Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 4650

Search results for: finite elements

4650 Modeling of Complex Structures: Shear Wall with Openings and Stiffened Shells

Authors: Temami Oussama, Bessais Lakhdar, Hamadi Djamal, Abderrahmani Sifeddine

Abstract:

The analysis of complex structures encourages the engineer to make simplifying assumptions, sometimes attempting the analysis of the whole structure as complex as it is, and it can be done using the finite element method (FEM). In the modeling of complex structures by finite elements, various elements can be used: beam element, membrane element, solid element, plates and shells elements. These elements formulated according to the classical formulation and do not generally share the same nodal degrees of freedom, which complicates the development of a compatible model. The compatibility of the elements with each other is often a difficult problem for modeling complicated structure. This compatibility is necessary to ensure the convergence. To overcome this problem, we have proposed finite elements with a rotational degree of freedom. The study used is based on the strain approach formulation with 2D and 3D formulation with different degrees of freedom at each node. For the comparison and confrontation of results; the finite elements available in ABAQUS/Standard are used.

Keywords: compatibility requirement, complex structures, finite elements, modeling, strain approach

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4649 Numerical Modelling of Dry Stone Masonry Structures Based on Finite-Discrete Element Method

Authors: Ž. Nikolić, H. Smoljanović, N. Živaljić

Abstract:

This paper presents numerical model based on finite-discrete element method for analysis of the structural response of dry stone masonry structures under static and dynamic loads. More precisely, each discrete stone block is discretized by finite elements. Material non-linearity including fracture and fragmentation of discrete elements as well as cyclic behavior during dynamic load are considered through contact elements which are implemented within a finite element mesh. The application of the model was conducted on several examples of these structures. The performed analysis shows high accuracy of the numerical results in comparison with the experimental ones and demonstrates the potential of the finite-discrete element method for modelling of the response of dry stone masonry structures.

Keywords: dry stone masonry structures, dynamic load, finite-discrete element method, static load

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4648 E-Bike FE Model Analysis: Connection Stiffness of Elements with Different DOFs

Authors: Lele Zhang, Hui Leng Choo, Alexander Konyukhov, Shuguang Li

Abstract:

Finite Element (FE) model of simplified e-bike structure was generated by main frame with two tiers, which consisted of pipe, mass, beam, and shell elements (pipe 289, beam188, shell 181, shell 281, combin14, link11, mass21). These elements would be introduced and demonstrated using mathematical formulas. Based on coupling theory, constrain equations was proposed. Exporting all the parameters obtained from theory part, the connection stiffness matrix of the whole e-bike structure between each of these elements was detected.

Keywords: coupling theory, stiffness matrix, e-bike, finite element model

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4647 Finite Element Analysis of Thermally-Induced Bistable Plate Using Four Plate Elements

Authors: Jixiao Tao, Xiaoqiao He

Abstract:

The present study deals with the finite element (FE) analysis of thermally-induced bistable plate using various plate elements. The quadrilateral plate elements include the 4-node conforming plate element based on the classical laminate plate theory (CLPT), the 4-node and 9-node Mindlin plate element based on the first-order shear deformation laminated plate theory (FSDT), and a displacement-based 4-node quadrilateral element (RDKQ-NL20). Using the von-Karman’s large deflection theory and the total Lagrangian (TL) approach, the nonlinear FE governing equations for plate under thermal load are derived. Convergence analysis for four elements is first conducted. These elements are then used to predict the stable shapes of thermally-induced bistable plate. Numerical test shows that the plate element based on FSDT, namely the 4-node and 9-node Mindlin, and the RDKQ-NL20 plate element can predict two stable cylindrical shapes while the 4-node conforming plate predicts a saddles shape. Comparing the simulation results with ABAQUS, the RDKQ-NL20 element shows the best accuracy among all the elements.

Keywords: Bistable, finite element method, geometrical nonlinearity, quadrilateral plate elements

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4646 Finite Element Approximation of the Heat Equation under Axisymmetry Assumption

Authors: Raphael Zanella

Abstract:

This works deals with the finite element approximation of axisymmetric problems. The weak formulation of the heat equation under the axisymmetry assumption is established for continuous finite elements. The weak formulation is implemented in a C++ solver with implicit march-in-time. The code is verified by space and time convergence tests using a manufactured solution. The solving of an example problem with an axisymmetric formulation is compared to that with a full-3D formulation. Both formulations lead to the same result, but the code based on the axisymmetric formulation is much faster due to the lower number of degrees of freedom. This confirms the correctness of our approach and the interest in using an axisymmetric formulation when it is possible.

Keywords: axisymmetric problem, continuous finite elements, heat equation, weak formulation

Procedia PDF Downloads 80
4645 Regularity and Maximal Congruence in Transformation Semigroups with Fixed Sets

Authors: Chollawat Pookpienlert, Jintana Sanwong

Abstract:

An element a of a semigroup S is called left (right) regular if there exists x in S such that a=xa² (a=a²x) and said to be intra-regular if there exist u,v in such that a=ua²v. Let T(X) be the semigroup of all full transformations on a set X under the composition of maps. For a fixed nonempty subset Y of X, let Fix(X,Y)={α ™ T(X) : yα=y for all y ™ Y}, where yα is the image of y under α. Then Fix(X,Y) is a semigroup of full transformations on X which fix all elements in Y. Here, we characterize left regular, right regular and intra-regular elements of Fix(X,Y) which characterizations are shown as follows: For α ™ Fix(X,Y), (i) α is left regular if and only if Xα\Y = Xα²\Y, (ii) α is right regular if and only if πα = πα², (iii) α is intra-regular if and only if | Xα\Y | = | Xα²\Y | such that Xα = {xα : x ™ X} and πα = {xα⁻¹ : x ™ Xα} in which xα⁻¹ = {a ™ X : aα=x}. Moreover, those regularities are equivalent if Xα\Y is a finite set. In addition, we count the number of those elements of Fix(X,Y) when X is a finite set. Finally, we determine the maximal congruence ρ on Fix(X,Y) when X is finite and Y is a nonempty proper subset of X. If we let | X \Y | = n, then we obtain that ρ = (Fixn x Fixn) ∪ (H ε x H ε) where Fixn = {α ™ Fix(X,Y) : | Xα\Y | < n} and H ε is the group of units of Fix(X,Y). Furthermore, we show that the maximal congruence is unique.

Keywords: intra-regular, left regular, maximal congruence, right regular, transformation semigroup

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4644 A Comparative Study between Displacement and Strain Based Formulated Finite Elements Applied to the Analysis of Thin Shell Structures

Authors: Djamal Hamadi, Oussama Temami, Abdallah Zatar, Sifeddine Abderrahmani

Abstract:

The analysis and design of thin shell structures is a topic of interest in a variety of engineering applications. In structural mechanics problems the analyst seeks to determine the distribution of stresses throughout the structure to be designed. It is also necessary to calculate the displacements of certain points of the structure to ensure that specified allowable values are not exceeded. In this paper a comparative study between displacement and strain based finite elements applied to the analysis of some thin shell structures is presented. The results obtained from some examples show the efficiency and the performance of the strain based approach compared to the well known displacement formulation.

Keywords: displacement formulation, finite elements, strain based approach, shell structures

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4643 Seismic Bearing Capacity Estimation of Shallow Foundations on Dense Sand Underlain by Loose Sand Strata by Using Finite Elements Limit Analysis

Authors: Pragyan Paramita Das, Vishwas N. Khatri

Abstract:

By using the lower- and upper- bound finite elements to limit analysis in conjunction with second-order conic programming (SOCP), the effect of seismic forces on the bearing capacity of surface strip footing resting on dense sand underlain by loose sand deposit is explored. The soil is assumed to obey the Mohr-Coulomb’s yield criterion and an associated flow rule. The angle of internal friction (ϕ) of the top and the bottom layer is varied from 42° to 44° and 32° to 34° respectively. The coefficient of seismic acceleration is varied from 0 to 0.3. The variation of bearing capacity with different thickness of top layer for various seismic acceleration coefficients is generated. A comparison will be made with the available solutions from literature wherever applicable.

Keywords: bearing capacity, conic programming, finite elements, seismic forces

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4642 Efficiency of the Strain Based Approach Formulation for Plate Bending Analysis

Authors: Djamal Hamadi, Sifeddine Abderrahmani, Toufik Maalem, Oussama Temami

Abstract:

In recent years many finite elements have been developed for plate bending analysis. The formulated elements are based on the strain based approach. This approach leads to the representation of the displacements by higher order polynomial terms without the need for the introduction of additional internal and unnecessary degrees of freedom. Good convergence can also be obtained when the results are compared with those obtained from the corresponding displacement based elements, having the same total number of degrees of freedom. Furthermore, the plate bending elements are free from any shear locking since they converge to the Kirchhoff solution for thin plates contrarily for the corresponding displacement based elements. In this paper the efficiency of the strain based approach compared to well known displacement formulation is presented. The results obtained by a new formulated plate bending element based on the strain approach and Kirchhoff theory are compared with some others elements. The good convergence of the new formulated element is confirmed.

Keywords: displacement fields, finite elements, plate bending, Kirchhoff theory, strain based approach

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4641 Structural Identification for Layered Composite Structures through a Wave and Finite Element Methodology

Authors: Rilwan Kayode Apalowo, Dimitrios Chronopoulos

Abstract:

An approach for identifying the geometric and material characteristics of layered composite structures through an inverse wave and finite element methodology is proposed. These characteristics are obtained through multi-frequency single shot measurements. However, it is established that the frequency regime of the measurements does not matter, meaning that both ultrasonic and structural dynamics frequency spectra can be employed. Taking advantage of a full FE (finite elements) description of the periodic composite, the scheme is able to account for arbitrarily complex structures. In order to demonstrate the robustness of the presented scheme, it is applied to a sandwich composite panel and results are compared with that of experimental characterization techniques. Excellent agreement is obtained with the experimental measurements.

Keywords: structural identification, non-destructive evaluation, finite elements, wave propagation, layered structures, ultrasound

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4640 Orthosis and Finite Elements: A Study for Development of New Designs through Additive Manufacturing

Authors: M. Volpini, D. Alves, A. Horta, M. Borges, P. Reis

Abstract:

The gait pattern in people that present motor limitations foment the demand for auxiliary locomotion devices. These artifacts for movement assistance vary according to its shape, size and functional features, following the clinical applications desired. Among the ortheses of lower limbs, the ankle-foot orthesis aims to improve the ability to walk in people with different neuromuscular limitations, although they do not always answer patients' expectations for their aesthetic and functional characteristics. The purpose of this study is to explore the possibility of using new design in additive manufacturer to reproduce the shape and functional features of a ankle-foot orthesis in an efficient and modern way. Therefore, this work presents a study about the performance of the mechanical forces through the analysis of finite elements in an ankle-foot orthesis. It will be demonstrated a study of distribution of the stress on the orthopedic device in orthostatism and during the movement in the course of patient's walk.

Keywords: additive manufacture, new designs, orthoses, finite elements

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4639 Relevancy Measures of Errors in Displacements of Finite Elements Analysis Results

Authors: A. B. Bolkhir, A. Elshafie, T. K. Yousif

Abstract:

This paper highlights the methods of error estimation in finite element analysis (FEA) results. It indicates that the modeling error could be eliminated by performing finite element analysis with successively finer meshes or by extrapolating response predictions from an orderly sequence of relatively low degree of freedom analysis results. In addition, the paper eliminates the round-off error by running the code at a higher precision. The paper provides application in finite element analysis results. It draws a conclusion based on results of application of methods of error estimation.

Keywords: finite element analysis (FEA), discretization error, round-off error, mesh refinement, richardson extrapolation, monotonic convergence

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4638 Formulating the Stochastic Finite Elements for Free Vibration Analysis of Plates with Variable Elastic Modulus

Authors: Mojtaba Aghamiri Esfahani, Mohammad Karkon, Seyed Majid Hosseini Nezhad, Reza Hosseini-Ara

Abstract:

In this study, the effect of uncertainty in elastic modulus of a plate on free vibration response is investigated. For this purpose, the elastic modulus of the plate is modeled as stochastic variable with normal distribution. Moreover, the distance autocorrelation function is used for stochastic field. Then, by applying the finite element method and Monte Carlo simulation, stochastic finite element relations are extracted. Finally, with a numerical test, the effect of uncertainty in the elastic modulus on free vibration response of a plate is studied. The results show that the effect of uncertainty in elastic modulus of the plate cannot play an important role on the free vibration response.

Keywords: stochastic finite elements, plate bending, free vibration, Monte Carlo, Neumann expansion method.

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4637 Evaluation of Dynamic Behavior of a Rotor-Bearing System in Operating Conditions

Authors: Mohammad Hadi Jalali, Behrooz Shahriari, Mostafa Ghayour, Saeed Ziaei-Rad, Shahram Yousefi

Abstract:

Most flexible rotors can be considered as beam-like structures. In many cases, rotors are modeled as one-dimensional bodies, made basically of beam-like shafts with rigid bodies attached to them. This approach is typical of rotor dynamics, both analytical and numerical, and several rotor dynamic codes, based on the finite element method, follow this trend. In this paper, a finite element model based on Timoshenko beam elements is utilized to analyze the lateral dynamic behavior of a certain rotor-bearing system in operating conditions.

Keywords: finite element method, Timoshenko beam elements, operational deflection shape, unbalance response

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4636 Simulation and Modeling of High Voltage Pulse Transformer

Authors: Zahra Emami, H. Reza Mesgarzade, A. Morad Ghorbami, S. Reza Motahari

Abstract:

This paper presents a method for calculation of parasitic elements consisting of leakage inductance and parasitic capacitance in a high voltage pulse transformer. The parasitic elements of pulse transformers significantly influence the resulting pulse shape of a power modulator system. In order to prevent the effects on the pulse shape before constructing the transformer an electrical model is needed. The technique procedures for computing these elements are based on finite element analysis. The finite element model of pulse transformer is created using software "Ansys Maxwell 3D". Finally, the transformer parasitic elements is calculated and compared with the value obtained from the actual test and pulse modulator is simulated and results is compared with actual test of pulse modulator. The results obtained are very similar with the test values.

Keywords: pulse transformer, simulation, modeling, Maxwell 3D, modulator

Procedia PDF Downloads 345
4635 Reduction of Rotor-Bearing-Support Finite Element Model through Substructuring

Authors: Abdur Rosyid, Mohamed El-Madany, Mohanad Alata

Abstract:

Due to simplicity and low cost, rotordynamic system is often modeled by using lumped parameters. Recently, finite elements have been used to model rotordynamic system as it offers higher accuracy. However, it involves high degrees of freedom. In some applications such as control design, this requires higher cost. For this reason, various model reduction methods have been proposed. This work demonstrates the quality of model reduction of rotor-bearing-support system through substructuring. The quality of the model reduction is evaluated by comparing some first natural frequencies, modal damping ratio, critical speeds and response of both the full system and the reduced system. The simulation shows that the substructuring is proven adequate to reduce finite element rotor model in the frequency range of interest as long as the numbers and the locations of master nodes are determined appropriately. However, the reduction is less accurate in an unstable or nearly-unstable system.

Keywords: rotordynamic, finite element model, timoshenko beam, 3D solid elements, Guyan reduction method

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4634 Accuracy of VCCT for Calculating Stress Intensity Factor in Metal Specimens Subjected to Bending Load

Authors: Sanjin Kršćanski, Josip Brnić

Abstract:

Virtual Crack Closure Technique (VCCT) is a method used for calculating stress intensity factor (SIF) of a cracked body that is easily implemented on top of basic finite element (FE) codes and as such can be applied on the various component geometries. It is a relatively simple method that does not require any special finite elements to be used and is usually used for calculating stress intensity factors at the crack tip for components made of brittle materials. This paper studies applicability and accuracy of VCCT applied on standard metal specimens containing trough thickness crack, subjected to an in-plane bending load. Finite element analyses were performed using regular 4-node, regular 8-node and a modified quarter-point 8-node 2D elements. Stress intensity factor was calculated from the FE model results for a given crack length, using data available from FE analysis and a custom programmed algorithm based on virtual crack closure technique. Influence of the finite element size on the accuracy of calculated SIF was also studied. The final part of this paper includes a comparison of calculated stress intensity factors with results obtained from analytical expressions found in available literature and in ASTM standard. Results calculated by this algorithm based on VCCT were found to be in good correlation with results obtained with mentioned analytical expressions.

Keywords: VCCT, stress intensity factor, finite element analysis, 2D finite elements, bending

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4633 Finite Element Modeling Techniques of Concrete in Steel and Concrete Composite Members

Authors: J. Bartus, J. Odrobinak

Abstract:

The paper presents a nonlinear analysis 3D model of composite steel and concrete beams with web openings using the Finite Element Method (FEM). The core of the study is the introduction of basic modeling techniques comprehending the description of material behavior, appropriate elements selection, and recommendations for overcoming problems with convergence. Results from various finite element models are compared in the study. The main objective is to observe the concrete failure mechanism and its influence on the structural performance of numerical models of the beams at particular load stages. The bearing capacity of beams, corresponding deformations, stresses, strains, and fracture patterns were determined. The results show how load-bearing elements consisting of concrete parts can be analyzed using FEM software with various options to create the most suitable numerical model. The paper demonstrates the versatility of Ansys software usage for structural simulations.

Keywords: Ansys, concrete, modeling, steel

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4632 Material Failure Process Simulation by Improved Finite Elements with Embedded Discontinuities

Authors: Gelacio Juárez-Luna, Gustavo Ayala, Jaime Retama-Velasco

Abstract:

This paper shows the advantages of the material failure process simulation by improve finite elements with embedded discontinuities, using a new definition of traction vector, dependent on the discontinuity length and the angle. Particularly, two families of this kind of elements are compared: kinematically optimal symmetric and statically and kinematically optimal non-symmetric. The constitutive model to describe the behavior of the material in the symmetric formulation is a traction-displacement jump relationship equipped with softening after reaching the failure surface. To show the validity of this symmetric formulation, representative numerical examples illustrating the performance of the proposed formulation are presented. It is shown that the non-symmetric family may over or underestimate the energy required to create a discontinuity, as this effect is related with the total length of the discontinuity, fact that is not noticed when the discontinuity path is a straight line.

Keywords: variational formulation, strong discontinuity, embedded discontinuities, strain localization

Procedia PDF Downloads 378
4631 Optimization of Assembly and Welding of Complex 3D Structures on the Base of Modeling with Use of Finite Elements Method

Authors: M. N. Zelenin, V. S. Mikhailov, R. P. Zhivotovsky

Abstract:

It is known that residual welding deformations give negative effect to processability and operational quality of welded structures, complicating their assembly and reducing strength. Therefore, selection of optimal technology, ensuring minimum welding deformations, is one of the main goals in developing a technology for manufacturing of welded structures. Through years, JSC SSTC has been developing a theory for estimation of welding deformations and practical activities for reducing and compensating such deformations during welding process. During long time a methodology was used, based on analytic dependence. This methodology allowed defining volumetric changes of metal due to welding heating and subsequent cooling. However, dependences for definition of structures deformations, arising as a result of volumetric changes of metal in the weld area, allowed performing calculations only for simple structures, such as units, flat sections and sections with small curvature. In case of complex 3D structures, estimations on the base of analytic dependences gave significant errors. To eliminate this shortage, it was suggested to use finite elements method for resolving of deformation problem. Here, one shall first calculate volumes of longitudinal and transversal shortenings of welding joints using method of analytic dependences and further, with obtained shortenings, calculate forces, which action is equivalent to the action of active welding stresses. Further, a finite-elements model of the structure is developed and equivalent forces are added to this model. Having results of calculations, an optimal sequence of assembly and welding is selected and special measures to reduce and compensate welding deformations are developed and taken.

Keywords: residual welding deformations, longitudinal and transverse shortenings of welding joints, method of analytic dependences, finite elements method

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4630 Multi-Disciplinary Optimisation Methodology for Aircraft Load Prediction

Authors: Sudhir Kumar Tiwari

Abstract:

The paper demonstrates a methodology that can be used at an early design stage of any conventional aircraft. This research activity assesses the feasibility derivation of methodology for aircraft loads estimation during the various phases of design for a transport category aircraft by utilizing potential of using commercial finite element analysis software, which may drive significant time saving. Early Design phase have limited data and quick changing configuration results in handling of large number of load cases. It is useful to idealize the aircraft as a connection of beams, which can be very accurately modelled using finite element analysis (beam elements). This research explores the correct approach towards idealizing an aircraft using beam elements. FEM Techniques like inertia relief were studied for implementation during course of work. The correct boundary condition technique envisaged for generation of shear force, bending moment and torque diagrams for the aircraft. The possible applications of this approach are the aircraft design process, which have been investigated.

Keywords: multi-disciplinary optimization, aircraft load, finite element analysis, stick model

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4629 Comparison between the Quadratic and the Cubic Linked Interpolation on the Mindlin Plate Four-Node Quadrilateral Finite Elements

Authors: Dragan Ribarić

Abstract:

We employ the so-called problem-dependent linked interpolation concept to develop two cubic 4-node quadrilateral Mindlin plate finite elements with 12 external degrees of freedom. In the problem-independent linked interpolation, the interpolation functions are independent of any problem material parameters and the rotation fields are not expressed in terms of the nodal displacement parameters. On the contrary, in the problem-dependent linked interpolation, the interpolation functions depend on the material parameters and the rotation fields are expressed in terms of the nodal displacement parameters. Two cubic 4-node quadrilateral plate elements are presented, named Q4-U3 and Q4-U3R5. The first one is modelled with one displacement and two rotation degrees of freedom in every of the four element nodes and the second element has five additional internal degrees of freedom to get polynomial completeness of the cubic form and which can be statically condensed within the element. Both elements are able to pass the constant-bending patch test exactly as well as the non-zero constant-shear patch test on the oriented regular mesh geometry in the case of cylindrical bending. In any mesh shape, the elements have the correct rank and only the three eigenvalues, corresponding to the solid body motions are zero. There are no additional spurious zero modes responsible for instability of the finite element models. In comparison with the problem-independent cubic linked interpolation implemented in Q9-U3, the nine-node plate element, significantly less degrees of freedom are employed in the model while retaining the interpolation conformity between adjacent elements. The presented elements are also compared to the existing problem-independent quadratic linked-interpolation element Q4-U2 and to the other known elements that also use the quadratic or the cubic linked interpolation, by testing them on several benchmark examples. Simple functional upgrading from the quadratic to the cubic linked interpolation, implemented in Q4-U3 element, showed no significant improvement compared to the quadratic linked form of the Q4-U2 element. Only when the additional bubble terms are incorporated in the displacement and rotation function fields, which complete the full cubic linked interpolation form, qualitative improvement is fulfilled in the Q4-U3R5 element. Nevertheless, the locking problem exists even for the both presented elements, like in all pure displacement elements when applied to very thin plates modelled by coarse meshes. But good and even slightly better performance can be noticed for the Q4-U3R5 element when compared with elements from the literature, if the model meshes are moderately dense and the plate thickness not extremely thin. In some cases, it is comparable to or even better than Q9-U3 element which has as many as 12 more external degrees of freedom. A significant improvement can be noticed in particular when modeling very skew plates and models with singularities in the stress fields as well as circular plates with distorted meshes.

Keywords: Mindlin plate theory, problem-independent linked interpolation, problem-dependent interpolation, quadrilateral displacement-based plate finite elements

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4628 Photoelastic Analysis and Finite Elements Analysis of a Stress Field Developed in a Double Edge Notched Specimen

Authors: A. Bilek, M. Beldi, T. Cherfi, S. Djebali, S. Larbi

Abstract:

Finite elements analysis and photoelasticity are used to determine the stress field developed in a double edge notched specimen loaded in tension. The specimen is cut in a birefringent plate. Experimental isochromatic fringes are obtained with circularly polarized light on the analyzer of a regular polariscope. The fringes represent the loci of points of equal maximum shear stress. In order to obtain the stress values corresponding to the fringe orders recorded in the notched specimen, particularly in the neighborhood of the notches, a calibrating disc made of the same material is loaded in compression along its diameter in order to determine the photoelastic fringe value. This fringe value is also used in the finite elements solution in order to obtain the simulated photoelastic fringes, the isochromatics as well as the isoclinics. A color scale is used by the software to represent the simulated fringes on the whole model. The stress concentration factor can be readily obtained at the notches. Good agreements are obtained between the experimental and the simulated fringe patterns and between the graphs of the shear stress particularly in the neighborhood of the notches. The purpose in this paper is to show that one can obtain rapidly and accurately, by the finite element analysis, the isochromatic and the isoclinic fringe patterns in a stressed model as the experimental procedure can be time consuming. Stress fields can therefore be analyzed in three dimensional models as long as the meshing and the limit conditions are properly set in the program.

Keywords: isochromatic fringe, isoclinic fringe, photoelasticity, stress concentration factor

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4627 Dynamic Relaxation and Isogeometric Analysis for Finite Deformation Elastic Sheets with Combined Bending and Stretching

Authors: Nikhil Padhye, Ellen Kintz, Dan Dorci

Abstract:

Recent years have seen a rising interest in study and applications of materially uniform thin-structures (plates/shells) subject to finite-bending and stretching deformations. We introduce a well-posed 2D-model involving finite-bending and stretching of thin-structures to approximate the three-dimensional equilibria. Key features of this approach include: Non-Uniform Rational B-Spline (NURBS)-based spatial discretization for finite elements, method of dynamic relaxation to predict stable equilibria, and no a priori kinematic assumption on the deformation fields. The approach is validated against the benchmark problems,and the use of NURBS for spatial discretization facilitates exact spatial representation and computation of curvatures (due to C1-continuity of interpolated displacements) for this higher-order accuracy 2D-model.

Keywords: Isogeometric Analysis, Plates/Shells , Finite Element Methods, Dynamic Relaxation

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4626 Rotor Dynamic Analysis for a Shaft Train by Using Finite Element Method

Authors: M. Najafi

Abstract:

In the present paper, a large turbo-generator shaft train including a heavy-duty gas turbine engine, a coupling, and a generator is established. The method of analysis is based on finite element simplified model for lateral and torsional vibration calculation. The basic elements of rotor are the shafts and the disks which are represented as circular cross section flexible beams and rigid body elements, respectively. For more accurate results, the gyroscopic effect and bearing dynamics coefficients and function of rotation are taken into account, and for the influence of shear effect, rotor has been modeled in the form of Timoshenko beam. Lateral critical speeds, critical speed map, damped mode shapes, Campbell diagram, zones of instability, amplitudes, phase angles response due to synchronous forces of excitation and amplification factor are calculated. Also, in the present paper, the effect of imbalanced rotor and effects of changing in internal force and temperature are studied.

Keywords: rotor dynamic analysis, finite element method, shaft train, Campbell diagram

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4625 Elastohydrodynamic Lubrication Study Using Discontinuous Finite Volume Method

Authors: Prawal Sinha, Peeyush Singh, Pravir Dutt

Abstract:

Problems in elastohydrodynamic lubrication have attracted a lot of attention in the last few decades. Solving a two-dimensional problem has always been a big challenge. In this paper, a new discontinuous finite volume method (DVM) for two-dimensional point contact Elastohydrodynamic Lubrication (EHL) problem has been developed and analyzed. A complete algorithm has been presented for solving such a problem. The method presented is robust and easily parallelized in MPI architecture. GMRES technique is implemented to solve the matrix obtained after the formulation. A new approach is followed in which discontinuous piecewise polynomials are used for the trail functions. It is natural to assume that the advantages of using discontinuous functions in finite element methods should also apply to finite volume methods. The nature of the discontinuity of the trail function is such that the elements in the corresponding dual partition have the smallest support as compared with the Classical finite volume methods. Film thickness calculation is done using singular quadrature approach. Results obtained have been presented graphically and discussed. This method is well suited for solving EHL point contact problem and can probably be used as commercial software.

Keywords: elastohydrodynamic, lubrication, discontinuous finite volume method, GMRES technique

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4624 3D Modelling and Numerical Analysis of Human Inner Ear by Means of Finite Elements Method

Authors: C. Castro-Egler, A. Durán-Escalante, A. García-González

Abstract:

This paper presents a method to generate a finite element model of the human auditory inner ear system. The geometric model has been realized using 2D images from a virtual model of temporal bones. A point cloud has been gotten manually from those images to construct a whole mesh with hexahedral elements. The main difference with the predecessor models is the spiral shape of the cochlea with its three scales completely defined: scala tympani, scala media and scala vestibuli; which are separate by basilar membrane and Reissner membrane. To validate this model, numerical simulations have been realised with two models: an isolated inner ear and a whole model of human auditory system. Ideal conditions of displacement are applied over the oval window in the isolated Inner Ear model. The whole model is made up of the outer auditory channel, the tympani, the ossicular chain, and the inner ear. The boundary condition for the whole model is 1Pa over the auditory channel entrance. The numerical simulations by FEM have been done using a harmonic analysis with a frequency range between 100-10.000 Hz with an interval of 100Hz. The following results have been carried out: basilar membrane displacement; the scala media pressure according to the cochlea length and the transfer function of the middle ear normalized with the pressure in the tympanic membrane. The basilar membrane displacements and the pressure in the scala media make it possible to validate the response in frequency of the basilar membrane.

Keywords: finite elements method, human auditory system model, numerical analysis, 3D modelling cochlea

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4623 Forced Vibration of a Planar Curved Beam on Pasternak Foundation

Authors: Akif Kutlu, Merve Ermis, Nihal Eratlı, Mehmet H. Omurtag

Abstract:

The objective of this study is to investigate the forced vibration analysis of a planar curved beam lying on elastic foundation by using the mixed finite element method. The finite element formulation is based on the Timoshenko beam theory. In order to solve the problems in frequency domain, the element matrices of two nodded curvilinear elements are transformed into Laplace space. The results are transformed back to the time domain by the well-known numerical Modified Durbin’s transformation algorithm. First, the presented finite element formulation is verified through the forced vibration analysis of a planar curved Timoshenko beam resting on Winkler foundation and the finite element results are compared with the results available in the literature. Then, the forced vibration analysis of a planar curved beam resting on Winkler-Pasternak foundation is conducted.

Keywords: curved beam, dynamic analysis, elastic foundation, finite element method

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4622 Fracture Behaviour of Functionally Graded Materials Using Graded Finite Elements

Authors: Mohamad Molavi Nojumi, Xiaodong Wang

Abstract:

In this research fracture behaviour of linear elastic isotropic functionally graded materials (FGMs) are investigated using modified finite element method (FEM). FGMs are advantageous because they enhance the bonding strength of two incompatible materials, and reduce the residual stress and thermal stress. Ceramic/metals are a main type of FGMs. Ceramic materials are brittle. So, there is high possibility of crack existence during fabrication or in-service loading. In addition, damage analysis is necessary for a safe and efficient design. FEM is a strong numerical tool for analyzing complicated problems. Thus, FEM is used to investigate the fracture behaviour of FGMs. Here an accurate 9-node biquadratic quadrilateral graded element is proposed in which the influence of the variation of material properties is considered at the element level. The stiffness matrix of graded elements is obtained using the principle of minimum potential energy. The implementation of graded elements prevents the forced sudden jump of material properties in traditional finite elements for modelling FGMs. Numerical results are verified with existing solutions. Different numerical simulations are carried out to model stationary crack problems in nonhomogeneous plates. In these simulations, material variation is supposed to happen in directions perpendicular and parallel to the crack line. Two special linear and exponential functions have been utilized to model the material gradient as they are mostly discussed in literature. Also, various sizes of the crack length are considered. A major difference in the fracture behaviour of FGMs and homogeneous materials is related to the break of material symmetry. For example, when the material gradation direction is normal to the crack line, even under applying the mode I loading there exists coupled modes I and II of fracture which originates from the induced shear in the model. Therefore, the necessity of the proper modelling of the material variation should be considered in capturing the fracture behaviour of FGMs specially, when the material gradient index is high. Fracture properties such as mode I and mode II stress intensity factors (SIFs), energy release rates, and field variables near the crack tip are investigated and compared with results obtained using conventional homogeneous elements. It is revealed that graded elements provide higher accuracy with less effort in comparison with conventional homogeneous elements.

Keywords: finite element, fracture mechanics, functionally graded materials, graded element

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4621 A Finite Element/Finite Volume Method for Dam-Break Flows over Deformable Beds

Authors: Alia Alghosoun, Ashraf Osman, Mohammed Seaid

Abstract:

A coupled two-layer finite volume/finite element method was proposed for solving dam-break flow problem over deformable beds. The governing equations consist of the well-balanced two-layer shallow water equations for the water flow and a linear elastic model for the bed deformations. Deformations in the topography can be caused by a brutal localized force or simply by a class of sliding displacements on the bathymetry. This deformation in the bed is a source of perturbations, on the water surface generating water waves which propagate with different amplitudes and frequencies. Coupling conditions at the interface are also investigated in the current study and two mesh procedure is proposed for the transfer of information through the interface. In the present work a new procedure is implemented at the soil-water interface using the finite element and two-layer finite volume meshes with a conservative distribution of the forces at their intersections. The finite element method employs quadratic elements in an unstructured triangular mesh and the finite volume method uses the Rusanove to reconstruct the numerical fluxes. The numerical coupled method is highly efficient, accurate, well balanced, and it can handle complex geometries as well as rapidly varying flows. Numerical results are presented for several test examples of dam-break flows over deformable beds. Mesh convergence study is performed for both methods, the overall model provides new insight into the problems at minimal computational cost.

Keywords: dam-break flows, deformable beds, finite element method, finite volume method, hybrid techniques, linear elasticity, shallow water equations

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