Bilinear Quadrilateral (Q4): CQUAD4 in GENESIS


 Blake Allison
 1 years ago
 Views:
Transcription
1 Bilinear Quadrilateral (Q4): CQUAD4 in GENESIS The Q4 element has four nodes and eight nodal dof. The shape can be any quadrilateral; we ll concentrate on a rectangle now. The displacement field in terms of generalized coordinates: So, u and v fields are bilinear in x and y (i.e., product of two linear polynomials). Because of form, sides are stiffer than diagonalsartificial anisotropy! 1
2 Q4: The strain fields The strain field in the element: Observation 1: ε x f(x) Q4 cannot exactly model the following beam where ε x x 2
3 Q4: Behavior in Pure Bending of a Beam Observation 2: When β 4 0, ε x varies linearly in y and γ xy 0. The former is a desirable characteristic of Q4 if a beam in pure bending is to be modeled because normal strain varies linearly along the depth coordinate of a beam in pure bending but γ xy 0 is undesirable because there is no shear strain. Fig. (a) is the correct deformation in pure bending while (b) is the deformation of Q4 (the sides remain straight). Physical interpretation: applied moment is resisted by a spurious shear stress as well as flexural (normal) stresses. the Q4 element is too stiff in bending! 3
4 Q4: The displacement field Generalized coordinates β i can be computed in terms of nodal dof and the displacement field can be expressed as where matrix N is 2x8 and the shape functions are 4
5 Q4: The Shape (Interpolation) Functions Note: N 1 =1, N 2 =N 3 =N 4 =0 at x=a, y=b, which is node 1, so that u= N 1 u 1 = u 1 at that node. Similarly N i =1 while all other Ns are zero at node i. Fig See Eqn for the expression of strains in terms of the shape functions (ε= Nd). All in all, Q4 converges properly with mesh refinement and works better than CST in most problems. 5
6 Improved Bilinear Quadrilateral (Q6): None in GENESIS Q4 element is overstiff in bending. For the following problem, it gives deflections and flexural stresses smaller than the exact values and the shear stresses are greatly in error: 6
7 Q6 Element: Displacement Field The problem with Q4 element can be overcome when a new element (Q6) is defined with the following displacement field: where the summation terms alone define Q4 and ξ=x/a, η=y/b. The additional terms are often called bubble modes The addition of quadratic terms in ξ and η allows, for example, ε x to vary linearly in x so that pure bending can be represented exactly and bending due to a transverse loading can be modeled accurately with rectangular Q6 elements. The addition of quadratic terms also allows a vanishing shear strain γ xy as is proper for pure bending. 7
8 Modeling Bending with the Q6 Element g 1 through g 4 are additional dof but not nodal dof. They are called internal dof. Q6 thus has 12 dof. Modeling the previous bending problem with Q6 elements gives the following stresses: 8
9 Quadratic Quadrilateral (Q8): None in GENESIS Q8 has 4 corner nodes and 4 side nodes and 16 nodal dof. 9
10 Quadratic Quadrilateral (Q8): Displacement field The displacement field, which is quadratic in x and y: Two shape functions: Observe from the displacement field: the edges x=±a deform into a parabola (i.e., quadratic displacement in y) (same for y=±b) 10
11 The strain field: Quadratic Quadrilateral (Q8): Strains Strains have linear and quadratic terms. Hence, Q8 can represent a good deal of strain states exactly. For example, states of constant strain, bending strain, etc. 11
12 Quadratic Quadrilateral (Q8): Curved Elements Q8 is useful when curved boundaries such as at a hole are to be represented, which are approximated better with elements having side nodes. But, curving a side distorts an element and is undesirable unless necessary. Therefore, internal element sides should be straight. A side node may be shifted toward a corner where there is stress concentration such as at a crack tip. Hence Q8 is useful for such problems also. 12
13 Elements with Drilling DOF Drilling dof: rotational dof about an axis normal to the plane. An LST with these added to each node has 9 dof. This dof allows twisting and bending rotations of shells under some loads to be represented. 13
Finite element modelling of structural mechanics problems
1 Finite element modelling of structural mechanics problems Kjell Magne Mathisen Department of Structural Engineering Norwegian University of Science and Technology Lecture 10: Geilo Winter School  January,
More informationBHAR AT HID AS AN ENGIN E ERI N G C O L L E G E NATTR A MPA LL I
BHAR AT HID AS AN ENGIN E ERI N G C O L L E G E NATTR A MPA LL I 635 8 54. Third Year M E C H A NICAL VI S E M ES TER QUE S T I ON B ANK Subject: ME 6 603 FIN I T E E LE ME N T A N A L YSIS UNI T  I INTRODUCTION
More informationFinite Element Modeling and Analysis. CE 595: Course Part 2 Amit H. Varma
Finite Element Modeling and Analysis CE 595: Course Part 2 Amit H. Varma Discussion of planar elements Constant Strain Triangle (CST)  easiest and simplest finite element Displacement field in terms of
More informationCode No: RT41033 R13 Set No. 1 IV B.Tech I Semester Regular Examinations, November  2016 FINITE ELEMENT METHODS (Common to Mechanical Engineering, Aeronautical Engineering and Automobile Engineering)
More informationLecture 15 Strain and stress in beams
Spring, 2019 ME 323 Mechanics of Materials Lecture 15 Strain and stress in beams Reading assignment: 6.1 6.2 News: Instructor: Prof. Marcial Gonzalez Last modified: 1/6/19 9:42:38 PM Beam theory (@ ME
More informationAERSYS KNOWLEDGE UNIT
7016 1. INTRODUCTION The scope of this document is to provide a clarification and a deeper understanding of the two different ways to move the mid plane of the element out of the nodal plane. Although
More informationJEPPIAAR ENGINEERING COLLEGE
JEPPIAAR ENGINEERING COLLEGE Jeppiaar Nagar, Rajiv Gandhi Salai 600 119 DEPARTMENT OFMECHANICAL ENGINEERING QUESTION BANK VI SEMESTER ME6603 FINITE ELEMENT ANALYSIS Regulation 013 SUBJECT YEAR /SEM: III
More informationCHAPTER THREE SYMMETRIC BENDING OF CIRCLE PLATES
CHAPTER THREE SYMMETRIC BENDING OF CIRCLE PLATES * Governing equations in beam and plate bending ** Solution by superposition 1.1 From Beam Bending to Plate Bending 1.2 Governing Equations For Symmetric
More informationBending of Simply Supported Isotropic and Composite Laminate Plates
Bending of Simply Supported Isotropic and Composite Laminate Plates Ernesto GutierrezMiravete 1 Isotropic Plates Consider simply a supported rectangular plate of isotropic material (length a, width b,
More informationIntroduction to Structural Member Properties
Introduction to Structural Member Properties Structural Member Properties Moment of Inertia (I): a mathematical property of a crosssection (measured in inches 4 or in 4 ) that gives important information
More informationFinite Element Method in Geotechnical Engineering
Finite Element Method in Geotechnical Engineering Short Course on + Dynamics Boulder, Colorado January 58, 2004 Stein Sture Professor of Civil Engineering University of Colorado at Boulder Contents Steps
More informationChapter 5 Structural Elements: The truss & beam elements
Institute of Structural Engineering Page 1 Chapter 5 Structural Elements: The truss & beam elements Institute of Structural Engineering Page 2 Chapter Goals Learn how to formulate the Finite Element Equations
More informationChapter 12 Plate Bending Elements. Chapter 12 Plate Bending Elements
CIVL 7/8117 Chapter 12  Plate Bending Elements 1/34 Chapter 12 Plate Bending Elements Learning Objectives To introduce basic concepts of plate bending. To derive a common plate bending element stiffness
More informationFLEXIBILITY METHOD FOR INDETERMINATE FRAMES
UNIT  I FLEXIBILITY METHOD FOR INDETERMINATE FRAMES 1. What is meant by indeterminate structures? Structures that do not satisfy the conditions of equilibrium are called indeterminate structure. These
More informationMAE 323: Chapter 6. Structural Models
Common element types for structural analyis: oplane stress/strain, Axisymmetric obeam, truss,spring oplate/shell elements o3d solid ospecial: Usually used for contact or other constraints What you need
More informationCIVL 7/8117 Chapter 4  Development of Beam Equations  Part 2 1/34. Chapter 4b Development of Beam Equations. Learning Objectives
CIV 7/87 Chapter 4  Development of Beam Equations  Part /4 Chapter 4b Development of Beam Equations earning Objectives To introduce the workequivalence method for replacing distributed loading by a
More informationChapter 3: BASIC ELEMENTS. solid mechanics)
Chapter 3: BASIC ELEMENTS Section 3.: Preliminaries (review of solid mechanics) Outline Most structural analsis FE codes are displacement based In this chapter we discuss interpolation methods and elements
More informationUsing MATLAB and. Abaqus. Finite Element Analysis. Introduction to. Amar Khennane. Taylor & Francis Croup. Taylor & Francis Croup,
Introduction to Finite Element Analysis Using MATLAB and Abaqus Amar Khennane Taylor & Francis Croup Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Croup, an informa business
More informationGeneral elastic beam with an elastic foundation
General elastic beam with an elastic foundation Figure 1 shows a beamcolumn on an elastic foundation. The beam is connected to a continuous series of foundation springs. The other end of the foundation
More informationInstitute of Structural Engineering Page 1. Method of Finite Elements I. Chapter 2. The Direct Stiffness Method. Method of Finite Elements I
Institute of Structural Engineering Page 1 Chapter 2 The Direct Stiffness Method Institute of Structural Engineering Page 2 Direct Stiffness Method (DSM) Computational method for structural analysis Matrix
More informationUsing the finite element method of structural analysis, determine displacements at nodes 1 and 2.
Question 1 A pinjointed plane frame, shown in Figure Q1, is fixed to rigid supports at nodes and 4 to prevent their nodal displacements. The frame is loaded at nodes 1 and by a horizontal and a vertical
More informationLecture 7: The Beam Element Equations.
4.1 Beam Stiffness. A Beam: A long slender structural component generally subjected to transverse loading that produces significant bending effects as opposed to twisting or axial effects. MECH 40: Finite
More informationDue Tuesday, September 21 st, 12:00 midnight
Due Tuesday, September 21 st, 12:00 midnight The first problem discusses a plane truss with inclined supports. You will need to modify the MatLab software from homework 1. The next 4 problems consider
More informationME 1401 FINITE ELEMENT ANALYSIS UNIT I PART A. 2. Why polynomial type of interpolation functions is mostly used in FEM?
SHRI ANGALAMMAN COLLEGE OF ENGINEERING AND TECHNOLOGY (An ISO 9001:2008 Certified Institution) SIRUGANOOR, TIRUCHIRAPPALLI 621 105 Department of Mechanical Engineering ME 1401 FINITE ELEMENT ANALYSIS 1.
More informationSteps in the Finite Element Method. Chung Hua University Department of Mechanical Engineering Dr. Ching I Chen
Steps in the Finite Element Method Chung Hua University Department of Mechanical Engineering Dr. Ching I Chen General Idea Engineers are interested in evaluating effects such as deformations, stresses,
More informationPresented By: EAS 6939 Aerospace Structural Composites
A Beam Theory for Laminated Composites and Application to Torsion Problems Dr. BhavaniV. Sankar Presented By: Sameer Luthra EAS 6939 Aerospace Structural Composites 1 Introduction Composite beams have
More informationQuintic beam closed form matrices (revised 2/21, 2/23/12) General elastic beam with an elastic foundation
General elastic beam with an elastic foundation Figure 1 shows a beamcolumn on an elastic foundation. The beam is connected to a continuous series of foundation springs. The other end of the foundation
More informationCIVE1060 Engineering Computation and Simulation Examination, December 12, 2017 / Niiranen
CIVE16 Engineering Computation and Simulation Examination, December 12, 217 / Niiranen This examination consists of 3 problems rated by the standard scale 1...6. Problem 1 Let us consider a long and tall
More informationME 475 Modal Analysis of a Tapered Beam
ME 475 Modal Analysis of a Tapered Beam Objectives: 1. To find the natural frequencies and mode shapes of a tapered beam using FEA.. To compare the FE solution to analytical solutions of the vibratory
More informationChapter 6 2D Elements Plate Elements
Institute of Structural Engineering Page 1 Chapter 6 2D Elements Plate Elements Method of Finite Elements I Institute of Structural Engineering Page 2 Continuum Elements Plane Stress Plane Strain Toda
More informationFinite Element MethodPart II Isoparametric FE Formulation and some numerical examples Lecture 29 Smart and Micro Systems
Finite Element MethodPart II Isoparametric FE Formulation and some numerical examples Lecture 29 Smart and Micro Systems Introduction Till now we dealt only with finite elements having straight edges.
More informationShape Function Generation and Requirements
Shape Function Generation and Requirements Requirements Requirements (A) Interpolation condition. Takes a unit value at node i, and is zero at all other nodes. Requirements (B) Local support condition.
More informationFinite Element Analysis Prof. Dr. B. N. Rao Department of Civil Engineering Indian Institute of Technology, Madras. Module  01 Lecture  13
Finite Element Analysis Prof. Dr. B. N. Rao Department of Civil Engineering Indian Institute of Technology, Madras (Refer Slide Time: 00:25) Module  01 Lecture  13 In the last class, we have seen how
More informationInterpolation Functions for General Element Formulation
CHPTER 6 Interpolation Functions 6.1 INTRODUCTION The structural elements introduced in the previous chapters were formulated on the basis of known principles from elementary strength of materials theory.
More information3. BEAMS: STRAIN, STRESS, DEFLECTIONS
3. BEAMS: STRAIN, STRESS, DEFLECTIONS The beam, or flexural member, is frequently encountered in structures and machines, and its elementary stress analysis constitutes one of the more interesting facets
More informationTransactions on Modelling and Simulation vol 9, 1995 WIT Press, ISSN X
An alternative boundary element formulation for plate bending analysis J.B. Paiva, L.O. Neto Structures Department, Sao Carlos Civil Engineering School, f, BrazzY Abstract This work presents an alternative
More informationThe Finite Element Method for Solid and Structural Mechanics
The Finite Element Method for Solid and Structural Mechanics Sixth edition O.C. Zienkiewicz, CBE, FRS UNESCO Professor of Numerical Methods in Engineering International Centre for Numerical Methods in
More informationA study of moderately thick quadrilateral plate elements based on the absolute nodal coordinate formulation
Multibody Syst Dyn (2014) 31:309 338 DOI 10.1007/s1104401393836 A study of moderately thick quadrilateral plate elements based on the absolute nodal coordinate formulation Marko K. Matikainen Antti
More informationChapter 3. Load and Stress Analysis
Chapter 3 Load and Stress Analysis 2 Shear Force and Bending Moments in Beams Internal shear force V & bending moment M must ensure equilibrium Fig. 3 2 Sign Conventions for Bending and Shear Fig. 3 3
More informationCitation Composite Structures, 2000, v. 50 n. 2, p
Title Predictorcorrector procedures for analysis of laminated plates using standard Mindlin finite element models Author(s) Sze, KY; He, LW; Cheung, YK Citation Composite Structures, 000, v. 50 n., p.
More informationDHANALAKSHMI COLLEGE OF ENGINEERING, CHENNAI DEPARTMENT OF MECHANICAL ENGINEERING ME 6603 FINITE ELEMENT ANALYSIS PART A (2 MARKS)
DHANALAKSHMI COLLEGE OF ENGINEERING, CHENNAI DEPARTMENT OF MECHANICAL ENGINEERING ME 6603 FINITE ELEMENT ANALYSIS UNIT I : FINITE ELEMENT FORMULATION OF BOUNDARY VALUE PART A (2 MARKS) 1. Write the types
More informationABHELSINKI UNIVERSITY OF TECHNOLOGY
ABHELSINKI UNIVERSITY OF TECHNOLOGY TECHNISCHE UNIVERSITÄT HELSINKI UNIVERSITE DE TECHNOLOGIE D HELSINKI A posteriori error analysis for the Morley plate element Jarkko Niiranen Department of Structural
More informationBasic Energy Principles in Stiffness Analysis
Basic Energy Principles in Stiffness Analysis StressStrain Relations The application of any theory requires knowledge of the physical properties of the material(s) comprising the structure. We are limiting
More informationNomenclature. Length of the panel between the supports. Width of the panel between the supports/ width of the beam
omenclature a b c f h Length of the panel between the supports Width of the panel between the supports/ width of the beam Sandwich beam/ panel core thickness Thickness of the panel face sheet Sandwich
More informationENGN 2340 Final Project Report. Optimization of Mechanical Isotropy of Soft Network Material
ENGN 2340 Final Project Report Optimization of Mechanical Isotropy of Soft Network Material Enrui Zhang 12/15/2017 1. Introduction of the Problem This project deals with the stressstrain response of a
More informationtwenty one concrete construction: shear & deflection ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2014 lecture
ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2014 lecture twenty one concrete construction: Copyright Kirk Martini shear & deflection Concrete Shear 1 Shear in Concrete
More informationInternational Journal of Advanced Engineering Technology EISSN
Research Article INTEGRATED FORCE METHOD FOR FIBER REINFORCED COMPOSITE PLATE BENDING PROBLEMS Doiphode G. S., Patodi S. C.* Address for Correspondence Assistant Professor, Applied Mechanics Department,
More informationDeflections and Strains in Cracked Shafts due to Rotating Loads: A Numerical and Experimental Analysis
Rotating Machinery, 10(4): 283 291, 2004 Copyright c Taylor & Francis Inc. ISSN: 1023621X print / 15423034 online DOI: 10.1080/10236210490447728 Deflections and Strains in Cracked Shafts due to Rotating
More informationME FINITE ELEMENT ANALYSIS FORMULAS
ME 2353  FINITE ELEMENT ANALYSIS FORMULAS UNIT I FINITE ELEMENT FORMULATION OF BOUNDARY VALUE PROBLEMS 01. Global Equation for Force Vector, {F} = [K] {u} {F} = Global Force Vector [K] = Global Stiffness
More informationFinite Element Analysis Prof. Dr. B. N. Rao Department of Civil Engineering Indian Institute of Technology, Madras. Module  01 Lecture  11
Finite Element Analysis Prof. Dr. B. N. Rao Department of Civil Engineering Indian Institute of Technology, Madras Module  01 Lecture  11 Last class, what we did is, we looked at a method called superposition
More informationUncorrected Proof Available online at
Available online at www.sciencedirect.com ScienceDirect Procedia Engineering00 (2017) 000 000 www.elsevier.com/locate/procedia Sustainable Civil Engineering Structures and Construction Materials, SCESCM
More informationModule 4 : Deflection of Structures Lecture 4 : Strain Energy Method
Module 4 : Deflection of Structures Lecture 4 : Strain Energy Method Objectives In this course you will learn the following Deflection by strain energy method. Evaluation of strain energy in member under
More informationAbstract. keywords: finite elements, beams, Hermitian interpolation, shape functions
Generation of shape functions for straight beam elements Charles E. Augarde Originally published in Computers and Structures, 68 (1998) 555560 Corrections highlighted. Abstract Straight beam finite elements
More informationCIVL4332 L1 Introduction to Finite Element Method
CIVL L Introduction to Finite Element Method CIVL L Introduction to Finite Element Method by Joe Gattas, Faris Albermani Introduction The FEM is a numerical technique for solving physical problems such
More informationStress analysis of a stepped bar
Stress analysis of a stepped bar Problem Find the stresses induced in the axially loaded stepped bar shown in Figure. The bar has crosssectional areas of A ) and A ) over the lengths l ) and l ), respectively.
More informationConsider an elastic spring as shown in the Fig.2.4. When the spring is slowly
.3 Strain Energy Consider an elastic spring as shown in the Fig..4. When the spring is slowly pulled, it deflects by a small amount u 1. When the load is removed from the spring, it goes back to the original
More information3. Numerical integration
3. Numerical integration... 3. Onedimensional quadratures... 3. Two and threedimensional quadratures... 3.3 Exact Integrals for Straight Sided Triangles... 5 3.4 Reduced and Selected Integration...
More informationFEA CODE WITH MATLAB. Finite Element Analysis of an Arch ME 5657 FINITE ELEMENT METHOD. Submitted by: ALPAY BURAK DEMIRYUREK
FEA CODE WITH MATAB Finite Element Analysis of an Arch ME 5657 FINITE EEMENT METHOD Submitted by: APAY BURAK DEMIRYUREK This report summarizes the finite element analysis of an archbeam with using matlab.
More informationGeometrydependent MITC method for a 2node isobeam element
Structural Engineering and Mechanics, Vol. 9, No. (8) 33 Geometrydependent MITC method for a node isobeam element PhillSeung Lee Samsung Heavy Industries, Seocho, Seoul 37857, Korea HyuChun Noh
More informationG. R. Liu 1,2,, Received 17 July 2008; Revised 6 June 2009; Accepted 23 June 2009 KEY WORDS:
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Int. J. Numer. Meth. Engng 2010; 81:1127 1156 Published online 17 August 2009 in Wiley InterScience (www.interscience.wiley.com)..2720 A G space
More informationELASTICITY AND FRACTURE MECHANICS. Vijay G. Ukadgaonker
THEORY OF ELASTICITY AND FRACTURE MECHANICS y x Vijay G. Ukadgaonker Theory of Elasticity and Fracture Mechanics VIJAY G. UKADGAONKER Former Professor Indian Institute of Technology Bombay Delhi110092
More informationInstitute of Structural Engineering Page 1. Method of Finite Elements I. Chapter 2. The Direct Stiffness Method. Method of Finite Elements I
Institute of Structural Engineering Page 1 Chapter 2 The Direct Stiffness Method Institute of Structural Engineering Page 2 Direct Stiffness Method (DSM) Computational method for structural analysis Matrix
More informationApplication of Finite Element Method to Create Animated Simulation of Beam Analysis for the Course of Mechanics of Materials
International Conference on Engineering Education and Research "Progress Through Partnership" 4 VSBTUO, Ostrava, ISSN 15635 Application of Finite Element Method to Create Animated Simulation of Beam
More informationPlane and axisymmetric models in Mentat & MARC. Tutorial with some Background
Plane and axisymmetric models in Mentat & MARC Tutorial with some Background Eindhoven University of Technology Department of Mechanical Engineering Piet J.G. Schreurs Lambèrt C.A. van Breemen March 6,
More informationWorkshop 8. Lateral Buckling
Workshop 8 Lateral Buckling cross section A transversely loaded member that is bent about its major axis may buckle sideways if its compression flange is not laterally supported. The reason buckling occurs
More informationMECE8001 FINITE ELEMENT ANALYSIS
MECE800 FINIE EEMEN ANAYSIS 07  WHY FINIE EEMENS AND IS HEORY? Design of machines and structures: Solution to stress or displacement by analytical method is often impossible due to complex geometry,
More informationTable of Contents. Preface...xvii. Part 1. Level
Preface...xvii Part 1. Level 1... 1 Chapter 1. The Basics of Linear Elastic Behavior... 3 1.1. Cohesion forces... 4 1.2. The notion of stress... 6 1.2.1. Definition... 6 1.2.2. Graphical representation...
More informationCRITERIA FOR SELECTION OF FEM MODELS.
CRITERIA FOR SELECTION OF FEM MODELS. Prof. P. C.Vasani,Applied Mechanics Department, L. D. College of Engineering,Ahmedabad 380015 Ph.(079) 7486320 [R] Email:pcvim@eth.net 1. Criteria for Convergence.
More informationLecture 8: Assembly of beam elements.
ecture 8: Assembly of beam elements. 4. Example of Assemblage of Beam Stiffness Matrices. Place nodes at the load application points. Assembling the two sets of element equations (note the common elemental
More informationINTERNATIONAL JOURNAL OF PURE AND APPLIED RESEARCH IN ENGINEERING AND TECHNOLOGY
INTERNATIONAL JOURNAL OF PURE AND APPLIED RESEARCH IN ENGINEERING AND TECHNOLOGY A PATH FOR HORIZING YOUR INNOVATIVE WORK SPECIAL ISSUE FOR INTERNATIONAL LEVEL CONFERENCE "ADVANCES IN SCIENCE, TECHNOLOGY
More information7 TRANSVERSE SHEAR transverse shear stress longitudinal shear stresses
7 TRANSVERSE SHEAR Before we develop a relationship that describes the shearstress distribution over the cross section of a beam, we will make some preliminary remarks regarding the way shear acts within
More informationDEFLECTION OF BEAMS WlTH SPECIAL REFERENCE TO SHEAR DEFORMATIONS
DEFLECTION OF BEAMS WlTH SPECIAL REFERENCE TO SHEAR DEFORMATIONS THE INFLUENCE OF THE FORM OF A WOODEN BEAM ON ITS STIFFNESS AND STRENGTHI (REPRINT FROM NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS REPORT
More informationUNCONVENTIONAL FINITE ELEMENT MODELS FOR NONLINEAR ANALYSIS OF BEAMS AND PLATES
UNCONVENTIONAL FINITE ELEMENT MODELS FOR NONLINEAR ANALYSIS OF BEAMS AND PLATES A Thesis by WOORAM KIM Submitted to the Office of Graduate Studies of Texas A&M University in partial fulfillment of the
More informationLecture 13: 2D Problems using CST
Lecture D Problems using CST APL705 Finite Element Method Twodimensional Problems using Constant Strain Triangles To formulate D problems we will follow similar steps as in the case of D FE modeling.
More informationCHAPTER 6 BENDING Part 1
Ishik University / Sulaimani Civil Engineering Department Mechanics of Materials CE 211 CHAPTER 6 BENDING Part 11 CHAPTER 6 Bending Outlines of this chapter: 6.1. Chapter Objectives 6.2. Shear and
More informationFINITE ELEMENT ANALYSIS OF TAPERED COMPOSITE PLATE GIRDER WITH A NONLINEAR VARYING WEB DEPTH
Journal of Engineering Science and Technology Vol. 12, No. 11 (2017) 28392854 School of Engineering, Taylor s University FINITE ELEMENT ANALYSIS OF TAPERED COMPOSITE PLATE GIRDER WITH A NONLINEAR VARYING
More informationε t increases from the compressioncontrolled Figure 9.15: Adjusted interaction diagram
CHAPTER NINE COLUMNS 4 b. The modified axial strength in compression is reduced to account for accidental eccentricity. The magnitude of axial force evaluated in step (a) is multiplied by 0.80 in case
More informationMechanics of Solids notes
Mechanics of Solids notes 1 UNIT II Pure Bending Loading restrictions: As we are aware of the fact internal reactions developed on any crosssection of a beam may consists of a resultant normal force,
More informationDeflections and Strains in Cracked Shafts Due to Rotating Loads: A Numerical and Experimental Analysis
International Journal of Rotating Machinery, 9: 303 311, 2003 Copyright c Taylor & Francis Inc. ISSN: 1023621X DOI: 10.1080/10236210390147416 Deflections and Strains in Cracked Shafts Due to Rotating
More informationACCURATE MODELLING OF STRAIN DISCONTINUITIES IN BEAMS USING AN XFEM APPROACH
VI International Conference on Adaptive Modeling and Simulation ADMOS 213 J. P. Moitinho de Almeida, P. Díez, C. Tiago and N. Parés (Eds) ACCURATE MODELLING OF STRAIN DISCONTINUITIES IN BEAMS USING AN
More informationMethods of Analysis. Force or Flexibility Method
INTRODUCTION: The structural analysis is a mathematical process by which the response of a structure to specified loads is determined. This response is measured by determining the internal forces or stresses
More informationPlate analysis using classical or Reissner Mindlin theories
Plate analysis using classical or Reissner Mindlin theories L. Palermo Jr. Faculty of Civil Engineering, State Universiv at Campinas, Brazil Abstract Plates can be solved with classical or ReissnerMindlin
More informationStructural Dynamics Lecture Eleven: Dynamic Response of MDOF Systems: (Chapter 11) By: H. Ahmadian
Structural Dynamics Lecture Eleven: Dynamic Response of MDOF Systems: (Chapter 11) By: H. Ahmadian ahmadian@iust.ac.ir Dynamic Response of MDOF Systems: ModeSuperposition Method ModeSuperposition Method:
More informationMIXED RECTANGULAR FINITE ELEMENTS FOR PLATE BENDING
144 MIXED RECTANGULAR FINITE ELEMENTS FOR PLATE BENDING J. N. Reddy* and ChenShyhTsay School of Aerospace, Mechanical and Nuclear Engineering, University of Oklahoma, Norman, Oklahoma The paper describes
More informationExample 3.7 Consider the undeformed configuration of a solid as shown in Figure 3.60.
162 3. The linear 3D elasticity mathematical model The 3D elasticity model is of great importance, since it is our highest order hierarchical model assuming linear elastic behavior. Therefore, it provides
More informationNonlinear bending analysis of laminated composite stiffened plates
Nonlinear bending analysis of laminated composite stiffened plates * S.N.Patel 1) 1) Dept. of Civi Engineering, BITS Pilani, Pilani Campus, Pilani333031, (Raj), India 1) shuvendu@pilani.bitspilani.ac.in
More informationM.S Comprehensive Examination Analysis
UNIVERSITY OF CALIFORNIA, BERKELEY Spring Semester 2014 Dept. of Civil and Environmental Engineering Structural Engineering, Mechanics and Materials Name:......................................... M.S Comprehensive
More informationPLAT DAN CANGKANG (TKS 4219)
PLAT DAN CANGKANG (TKS 4219) SESI I: PLATES Dr.Eng. Achfas Zacoeb Dept. of Civil Engineering Brawijaya University INTRODUCTION Plates are straight, plane, twodimensional structural components of which
More informationPURE BENDING. If a simply supported beam carries two point loads of 10 kn as shown in the following figure, pure bending occurs at segment BC.
BENDING STRESS The effect of a bending moment applied to a crosssection of a beam is to induce a state of stress across that section. These stresses are known as bending stresses and they act normally
More informationEffect of Mass Matrix Formulation Schemes on Dynamics of Structures
Effect of Mass Matrix Formulation Schemes on Dynamics of Structures Swapan Kumar Nandi Tata Consultancy Services GEDC, 185 LR, Chennai 600086, India Sudeep Bosu Tata Consultancy Services GEDC, 185 LR,
More informationOn the Sensitivity of Finite Elements
Universität ität Stuttgarttt t Fakultät Bau und Umweltingenieurwissenschaften Baustatik und Baudynamik On the Sensitivity of Finite Elements to Mesh Distortions Manfred Bischoff, Benjamin Schneider Deepak
More informationUNIVERSITY OF HAWAII COLLEGE OF ENGINEERING DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING
UNIVERSITY OF HAWAII COLLEGE OF ENGINEERING DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING ACKNOWLEDGMENTS This report consists of the dissertation by Ms. Yan Jane Liu, submitted in partial fulfillment
More informationAN ALTERNATIVE TECHNIQUE FOR TANGENTIAL STRESS CALCULATION IN DISCONTINUOUS BOUNDARY ELEMENTS
th PanAmerican Congress of Applied Mechanics January 0408, 00, Foz do Iguaçu, PR, Brazil AN ALTERNATIVE TECHNIQUE FOR TANGENTIAL STRESS CALCULATION IN DISCONTINUOUS BOUNDARY ELEMENTS Otávio Augusto Alves
More information7. Hierarchical modeling examples
7. Hierarchical modeling examples The objective of this chapter is to apply the hierarchical modeling approach discussed in Chapter 1 to three selected problems using the mathematical models studied in
More informationBending Load & Calibration Module
Bending Load & Calibration Module Objectives After completing this module, students shall be able to: 1) Conduct laboratory work to validate beam bending stress equations. 2) Develop an understanding of
More informationPOE Practice Test  Materials
Class: Date: POE Practice Test  Materials Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A student weighs 150 lbs and is standing on a beam which spans
More informationChapter 4 Deflection and Stiffness
Chapter 4 Deflection and Stiffness Asst. Prof. Dr. Supakit Rooppakhun Chapter Outline Deflection and Stiffness 41 Spring Rates 42 Tension, Compression, and Torsion 43 Deflection Due to Bending 44 Beam
More informationUNIT I Thin plate theory, Structural Instability:
UNIT I Thin plate theory, Structural Instability: Analysis of thin rectangular plates subject to bending, twisting, distributed transverse load, combined bending and inplane loading Thin plates having
More informationCommon pitfalls while using FEM
Common pitfalls while using FEM J. Pamin Instytut Technologii Informatycznych w Inżynierii Lądowej Wydział Inżynierii Lądowej, Politechnika Krakowska email: JPamin@L5.pk.edu.pl With thanks to: R. de Borst
More informationUNIT II SLOPE DEFLECION AND MOMENT DISTRIBUTION METHOD
SIDDHARTH GROUP OF INSTITUTIONS :: PUTTUR Siddharth Nagar, Narayanavanam Road 517583 QUESTION BANK (DESCRIPTIVE) Subject with Code : SAII (13A01505) Year & Sem: IIIB.Tech & ISem Course & Branch: B.Tech
More information