Recent Advances in Finite element methods


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Recent Advances in Finite element methods

  1. 1. Staff Deve elopmen Progra nt amme (S SDP) on RECE ENT AD DVANCE IN F ES FINITE E ELEME ENT MOD DELLIN NG 19-30 January, 2009 Sponsored b by All In ndia Co ouncil fo Tech or hnical E Educati ion (AICTE New D E), Delhi Coo ordinator JOB THOMA AS Div vision of C Eng Civil gineering g School o Engine S of eering Coc chin Univ versity of Science and Te f e echnolog gy Coochin – 6 022, Kerala 682 , http://civ vil.cusat. 
  2. 2. Transverse Bending Analysis of Concrete Box-Girder Bridge Dr. Babu Kurian, Assistant Professor, Department of Civil Engineering, Mar Athanasius College of Engineering, Kothamangalam – 686 666.Box-girder bridges are widely used throughout the world because of their high structuefficiency as well as better aesthetics compared to open-web type sections. The crosection of the box-girder may take the form of single-cell, multi-spine or multi-cell. Tsingle and multi-cell box-girders (made of reinforced or pre-stressed concrete) wvertical or inclined webs are preferred as economic and aesthetic solutions for ovcrossings, under-crossings, viaducts, etc. The present trend in concrete box-girders isuse thinner webs and flanges in order to reduce self-weight.The various structural actions involved in box-girders are flexure, shear, torsion, warpiand distortion, in which the effects of distortion and warping are particularly significain thin-walled box-girder bridges. The typical box-girder behaves like a beam, butlongitudinal flexural action is accompanied by transverse bending, and is affecteddistortion and warping of the cross-section.In design practice, the longitudinal action and transverse action are often analyzseparately. The box-girder bridge is modelled as a beam for longitudinal action and aframe (of unit width) for transverse action. Here, the transverse action inducedvehicular loading is described. The Beam on Elastic Foundation (BEF) can be used for the transverse bending analyof single-cell box-girders. However, the BEF methods are not commonly adoptedpractice, as they require involved calculations. Three-dimensional finite element analy(3DFEA) provides an alternative computational method, which addresses both transverand longitudinal actions integrally.In design practice, the rigor of BEF and 3DFEA is often avoided, and simple framanalysis is carried out on a frame of unit width (Fig. 1), to obtain the transverse bendimoments. Longitudinal bending action is similarly simplified by modeling the bridgesa simple beam spanning between bearing supports. In thin-walled box sections warpistresses (in the longitudinal direction of the bridge) are developed due to torsion adistortion. To account for the error arising out of the neglect of this warping effect, tresults of simplified analysis are sometimes enhanced by some percentage (10 percentso).Errors in Simplified Frame Analysis (SFA)The errors in SFA can be attributed to the following: (i) Neglect of distortion analysis which can result in serious errors when t
  3. 3. FEM MODELLING OF NATURAL GEOTEXTILESK. S. BeenaReader, School of Engineering, Cochin University of Science and Technology, Kochi, Kerala – 682 022, INDIA, – The importance of Natural Geotextiles in Civil Engineering cannot be over emphasized, the majorapplication area being soil stabilization, erosion control and drainage. With the better understanding of the propertiesand functions of these materials, they can be utilized in a better way and this is possible by way of numerical modeling.In this paper using a three dimensional nonlinear finite element analysis, the versatility of the discrete analysis and theneed to represent the frictional properties of the natural geotextiles, while modeling, are emphasized. A modelfoundation using coir and bamboo as natural geotextiles is taken for the study and the results are compared withlaboratory models.1 INTRODUCTIONThe construction material Geotextile introduced new techniques, design and construction methods in Civil Engineering.These are made of long, flexible and thin fibrous material with high tensile strength. These characteristics are essentialfor good contact with soil particles and there by ensuring stress transfer by friction. The natural geotextiles like jute, coirand bamboo are having these characteristics and can be looked upon as an alternative for synthetic materials, especiallyin developing countries like India. One of the areas where these natural materials can be effectively used is in unpaved roads. Laid over subgradebefore placing the sub-base it act as a separating media which prevents the inter mixing of the material, it assist indrainage by removing excess water and provide improvement in bearing capacity by virtue of their reinforcement value.In the present study, the load deformation characteristic of a reinforced foundation bed is analysed, using coir andbamboo as reinforcement. The Finite Element Method has indeed become a highly useful tool for the numerical analysis of problemsinvolving soil and reinforcement. An early approach to considering reinforced soil has been based on “unit cell”approach suggested by Romstad et al. (1976), which introduces the effect of reinforcement in the constitutive law of thesoil matrix by homogenization methods. This approach may be appropriate only when there are numerous reinforcingelements that enable the soil reinforcement matrix to be considered as a homogeneous material. In many cases, thereinforcement elements and the interface behaviour need explicit modeling to get realistic results. Here a three-dimensional finite element analysis is resorted giving individual attention to soil, reinforcement and the interface.2 MECHANISM OF REINFORCEMENTThe mechanism of reinforcement in reducing the settlement can be explained (Beena, 1994) by considering a block ofsoil subjected to a compressive load under the effect of which it settles axially and deform laterally as an elastic mediumas shown in Fig.1 (a). The same block with reinforcement, having higher modulus of elasticity, included therein issubjected to the same load as shown in Fig.1 (b). If such reinforcement can be assumed to be perfectly bonded with thesurrounding soil, it is obvious that soil and the reinforcement must deform laterally by the same amount and this mustnecessarily be much smaller than the same in the unreinforced case. This is on account of the fact that the reinforcementpermits the soil to move laterally by the same distance both can move together. This naturally brings down the axialdeformation. It is obvious that under the integral action assumed in the above, the higher the modulus of thereinforcement lesser the settlement. This is subjected to a serious limitation when it comes to the soil and its reinforcement in terms of the bond thatcan develop between the two, for which one has to depend on frictional bonding due to mechanical friction
  4. 4. STRUCTURAL DAMAGE IDENTIFICATION IN LAYERED COMPOSITES USING FREQUENCY RESPONSE METHOD. Saraswathy B. 1, Asha V. 2, Lalu Mangal 3, Rahul Leslie4, Ramesh Kumar R. 5 1 Selection Grade Lecturer in Civil Engineering, T.K.M.College of Engg; Kollam, 2 Postgraduate student, T.K.M.College of Engg; Kollam, 3 Asst.Professor in Civil Engineering, T.K.M.College of Engg; Kollam, 4 Asst. Engineer, Design Wing, Kerala P.W.D, Trivandrum, 5 Structural Design and Engineering Group, VSSC, Trivandrum AbstractThis work aims to establish a vibration-based damage identification methodfor laminated composites. This new on-line technique uses the changes inFrequency Response Functions (FRFs) of a sound structure and that of adamaged structure for structural damage identification. There are strongneeds and requirements for on-line damage (delamination) detection andhealth-monitoring techniques of composite structures. Since damage alters thedynamic characteristics of a structure, several techniques based onexperimental modal analysis have been developed in recent years. Vibrationsignature, e.g.: modal properties or frequency response function data is asensitive indicator of structural physical integrity and thus can be used todetect damage. Most of the reported works are based on changes in modalparameters. A new damage detection and assessment method is proposedusing the FRF data.This newly developed technique covers the major steps ofdamage detection-existence, localization and extent, using the FrequencyResponse Function Curvature method.1. IntroductionAs structures degrade or experience damage from natural disasters, they willno longer behave as they were originally designed to, which could pose safetyand reliability hazards. Since damage will alter the stiffness, or energydissipation capabilities of a system, the measured dynamic response of thesystem will also change. Much like a human’s routine checkup at the doctor’soffice, structural health monitoring consists of observing a system’s responseperiodically and implementing damage diagnosis strategies. This helpsengineers to ensure that the structure is in good health, and if necessary, toemploy prompt measures to rectify any damage.
  5. 5. Finite Element Solution ofReynolds Equation using Matlab Dr. Jayadas N. H Reader Division of Mechanical Engineering School of Engineering, CUSAT
  6. 6. DYNAMIC BEHAVIOUR OF PILE IN A LAYERED SOIL MEDIUM Jaya K P Assistant Professor Structural Engineering Division Anna University, Chennai - 600 025 jayakp@annauniv.eduINTRODUCTIONConsidering the frequent occurrence of earthquakes all over the world, studies on the behaviour ofstructures under dynamic excitations are of great importance. There are many parameters affecting thedynamic response of structures, such as: the type of structure, type of foundation, soil characteristicsetc. The observations from the earthquake damaged sites show that, the local soil properties,underground and surface topography of soil medium and the foundation geometry have an importanteffect on the dynamic behaviour of structures. The local soil conditions and the interaction betweensoil and foundation will affect the dynamic behaviour of a structure in three different ways. i. The characteristics and frequency content of the motions that occur at the free surface of a soil deposit resting on a base rock, will differ from that of the motions generated at the top of base rock. The motions at the free surface of the soil layer are functions of soil properties as well as the type and frequency contents of the waves. In general, the motion is amplified. This is known as soil amplification effect. ii. The characteristics of the seismic motions will be modified by the presence of a rigid or stiff foundation, particularly for embedded foundations. The modification is due to the reflection of waves at the rigid face of the foundation. This phenomenon is referred to as the wave scattering or kinematic interaction effect. The base will experience some horizontal and rocking displacement. iii. The inertia forces in the structure during its vibration result in a base shear and an overturning moment, which will give rise to additional deformations and displacements. These will cause deformations in the surrounding soil and thus modify the motions at the base. This phenomena is known as inertial interaction effect.The total interaction effects between the unbounded soil media and the structure, resting on orembedded in the soil, can be referred to as Soil-Structure-Interaction (SSI) effects. It is possible tocharacterise SSI analysis methods in a number of ways: linear versus nonlinear cases, continuumversus discrete formulations, frequency-domain versus time-domain solutions, etc., For the presentdiscussion, two broad categories of solution techniques are distinguished, such as: the direct approachand the substructure approach.
  7. 7. STADD LabEXERCISE 2SPACE FRAME WITH STEEL DESIGN.A steel frame with truss members are analysed. After one analysis, member selectionrequested. Since member sizes change during the member selection, another analysisdone followed by final code checking to verify that the final sizes meet the requiremenof the code based on the latest analysis results. 5 8 3 15 7 10 18 6 13 9 25 17 20 2 28 16 23 19 35 27 30 12 38 26 33 29 37 4 40 22 36 39 14 32 1 24 11 34 Load 1 Y 21 X Z 31STAAD SPACESTART JOB INFORMATIONENGINEER DATE 13-Dec-08END JOB INFORMATIONINPUT WIDTH 79UNIT METER KNJOINT COORDINATES1 0 0 0; 2 0 6 0; 3 10 6 0; 4 10 0 0; 5 5 8.8 0; 6 5 6 0; 7 2.5 7.4 0;8 7.5 7.4 0; 9 2.5 6 0; 10 7.5 6 0; 11 0 0 3.5; 12 0 6 3.5; 13 10 6 3.5;14 10 0 3.5; 15 5 8.8 3.5; 16 5 6 3.5; 17 2.5 7.4 3.5; 18 7.5 7.4 3.5;19 2.5 6 3.5; 20 7.5 6 3.5; 21 0 0 7; 22 0 6 7; 23 10 6 7; 24 10 0 7;25 5 8.8 7; 26 5 6 7; 27 2.5 7.4 7; 28 7.5 7.4 7; 29 2.5 6 7; 30 7.5 6 7;31 0 0 10 5; 32 0 6 10 5; 33 10 6 10 5; 34 10 0 10 5; 35 5 8 8 10 5;
  8. 8. EXERCISE 1STAAD SPACE FRAME WITH CONCRETE DESIGN 4m 5m 6m 5m 5m 4m 5m 5m 6m 5m 6m 5m 4m 5m 5m 3.2 m 5m 3.2 m 6m 5m 5m 5m 3.2 m 3.2 m 6m 4m 6m 3.2 m 5m 3.2 3.2 m 6m 3.2 m 3.2 m 5m 3.2 m 6m 3.2 m Y X 3.2 m ZThe above example represents a space frame, and the members are made ofconcrete.Actual input is shown in bold lettering followed by explanationSTAAD SPACESTART JOB INFORMATIONENGINEER DATE 20-Nov-08END JOB INFORMATIONINPUT WIDTH 79UNIT METER KNJoint number followed by X, Y and Z coordinates are provided belowJOINT COORDINATES1 0 0 0; 2 16 0 0; 3 16 0 5; 4 0 0 5; 5 6 0 0; 6 12 0 0; 7 6 0 5; 8 12 0 5;
  9. 9. STAAD Pro Introduction STAAD.Pro is a general purpose program for performing the analysis and desiof a wide variety of types of structures. The basic three activities which are to be carriout to achieve that goal - a) model generation b) the calculations to obtain the analyticresults c) result verification - are all facilitated by tools contained in the programgraphical environmentTypes of StructuresA STRUCTURE can be defined as an assemblage of elements. STAAD is capableanalyzing and designing structures consisting of both frame, plate/shell and soelements. Almost any type of structure can be analyzed by STAAD. A SPACE structure, which is a three dimensional framed structure with loads appliedany plane, is the most general. A PLANE structure is bound by a global X-Y coordinate system with loads in the samplane. A TRUSS structure consists of truss members which can have only axial member forcand no bending in the members.Analysis FacilitiesThe following PERFORM ANALYSIS facilities are available in STAAD.1) Stiffness Analysis / Linear Static Analysis2) Second Order Static Analysis P-Delta Analysis Non-Linear Analysis Multi Linear Spring Support Member/Spring Tension/Compression only3) Dynamic Analysis
  10. 10. APPLICATION OF FINITE ELEMENT TECHNIQUE IN FREQUENCY ANALYSIS OF LOW-RISE MASONRY BUILDINGSS RaghunathProfessor, Department of Civil EngineeringBMS College of EngineeringBangalore 560019e-mail: is an assemblage of units (such as bricks, blocks, stones etc) bound togethewith the help of a binding material that is commonly known as mortar (cement, limemud mortar etc). It is therefore obvious that the structural (and architectural) properties omasonry is mainly governed by the strength, elastic and geometric properties of thmasonry units and the mortar. There are other factors which also influence the behaviouof masonry, such as; • Bond strength (between unit and mortar) • Slenderness ratio of masonry • Workmanship • Nature of loading and boundary conditions • Geometry of openings • Moisture transport between mortar and unit • Effects from weathering such as wetting/drying and creepIt may interesting to note that masonry components/buildings are essentially continuumstructures with strength and elastic property distributed all over the structure, hencconventional structural analysis may not reveal the true structural behaviour of masonryThis obviates the need to apply Finite Element Analysis (FEA) to study the nature ostresses developed in masonry. It is quite well known that FEA is a very powerful tool foanalysis of such continuum structure. The power and storage capacities of the moderday computers have given the researchers and designers a choice of wide variety of userfriendly commercial FE packages. These packages are often loaded with many modulethat are capable of handling different types of analysis such as linear and non-lineaanalysis, static and dynamic analysis, optimization, thermal analysis etc. They are alscomplemented with a wide variety of choice of ‘elements’. Almost all the packages arusually supplied with user-friendly pre-processor and post-processor. Indeed, nowadaythe use of such ubiquitous packages is quite common. However it is important to realizthat a prior understanding of structural masonry is very much essential before onanalyses the mathematical model.In this lecture notes the usefulness of adopting FEM technique in obtaining the naturafrequencies and mode shapes of box-type masonry buildings is highlighted
  11. 11. CONCEPTS OF FINITE ELEMENT ANALYSIS: 1D & 2D BOUNDARY VALUE PROBLEMS Dr. Palivela Subba Rao, JNTU College of Engineering, Kakinada, (AP).1.0 INTRODUCTION The nature is full of varieties of phenomena, viz., biological, chemical, geologiphysical etc. A phenomenon is defined as an interaction of various parameters involvedthe phenomenon influencing the phenomenon. All the phenomena in the in nature canexpressed either in terms of differential equations or in terms of integral equationsalgebraic equations mathematically called as mathematical models. These models help tscientists and engineers to predict and forecast quantities of their interest. Mathematimodels in terms of differential equations of the all phenomena in the nature are classifiedto three, viz., Boundary Value Problem (BVP), Initial Value Problem (IVP) and Eigen ValProblem (EVP). Specified boundary conditions decide the physical problem to be categorizas BVP or IVP or EVP. Problem is said to be BVP, if all the required boundary conditioare specified at different locations on the boundary of domain. Otherwise, it is said to be IVif the boundary conditions are specified at one point on the domain. Mathematical modewhich has multiple solutions, as in case of buckling problems, free vibration problem(different modes) are called as EVP. Here a few examples on Boundary value problems froengineering applications are discussed for understanding the concepts of Finite ElemeMethod.1.1 MATHEMATICAL MODELING OF A BAR PROBLEM: (Differential Equation The bar structure is a 1Dimensional member subjected to axial force as shownFig.1. In general, axial force on the bar structure may be either body force g ( x) / unit vol ,traction t ( x) / unit length or concentrated load, P or their combination. As the bar structureunder the action of loads, the each and every point of the bar will be displaced to nposition. The function (equation) indicating displacement at any point in the bar structurecalled as displacement function/ displacement field.
  12. 12. BEHAVIOUR OF A MULTIYSTOREY RC FRAME WITH OPEN STOREY AT MULTIPLE FLOORS Thomaskutty Jose 1 and Job Thomas 2 ABSTRACT: Reinforced concrete (RC) framed building having open storey at ground floor to provide parking facility and also having open storey at upper storey to provide recreational halls is vulnerable to the lateral deformation when subjected to earthquake loads. This paper presents the analytical results of a RC frame having soft stories (open halls) at multiple floors. An eight storey RC frame with a lecture hall (7m) and a verandah (2m) has been analyzed using STAAD package to study the effect of open halls at multiple floors. The brick infill walls have been modeled using plate/shell elements having no rotational stiffness. The columns and beams have been modeled using the 3D beam elements. The analytical results such as storey drift, bending moment and shear force in beams and columns have been compared. The analytical results indicate that the presence of open halls at multiple floors increases the maximum storey drift (of soft storey) significantly. Open storey at multiple floor in RC frames induces higher moment and shear force in columns This paper presents the details of design forces of structural elements of a RC frame with and without open stories at multiple levels. the soft ground storey of the RC building was foundINTRODUCTION to be significant when compared to the storey drift in the upper storeys having infill wall panels (Murthy et In multi-storey reinforced concrete (RC) al., 2003). However, the details of the results of RCbuildings meant for offices and hotels, many storey frame having soft or weak stories at multiple floorswill be intentionally left open without masonry walls were not found in the literature (Dasgupta andfor the conveniently utilizing the space in the future. Murthy 2003, Mahashabde et al. 2003).Often, structural engineers conveniently neglect theeffect of masonry walls in RC building. Analytical RESEARCH SIGNIFICANCEstudies by Murthy et al. (2003), Goel et al. (2002)Mahashbode et al. (2003) and Dasgupta et al. (2003) This paper presents the details of FE analysis of aindicated that infilled frame offers increased RC frame considering the stiffness contribution ofresistance against lateral loads. The difficulties to infill masonry wall panels. The conventional shellmodel the structural behavior of the infilled masonry element has been modified by releasing the rotationalpanels in the RC frames have been indicated in these stiffness and utilized for modeling the infilledliteratures (Dasgupta and Murthy 2003, Mahashabde masonry panels in RC frames. The analytical resultset al. 2003). This paper presents details of modeling of a RC frame with and without infill masonry panelsof masonry panels in FE analysis. at multiple floors have been discussed in this paper. The analytical results of the RC frames with weakstorey having no infill masonry walls in the ground DETAILS OF RC FRAMEfloor, to be used as car parking area, have beendiscussed in the literature (Dasgupta and Murthy An eight storey RC frame building with five2003, Mahashabde et al. 2003).The presence of infill rooms of size 7mx7m and having 2m wide verandhamasonry or reinforced concrete walls in upper storey has been analysed using STAAD package. The sizemakes them much stiffer than the open ground storey. of beams at foundation level and beam supporting 2.0Thus, the upper storeys, which are not soft, move span has been taken as 300mmx 300mm. The size ofalmost together as a single block when subjected to beam supporting 7m span has been taken aslateral loads (Murthy et al., 2003). The storey drift in 300mmx600mm. The size of column is taken as 500mmx 500mm. The RC frame having no masonry1 Lecturer in Civil Engineering, Carmel Polytechnic wall at ground floor, at two floors at the bottom, atCollege, Allapuzha, kerala three floors at bottom and at four floors at bottom2 have been considered in this study. The details are Lecturer, School of Engineering, Cochin given in Fig 1. The frame has been designated toUniversity, Kerala; Corresponding author, Email: indicate the storey at which the masonry wall is available. Thus, F1/2/3 is the designation of the
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