas of group theory, such as the classification of finite p-groups, where p is a prime. Therefore, our work has implications beyond the specific result we prove and can contribute to further research in algebraic structures.

Keywords: group theory, finite groups, cyclic groups, prime order, classification.

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Authors: A. Chellil, A. Nour, S. Lecheb , H. Mechakra, A. Bouderba, H. Kebir

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The study of the rotor dynamic in transient system allowed to determine the vibratory responses due to various excitations. This work presents a coupled gyroscopic effect in the defects of a rotor under dynamic loading. Calculations of different energies and virtual work from the various elements of the rotor are developed. To treat real systems a model of finite element was developed. This model of the rotor makes it possible to extract the frequencies and modal deformed, and to calculate the stresses in the critical zone. The study of the rotor in transient system allowed to determine the vibratory responses due to the unbalances, crack and various excitations.

Keywords: rotor, defect, finite element, numerical

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