Fea Laboratory Manual

 

SVKM’s NMIMS Mukesh Patel School of Technological Management and Engineering Vile parle (W), Mumbai -56

DEPARTMENT OF MECHANICAL ENGINEERING

FEA LABORATORY MANUAL

COURSE NAME

: FINITE ELEMENT ANALYSIS

COURSE CODE

: BTME07003 

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SVKM’s NMIMS Mukesh Patel School of Technology Management and Engineering Department of Mechanical Engineering Class: B. Tech. Mechanical Semester: VII Subject: Finite Element Analysis

Course Objective:

1. To provide the understanding of basics of Finite element method and a nd analysis. 2. To impart knowledge of one dimensional and two dimensional Finite element analysis. 3. To introduce the application of FEA in structural and thermal domain.

Course Outcome:

1. Understand the basics and mathematical aspect of FEA. 2. Apply concept of nodes and elements on structural one dimensional and two t wo dimensional engineering problems. 3. Use FEA software packages for solving complex problems Mapping of Experiments to Course Outcomes:

Experiment No 1 2 3 4 5 6

CO1

√ √

CO2

CO3

√ √ √ √ √ √

√ √ √ √

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SVKM’s NMIMS Mukesh Patel School of Technology Management and Engineering Department of Mechanical Engineering Class: B. Tech. Mechanical Semester: VII Subject: Finite Element Analysis

LIST OF EXPERIMENTS

Sr. No 1. 2

Name of Experiment

Structural analysis of a Bar of Constant cross section area Structural analysis of a Bar of tapered cross section area

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Stepped Bar Structural analysis of a Truss Structural analysis of Simply supported beam Thermal analysis of circular fins

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Introduction to ANSYS 16 Performing a Typical ANSYS Analysis:

The ANSYS program has many finite element analysis capabilities, ranging from a simple, linear, static analysis to a complex, nonlinear, transient dynamic analysis. The analysis guide manuals in the ANSYS documentation set describe specific procedures for performing analyses for different engineering disciplines. A typical ANSYS analysis has three distinct steps:   Build the model.   Apply loads and obtain the solution.  Review the results. 1. Building a Model

Building a finite element model requires more of an ANSYS user's time than any other part of the analysis. First, you specify a job name and analysis title. title . Then, you use the preprocessor to define the element types, element real constants, material materia l properties, and the model geometry. Specifying a Job name and Analysis Title

This task is not required for an analysis, but is recommended. 1.1.Defining the Job name

The job name is a name that identifies the ANSYS job. When you define a job name for an analysis, the job name becomes the first part of the name of all files the analysis creates. (The extension or suffix for these files' names is a file identifier such as .DB.) By using a job name for each analysis, you insure that no files are a re overwritten. If you do not specify a job name, all files receive the name FILE or file, depending on the operating system. GUI: Utility Menu>File>Change Job name 1.2.Defining Element Types

The ANSYS element library contains more than 100 different element types. Each element type has a unique number and a prefix that identifies the element category: BEAM4, PLANE77, SOLID96, etc. The following element categories are available The element type determines, among other things:   The degree-of-freedom set (which in turn implies the discipline-structural, thermal, magnetic, electric, quadrilateral, brick, etc.)   Whether the element lies in two-dimensional or three-dimensional space. For example, BEAM4, has six structural degrees of freedom (UX, UY, UZ, ROTX, ROTY, ROTZ), is a line element, and can be modeled in 3-D space. PLANE77 has a thermal degree of freedom (TEMP), is an eight-node quadrilateral element, and can be modeled only in 2-D space. 1.3.Defining Element Real Constants

Element real constants are properties that depend on the element type, such as cross-sectional  properties of a beam beam element. For example, real constants for BEA BEAM3, M3, the 2-D beam beam element, are area (AREA), moment of inertia (IZZ), height (HEIGHT), shear deflection constant (SHEARZ), initial strain (ISTRN), and added mass per unit length (ADDMAS). Not all element types require real constants, and different elements of the same type may have different real constant values.

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As with element types, each set of real constants has a reference number, and the table of reference number versus real constant set is called the real constant table. While defining the elements, you point to the appropriate real constant reference number using the REAL  command (Main Menu> Preprocessor>Create>E Preprocessor>Create>Elements>Elem lements>Elem Attributes). 1.4.Defining Material Properties

Most element types require material properties. Depending on the application, material  properties may be:   Linear or nonlinear   Isotropic, orthotropic, or anisotropic   Constant temperature or temperature-dependent. As with element types and real constants, each set of material properties has a material reference number. The table of material reference numbers versus material property sets is called the material table. Within one analysis, you may have multiple material property sets (to correspond with multiple materials used in the model). ANSYS identifies each set with a unique reference number. Main Menu > Preprocessor> Preprocessor> Material Props > Material Models. 1.  5.Creating the Model Geometry

Once you have defined material properties, the next step in an analysis is generating a finite element model-nodes and elements-that adequately describes the model geometry. There are two methods to create the finite element model: solid modeling and direct generation. With solid modeling, you describe the geometric shape of your model, and then instruct the ANSYS program to automatically mesh the geometry with nodes and elements. You can control the size and shape of the elements that the program creates. With direct generation, you "manually" define the location of each node and the connectivity of each element. Several convenience operations, such as copying patterns of existing nodes and elements, symmetry reflection, etc. are available. 2.  Apply Loads and Obtain the Solution

In this step, you use the SOLUTION processor to define the aanalysis nalysis type and analysis options, apply loads, specify load step options, and initiate the finite element solution. You also can apply loads using the PREP7 preprocessor. 2.1.Applying Loads The word loads as used in this manual includes boundary conditions (constraints, supports, or  boundary field specifications) as well as other externally externall y and internally applied loads. Loads in the ANSYS program are divided into six categories:   DOF Constraints   Forces   Surface Loads   Body Loads   Inertia Loads   Coupled-field Loads You can apply most of these loads either on the solid model (key points, lines, and areas) or the finite element model (nodes and elements). Two important load-related terms you need to know are load step and substep. A load step is simply a configuration of loads for which you obtain a solution. In a structural analysis, for example, you may apply wind loads in one load step and gravity in a second load step. Load steps are also useful in dividing a transient load history curve into several segments.

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2.  2.Solution: Solution >Solve >current LS. 3.  Review the results.

The postprocessing stage deals with the representation of results. Typically, the deformed shapes, displacements, strains and stresses, mode shape, temperature tempera ture distribution are computed at this stage. The user can choose the unknowns (field variable) of his interest according to the type of analysis. This stage includes the results and its it s interpretation, checks for accurac accuracy, y, etc. The results generated will form the report of the particular p articular problem.

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1. Structural analysis of a Bar of Constant cross section area  Problem Statement:  Consider the bar shown in figure below. Young’s modulus is 2.1×105  N/mm2  and Area is 500 mm 2. Determine the Nodal Displacement, Stress in each

element, Reaction forces.

Procedure 1. Ansys Main Menu – Preferences-Select – STRUCTURAL – h method- ok 2. Element type – Add/Edit/Delete – Add – Link – 3D Finit stn 180 – ok – close. 3.  Real constants – Add – ok – real constant set no 1 – c/s area – 500 – ok. 4.  Material Properties – material models – Structural – Linear – Elastic – Isotropic – EX– 2.1e5 – PRXY – 0.27 – ok – close. 5.  Modeling – Create – Nodes – In Active CS – Apply (first node is created) – x,y,z x ,y,z location in CS– 1000 (x value w.r.t first node) – ok (second node is created). 6.  Create – Elements – Auto numbered – Thru Nodes – pick 1 & 2 – ok (elements are created through nodes). 7.  Loads – Define loads – apply – Structural – Displacement – on Nodes- pick node 1 – apply DOFs to be constrained – All DOF – ok. 8.  Define loads – apply – Structural – Force/Moment – on Nodes- pick node 2 – apply – direction of For/Mom – FX – Force/Moment value – 1000 (+ve value) – ok. 9.  Solve – current LS – ok (Solution is done is displayed) di splayed) – close. 10. Element table – Define table – Add –‘Results data item’ – By Sequence num – LS –LS1 – ok. 11. Plot results – contour plot –Element table – item to be plotted LS,1, avg common nodesyes average- ok. 12. List Results – reaction solution – items to be listed – All items ite ms – ok (reaction forces will be displayed with the node numbers). 13. Plot results- nodal solution-ok-DOF solution- x component of displacement-ok.

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Analytical approach: Calculation: Given data:

P=_________N L=_________mm A=_________  mm2  E=_________ N/mm2  Deformation (δL) =PL/AE

(σ) = P/A

Conclusion: Ansys 

Theoretical

Deformation(mm)   Stress(N/mm2) Reaction (N)

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2. Structural analysis of a Bar of tapered cross section area  Problem Statement: Consider the Tapered bar shown in figure below. Determine the

 Nodal Displacement, Stress in each element, Reaction forces E = 2 x 10 5 N/mm2, Area at root, A1 = 1000 mm2, Area at the end, A2 = 500 mm2.

Procedure 1.  Ansys Main Menu – Preferences-Select – STRUCTURAL- h method– ok 2.  Element type – Add/Edit/Delete – Add – link, 3D Finit stn 180 – ok- close. 3.  Real constants – Add – ok – real r eal constant set no – 1 – cross-sectional AREA1 – 875 – applyok 4.  Add – ok – real constant set no – 2 – cross-sectional AREA 2 – 625-ok 5.  Material Properties – material models – Structural – Linear – Elastic – Isotropic – EX– 2e5 – PRXY – 0.3 – ok – close. 6.  Modeling – Create – keypoints– In Active CS, =0, Y=0 – Apply (first key point is created) – location in active ac tive CS, X= 187.5, Y=0, apply (second key point is created) - location in active CSX=375, Y=0(third key point is created) -ok. 7.  Modeling-Create – lines-straight lines-pick key points 1 & 2-ok- pick key points 2 & 3-ok 8. Meshing-mesh attributes-picked lines (pick the lines)-ok-material no= 1, real r eal constants set no=1, element type no =1, link 1, element section= none defined-pick the other line-okmaterial number 2-define material id 2- real constants set no = 2,element type no =2-element section= none defined-ok. 9.  Meshing-size controls-manual size-lines-all lines- no of element divisions=10(yes)-ok 10. Meshing-mesh tool-mesh-pick the lines-ok (the color changes to light blue) 11. Loads – Define loads – apply – Structural – Displacement – on key points- pick keypoint 1 – apply –DOFs to be constrained c onstrained – ALL DOF, displacement value=0 – ok. 12. Loads – Define loads – apply – Structural – Force/Moment – on key points- pick last key  point – apply – direction of For/Mom – FX – Force/Moment value – 1000 (+ ve value) – ok. 13. Solve – current LS – ok (Solution is done is displayed) di splayed) – close. 14. Element table – Define table – Add –‘Results data item’ – By Sequence num – LS –LS1 – ok. 15. Plot results – contour plot –Element table – item to be plotted LS, 1, avg common nodesyes average- ok.  

16. displayed List Results – reaction – items to be listed – All items ite ms – ok (reaction forces will be with the nodesolution numbers). 9

 

17. Plot results- nodal solution-ok-DOF solution- x component of displacement-ok. 18. Animation: PlotCtrls – Animate – Deformed shape – def+ undeformed-ok.

Analytical Approach Analytical approach:

Calculation: Given Data: Area at root, A1 = ____mm2  2 Area at the end, A2 2 = ___mm . E = _____ N/mm   L=___mm P =____N Area A1 = Π/4xd2 =_____ So, d1 =_____mm Similarly

d2 =____mm

Deformation (δL)

= ______mm

Conclusion: Ansys 

Theoretical

Deformation(mm)  Stress(N/mm2) Reaction(N)

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3. Structural analysis of a Stepped Bar Problem Statement: Consider the stepped bar shown in figure below. Determine the

 Nodal Displacement, Stress in each element, Reaction forces.

Procedure 1.  Ansys Main Menu – Preferences-Select – STRUCTURAL- h method – ok 2.  Element type – Add/Edit/Delete – Add – link, 3D Finit stn 180 – ok- close.  

3. applyok Real constants – Add – ok – real constant set no – 1 – cr cross-sectional oss-sectional AREA 1 – 900 – 4.  Add – ok – real constant set no – 2 – cross-sectional AREA 2 – 600-ok 5.  Material Properties – material models – Structural – Linear – Elastic – Isotropic – EX  – 2e5 – PRXY – 0.3- material- new material-define material id=2- Structural – Linear– Elastic – Isotropic – EX – 0.7e5 –PRXY – 0.3– ok – close. 6.  Modeling – Create – key points– In Active CS, =0, Y=0 – Apply (first key point is created) – location in active CS, X= 600, Y=0, apply (second key point is created) - location l ocation in active CS X=1100, Y=0(third key point is created) -ok. 7.  Modeling-Create – lines-straight lines-pick key points 1 & 2-ok- pick key points 2 & 3-ok 8.  Meshing-mesh attributes-picked lines (pick the lines)-ok-material no= 1, real constants set no = 1, element type no =1, link 1, element section= none defined-pick the other lineok-material number 2-define material id 2- real constants set no = 2, element type no =2element section= none defined-ok.size-lines-all lines- no of element divisions=10(yes)-ok 9. controls-manual   Meshing-size 10. Meshing-mesh tool-mesh-pick the lines-ok (the color changes to light blue) 11. Loads – Define loads – apply – Structural – Displacement – on key points- pick key  point 1 – apply –DOFs –DOFs to be constrained – ALL DOF, DOF, displacement value=0 – ok. 12. Loads – Define loads – apply – Structural – Force/Moment – on key points- pick last key point – apply – direction of For/Mom – FX – Force/Moment value – 500 (+ve value)  – ok. 13. Solve – current LS – ok (Solution is done is displayed) – close. c lose. 14. Element table – Define table – Add –‘Results data item’ – By Sequence num – LS –  LS1 – ok. 15. Plot results – contour plot –Element table – item to be plotted LS,1, avg common nodesyes average- ok. 16. List Results – reaction solution – items to be listed – All items – ok (reaction forces displayed the node numbers). 17. will Plot be resultsnodalwith solution-ok-DOF solution- x component of displacement-ok. 11

 

18. Animation: PlotCtrls – Animate – Deformed shape – def+ undeformed-ok.

Analytical approach:  Given data: P=_____N L1=_____mm L2=____mm A1=_____ mm2 A2=_____ mm2  E1=______ N/mm2  E2=_____ N/mm2  Deformation (δL1) = (PL/AE)1 = ________mm  Deformation (δL2) = (PL/AE)2 = ________mm  Total Deformation = δL1 + δL2  = _______ mm mm

Conclusion: Ansys 

Theoretical

Deformation(m)  Stress(N/mm2) Reaction(N)

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4.Structural analysis of Trusses Problem Statement: Consider the four bar truss shown in figure. For the given data, find Stress in each element, Reaction forces, Nodal displacement. E = 210 GPa, A = 0.1 m 2.

Procedure 1. Ansys Main Menu – Preferences-select – STRUCTURAL- h method – ok 2. Element type – Add/Edit/Delete – Add – Link – 3D Finit stn 180 – ok – close.

  3. Material Real constants – Add– –material ok – realmodels constant set no – 1 –– c/s area – 0.1 – ok –– Isotropic close. – EX– 4. Properties – Structural Linear Elastic

210e9– Ok – close. 5. Modeling – Create – Nodes – In Active CS – Apply (first node is created) – x,y,z location in CS– 4 (x value w.r.t first node) – apply (second node is created) – x,y,z location in CS – 4, 3 (x, y value w.r.t first node) – apply (third node is created) – 0, 3 (x, y value w.r.t first node) – ok (forth node is created). 6. Create–Elements–Elem Attributes – Material number – 1 – Real constant set number– 1 – ok 7. Auto numbered – Thru Nodes – pick 1 & 2 – apply appl y – pick 2 & 3 – apply – pick 3 & 1– apply pick 3 & 4 – ok (elements are created through nodes). 8.  Loads – Define loads – apply – Structural – Displacement – on Nodes – pick node 1 & 4 – apply – DOFs DOFs to be constrained – All DOF – ok – on Nodes – pick node 2 ––apply apply – DOFs to be constrained – UY – ok. 9.  Loads – Define loads – apply – Structural – Force/Moment – on Nodes- pick node 2 – – direction– ofonFor/Mom FX –node Force/Moment – 2000of (+ve 10. apply Force/Moment Nodes- –pick 3 – apply value – direction F value) or/Mom– ok. – FY – Force/Moment value – -2500 (-ve value) – ok. 11. Solve – current LS – ok (Solution is done is displayed) – close. 12. Element table – Define table – Add –‘Results data item’ – By Sequence num – LS – LS1  – ok. 13.  Plot results – contour plot –Element table – item to be plotted LS,1, avg common nodes- yes average- ok. 14. Reaction forces: List Results – reaction solution – items to be listed – All items – ok (reaction forces will be displayed with the node numbers). 15. Plot results- nodal solution-ok-DOF solution- Y component of displacement-ok. 16. Animation: PlotCtrls – Animate – Deformed shape – def+undeformed-ok.

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Analytical Approach Considering equilibrium conditions in X and Y directions dire ctions find the unknown ∑ 

=0

∑

=0

∑

a=0

Taking moment find the unknown reactions

Conclusion: ANSYS

Deformation(mm) 

Ux 

Uy

Stress(N/mm2)

Ele 1.

Ele 2

Ele 3

Ele 4

RX

RY

Reaction(N)

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5.Structural analysis of Simply Supported Beam Problem Statement: Compute the Shear force and bending moment diagrams for the

 beam shown and find the maximum deflection. Assume rectangular c/s area of 100 mm * 100mm, Young’s modulus of 210 MPa, Poisson’s ratio 0.27.

1.  Ansys Main Menu – Preferences-Select – STRUCTURAL- h method – ok 2.  Element type – Add/Edit/Delete – Add – BEAM – 2 node BEAM 188– ok- close. 3.  Material Properties – material models – Structural – Linear – Elastic – Isotropic – EX– 2.10e5– PRXY – 0.27 – ok – close. 4.  Sections-Beams-common sections- sub type- rectangle (1st element) -enter b=100, h=100- preview-ok. 5.  Modeling – Create – Nodes – In Active CS – Apply (first node is created) – x,y,z location in CS– 1000 (x value w.r.t first node) – apply (second node is created) – 2500 (x value w.r.t first node) – apply(third node is created)- x,y,z location in CS-3500 (x value w.r.t first node)-ok. 6.  Create – Elements – Auto numbered – Thru Nodes – pick 1 & 2 apply – pick 2 & 3 apply – pick 3 & 4 – ok (elements are created through nodes). 7.  Loads – Define loads – apply – Structural – Displacement – on Nodes- pick node 1 & 4 –apply –DOFs to be constrained – all DOF – ok. 8.  Loads – Define loads – apply – Structural – Force/Moment – on Nodes- pick node 2 –  apply – direction of For/Mom – FY – Force/Moment value – -2000(-ve value) – okForce/Moment – on Nodes- pick node 3 – apply –direction of For/Mom – FY –  Force/Moment value – -4000(-ve value) – ok. 9.  Solve – current LS – ok (Solution is done is displayed) – close. c lose. 10. Displacement: Plot Results – Contour plot – Nodal solution – DOF solution –  displacement vector sum – ok. 11. Stress: Plot Results – Contour plot – Nodal solution – stress – vonmises stress – ok. 12. Element table – Define table tabl e – Add – ‘Results data item’ – By Sequence num – SMISC  – SMISC, 6 – apply, By Sequence num – SMISC – SMISC, SMISC, 19 – apply, apply, By Sequence num  – SMISC – SMISC, 3 – apply, By Sequence num – SMISC – SMISC,16 – ok – close. 13. Plot results – contour plot – Line Element Results – Elem table item at node I –SMIS6  – Elem table item at node J – SMIS19 SMIS19 – ok (Shear force diagram will be displayed). 14. Plot results – contour plot – Line Element Results – Elem table item at node I –SMIS3  – Elem table item at node J – SMIS16 SMIS16 – ok (bending moment moment diagram will be displayed). 15. Reaction forces: List Results – reaction solution – items to be listed – All items – ok (reaction forces will be displayed with the node numbers).

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Conclusion:

Ansys Stress(N/mm2)

Max Stress

Min Stress

Max Total Shear Force

Max Total Bending Moment

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6. Thermal Analysis of circular fins  Problem Statement: Solve the 2-D heat conduction problem for the temperature distribution within the rectangular plate. Thermal conductivity of the plate, KXX=401 W/(mK).

60 mm

100 mm T = 300°C 300°C , Convection = 22 W /m2 °C

1.  Ansys Main Menu – Preferences-select – THERMAL- h method– ok 2.  Element type – Add/Edit/Delete – Add – Solid – Quad4node–55–ok–option –element  behavior K3 – Plane stress with thickness thickness – ok – close. 3.  Material Properties – material models – Thermal – Conductivity – Isotropic – KXX –401. 4.  Modeling – Create – Area – Rectangle – by dimensions – X1, X2, Y1, Y2 – 0, 10, 0,20 – ok. 5.  Meshing – Mesh Tool – Mesh Areas – Quad – Free – Mesh – pick all – ok. MeshTool – Refine – pick all – Level of refinement – 3 – ok. 6.  Loads – Define loads – apply – Thermal – Temperature Temperat ure – on Lines – select 1000 0Clines – apply – DOFs to be constrained – TEMP – Temp value – 1000 0C – ok. 7.  Loads – Define loads – apply – Thermal – Temperature – on Lines – select 1000 Clines – 8.   Read Solveresults-last – current LS – ok (Solution is done is displayed) – close. 9. set-ok 17

 

10. List results-nodal solution-select temperature-ok 11. Observe the nodal solution per node. 12. From the menu bar-plot ctrls-style-size and shape-display of the element-click on real constant multiplier=0.2, don’t change other values-ok. 13. Plot results-contour plot-nodal solution-temperature-deformed shape only-ok 14. Element table-define table-add-enter user label item=HTRANS, select by sequence no SMISC, 1-ok-close. 15. Element table-list table-select HTRANS-ok

Conclusion:

Ansys  Max Total Temp  Min Total Temp Max Heat Flux Min Heat Flux

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