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# FINELEMMTHMECHDESI ME512

U of L

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This 14 page Class Notes was uploaded by Maud Armstrong on Friday October 23, 2015. The Class Notes belongs to ME512 at University of Louisville taught by RogerBradshaw in Fall. Since its upload, it has received 74 views. For similar materials see /class/228364/me512-university-of-louisville in Mechanical Engineering at University of Louisville.

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Date Created: 10/23/15

ANSYS Elements ME 512 Prof Bradshaw Description 2 D HighFrequency Quadrilateral Solid 3D Tetrahedral HighFrequency 3D BrickWedge HighFrequency 2 D 4Node Mixed UP Hyperelastic Solid 3D 8 Node Mixed UP Hyperelastic Solid 2 D 8 Node Mixed UP Hyperelastic Solid 2 D Hyperelastic Solid 3D Hyperelastic Solid 3D 10Node Tetrahedral Mixed UP Hyperelastic Solid 2 D Infinite Boundary 2 D Infinite Solid 3D Infinite Solid 3D Infinite Boundary 3D Magnetic Interface 2 D 4Node Linear Interface 2 D 6Node Linear Interface 3D 16Node Quadratic Interface 3D 8 Node Linear Interface Name Description Nate IBEAM3 2 D Elastic Beam HWB BEAM4 3D Elastic Beam HF119 BEAM23 2 D Plastic Beam HF120 BEAM24 3D Thinwalled Beam HYPER56 BEAM44 3D Elastic Tapered Unsymmetric Beam HYPER58 BEAM54 2 D Elastic Tapered Unsymmetric Beam HYPER74 BEAM161 Explicit 3D Beam HYPER84 BEAM188 3D Finite Strain Beam HYPER86 IBEAM189 3D Finite Strain Beam HYPER158 CIRCU94 Piezoelectric Circuit INFIN9 CIRCU124 General Circuit INFIN110 CIRCU125 Common or Zener Diode INFIN111 WW INFIN47 COMBIN14 SpringDamper INTER115 COMBIN37 Control INTER192 COMBIN39 Nonlinear Spring INTER193 COMBIN40 Combination INTER194 COMBI165 Explicit SpringDamper INTER195 CONTAC12 2 D PointtoPoint Contact LINK1 CONTAC26 2 D PointtoGround Contact LINK8 CONTAC48 2 D PointtoSurface Contact LINK10 CONTAC49 3D PointtoSurface Contact LINK11 CONTAC52 3D PointtoPoint Contact LINK31 CONTA171 2 D 2 Node SurfacetoSurface Contact LINK32 CONTA172 2 D 3Node Surfaceto Surface Contact LINK33 CONTA173 3D 4Node SurfacetoSurface Contact LINK34 CONTA174 3D 8 Node Surfaceto Surface Contact LINK68 CONTA178 3D PointtoPoint Contact LINK160 FLUID29 2 D Acoustic Fluid LINK167 FLUID30 3D Acoustic Fluid LINK180 FLUID38 Dynamic Fluid Coupling FLUID79 2 D Contained Fluid FLUID80 3D Contained Fluid FLUID81 AxisymmetricHarmonic Contained Fluid FLUID116 ThermalFluid Pipe FLUID129 2 D Infinite Acoustic FLUID130 3D Infinite Acoustic FLUID141 2 D FluidThermal FLUID142 3D FluidThermal 2 D Spar or Truss 3D Spar or Truss Tensiononly or Compressiononly Spar Linear Actuator Radiation Link 2 D Conduction Bar 3D Conduction Bar Convection Link ThermalElectric Line Explicit 3D Spar or Truss Explicit TensionOnly Spar 3D Finite Strain Spar or Truss Structural Mass Thermal Mass Explicit 3D Structural Mass Stiffness Damping or Mass Matrix Superelement or Substructure Meshing Facet ANSYS Elements ME 512 Prof Bradshaw We Description Nate Description PIPE16 Elastic Straight Pipe SOLID45 3D Structural Solid PIPE17 Elastic Pipe Tee SOLID46 3D 8 Node Layered Structural Solid PIPE18 Elastic Curved Pipe Elbow SOLIDS 3D CoupledField Solid PIPE20 Plastic Straight Pipe SOLID62 3D MagnetoStructural Solid PIPE59 Immersed Pipe or Cable SOLID64 3D Anisotropic Structural Solid PIPE60 Plastic Curved Pipe Elbow SOLID65 3D Reinforced Concrete Solid PLANE2 2 D 6Node Triangular Structural Solid SOLID69 3D ThermalElectric Solid PLANE13 2 D CoupledField Solid SOLID70 3D Thermal Solid PLANE25 Axisymmetric Harmonic 4Node Structural Solid SOLID87 3D 10Node Tetrahedral Thermal Solid PLANE35 2 D 6Node Triangular Thermal Solid SOLID90 3D 20Node Thermal Solid PLANE42 2 D Structural Solid SOLID92 3D 10Node Tetrahedral Structural Solid PLANE53 2 D 8 Node Magnetic Solid SOLID95 3D 20 Node Structural Solid PLANESS 2 D Thermal Solid SOLID96 3D Magnetic Scalar Solid PLANE67 2 D ThermalElectric Solid SOLID97 3D Magnetic Solid PLANE75 AxisymmetricHarmonic 4Node Thermal Solid SOLID98 Tetrahedral CoupledField Solid PLANE77 2 D 8 Node Thermal Solid SOLID117 3D 20 Node Magnetic Solid PLANE78 AxisymmetricHarmonic 8 Node Thermal Solid SOLID122 3D 20 Node Electrostatic Solid PLANE82 2 D 8 Node Structural Solid SOLID123 3D 10Node Tetrahedral Electrostatic Solid PLANE83 AxisymmetricHarmonic 8 Node Structural Solid SOLID127 3D Tetrahedral Electrostatic Solid pElement PLANE121 2 D 8 Node Electrostatic Solid SOLID128 3D Brick Electrostatic Solid pElement PLANE145 2 D Quadrilateral Structural Solid pElement SOLID147 3D Brick Structural Solid pElement PLANE146 2 D Triangular Structural Solid pElement SOLID148 3D Tetrahedral Structural Solid pElement PLANE162 Explicit 2 D Structural Solid SOLID164 Explicit 3D Structural Solid PLANE182 2 D 4Node Structural Solid SOLID185 3D 8 Node Structural Solid PLANE183 2 D 8 Node Structural Solid SOLID186 3D 20 Node Structural Solid PHI I S1 I9 2 D3 D Pretension Element SOLID187 3D 10Node Tetrahedral Structural Solid ISHELL28 ShearTwist Panel SOLID191 3D 20 Node Layered Structural Solid SHELL41 Membrane Shell w Current Source SHELL43 4 Node Plastic Large Strain Shell SURF151 2 D Thermal Surface Effect SHELL51 Axisymmetric Structural Shell SURF152 3D Thermal Surface Effect SHELL57 Thermal Shell SURF153 2 D Structural Surface Effect SHELL61 AxisymmetricHarmonic Structural Shell SURF154 3D Structural Surface Effect SHELL63 Elastic Shell TARGE169 2 D Target Segment SHELL91 Nonlinear Layered Structural Shell TARGE17O 3D Target Segment SHELL93 8 Node Structural Shell TRANS109 2 D EIectroMechanical Solid SHELL99 Linear Layered Structural Shell TRANS126 EIectrostructural Transducer SHELL143 4 Node Plastic Small Strain Shell VISC0106 2 D 4Node Large Strain Solid SHELL150 8 Node Structural Shell pElement VISC0107 3D 8 Node Large Strain Solid SHELL157 ThermalElectric Shell VISC0108 2 D 8 Node Large Strain Solid SHELL163 Explicit Thin Structural Shell VISC088 2 D 8 Node Viscoelastic Solid SHELL181 Finite Strain Shell VISC089 3D 20 Node Viscoelastic Solid ANSYS Documentation Adaptive Meshing gt Note that not all elements suppott adaptive meshing Chapter 5 Adaptive N16511ng r V t warm ropemes m eragmg problems Table 51 Element Tm um Can Be I39m in Adaptive Meshing Tnnngulnr Structural SCIle l rKude Tetrahedml Structural Solid ANSYS Documentation Adaptive Meshing gt Using adaptive meshing in certain regions Chapter 5 Adaptive hIeshing 531 Selective Adap x ity mm g n m m Haw quotmmquot t n Selecmg lag pmu d a way ofluandlmg such mam Figure 51 Seec ve Adaprin ry mom in xed edge t a What Mesh b Mesh Downed mm an areas selected note excesswe mesh denstlv near ooncenuated load and constramts v d M 5 and 5 unselected ssh untamed mm areas c Unselect areas 5 and 6 to NW wmnannn ADAPT Solution of FEA Equation gt Recall fundamental equation of FEA K d r gt What have we done so far 0 Isoparametric elements 7 K 0 Isoparametric elements 7 r 0 Apply boundary conditions 7 combination of d r gt What is the next step 0 Solve for unknown displacemenm d 0 Once dis completely known unknown nodal loads r follow 0 Postprocessor 7 evaluate resulm gt How does ANSYS solve for d 0 Several different approaches can be used 7 Each based on different mathematical approaches 0 AN SYS 7 key step is optimizing solution methods for speed 0 Consider key issues and solvers that can be used Nature of K Matrix gt Consider the nature of the K matrix 0 Will consist mostly of 0 terms 0 Kij 0 7 Nodes ij are not connected directly by an element gt Example 7 spring problem from HW 2 Nodes 12 do not share an element 0 Nodes 23 do not share an element 0 Nodes 14 do not share an element 0 Simple model 7 only a few zero terms I000 Ilam k 2000 1m k 7 3000 lbm W V quotWquot quot 3 P z x 3mm x 4mm 5000 f5quot Illljll lllm quotMHI 7 7 I D 9 CD 3 7li 71W JHH gt Typical finite element model 0 Most elemenm connect a small number of nodes 0 Many elemenm 7 many zeros in K 0 We can use this fact to our advantage during solution Bandwidth v v v v Solve K d r where K is an n x n matrix se Gaussian reduction to solvck solution takes approximately m n3 3 operations Recall that K is mostly 0 terms Rearrange K so that Os 4 ltj l are away from the diagonal Bandwidth nb 7 the height of V nonzero band of values Called a banded matrix Banded K matrix Requires less storage Special solution methods 7 appro m nbZ n operations Ratio of the operations count for the two methods Signi cant reduction as n gem large mm K quot751mm K Solution Methods v v v Two basic classes of solvers for K d r Direct solvers 7 nd d exactly using various methods Iterative solvers 7 nd d approximately in an iterative fashion Sparse Direct Builds K matrix can optimize for handing Solves using LU decomposition approach Fast but requires signi cant storage and memory Frontal Direct Never builds full K matrix Instead solves repeatedly 7 i r certain elements solve for part of d repeat until done Looks like a solution wave passing over structure 7 Hence often referred to as a wavefront method Slower than sparse direct method but less storage memory needed Sparse direct method is the AN SYS default The frontal method used to be the ANSYS default Iterative Solution Methods gt Iterative solution methods seek answer that is good enough Answer is not exact but satisfactorily close per user input gt Consider how this method works RearrangeKdr7gtKdr0 Direct solution method for d satis es this equation exactly gt Iterative solution method Initial guess for solution do for given loads r Evaluate above expression 7 simple matrix multiplication K 10 r r0 Amount left over r0 is the residual 7 error in solution Use r0 to create a new guess d1 gt Repeat the procedure until satis ed with answer At this point the solution is converged 7 not exact but close User provides convergence criteria several types in ANSYS gt Iterative methods good for very large problems Solving a large problem using direct methods may not be practical MS Iterative Solution Methods gt Two major types of iterative solvers A 25 s gnaw lawn L b A 2x 0 gt GaussSeidel 7 break A into 3 parts L U I h Low Note7LandUarenot 1 3 t 5quot 7quu from LU decomposition 1C 3 5 3 x Gaogaa u 7 Lrx39 39 13 wa gt Conjugate gradient methods 2955 33 gtg 95 is wmwiy who 74 Ax b Immmtze 1 hium y 3 Solution Methods Overview Readmore if interest d e 39 Also resources such as Numerical Recipes for C Num 4quot Ant4 d mlm um Mamrmam 4 11 quot quot quot11 bl a rn xb In It I I a I I I I aux x hr Thequot new lypunlnumzrical mulladsiw mi untilm m u m Guns dialsnull m which the m wlnlinn can b mum in mlvnnce ma a tunaquot mu such I nu cum memoi in um um xunl39mma wuth emu nwnximnlion and impm il uupwiu by mpuudly peranle 39M md lux Haw mldmm m mm gt Handout from Advanced Engineering Math Kreyszig ANSYS Solution Methods gt Many choices 7 a few shown below amem 31 Sela Inka 1 sum Sekuinn Guiddines mag 1 ther Principle of Minimum Potential Energy gt Consider a system in static equilibrium I System is at rest under a loading condition I k 3 j gt Example 7 s1 ringmass under UravrtJ 7 X I Release from arbitrary location 1 I Mass oscillates with time I Eventually reaches rest position CZ Jc I This is the point of static equilibrium gt Principal of Minimum Potential Energy PMPE A body in static equilibrium is at its minimum potential energy state NOTE minimum PE is not the same as zero PE gt Application of PMPE to linear elastic structural analysis etermine an expression of PE in terms of variables I Find the variables that lead to the minimum value of PE I Resulting variables are those that lead to static equilibrium PMPE SpringMass Example gt Develop PE for springmass example quotK I Single variable 7 position x of the mass 1 i I Set x 0 as point ofzero spring load 3 M j I TWo components in springmass PE call it 7 x 7 Stored energy in spring lost energy ofmass TI ljsfyma UNL 2ka Wax inflamman M x gt Ve 394 5 M R 0401mm 944145 rawaj Plot 7 and seek its minimum value 7 note it is not Where 7 0 balm an x MM PE gt 0 Eiuilibnum Siie PMPE SpringMass Example gt Solve for equilibrium point 7 minimum of 1 Differentiate 7 in terms ofvariable 7 a L1 0 Na K I Seek value ofx When this becomes 0 T a O Kx M3 M9 Slain quot 3 kx 2 394 eauiimmu gt What if we begin at an x other than the equilibrium point I Excess PE 7 not in static equilibrium 7 motion of mass I Damping losses eventually brings mass to rest 7 static equilibrium gt Same result if we use a force to apply 7 load instead of a mass under gravity i I Force loses PE When it tmvels in x direction t 7 Source ofF gives up energy in moving x K d7r F L i 11lty 0kxFtgtx W7 1 F k PMPE and Finite Element Modeling gt Application of PMPE to finite element modeling I Springmass example has 1 DOF positionx I Finite element model has many DOFs nodal displacements d I Construct PE 7 in terms or the n DOFs d 7 Remember 7 is only a single scalar value representing system PE I Find the values of all d that minimize 7r 7 static equilibrium I We will see this is equivalent to the approach used in FEA gt A general body in FEA I Like springmass example there are two sources ofPE I 1 Internal stored energy in body 2 PE from external loads 5 I f Pom 6 4 i39m 1quot I Surface Trade aw MA Q 594 AWL owndump PE For General Finite Element Model T Pbmlquot A c4 Rf PM Snafuquot mchin ow Q CB L943 Ava OWVaurwt 5 P gt Potential energy of a general finite element model 0 Evaluate PE via a series of integrals 0 See Logan handout and textbook for further details as 35 p 7quot figva fgix cquot fTu quot r 39 LIZlama an 547 work our 57 r 5547 Esra vafzr L 774 4m Funquot Fran J 55 PE For General Finite Element Model gt Development of PE for a general finite element model 7ri gfJv fgiz av f7u as 44 v v e 5 t A N v 0 Various field quantities based upon nodal displacements A c N A a 3 NOTE this assmnesth 5 A 3 there are no thermal strains added needed eas quotf 392 4 gt Substitute into above 7 general expression for PE of model 0 N ote Tnat nodal d1sp1acements d can be pulled outside of integrals hid ffmav 339 57 4V rf rfds 3 PE Minimization for Finite Element Model waf e 4v 2 571sz 40 37sz 4s 3 f 5 gt How do we find the minimum value of 71 Springmass example was easy 7 l DOF gt 1 equation dndx 0 0 Finite element model withN DOFs gt N equations gt What are the N equations to minimize 7t 07 N ti 5 0 V 611 a 611 form1n1mum 7r 0 Equation development requires variational calculus not discussed gt Final result 7 the d that minimize 7t satisfy the following fgiggJOa lyrj Av 4 Lilliqu F V a V c S v 4 4 4 lt J r r quot quot bod K5141 max hag2m rpsz rm 0 Note that this step converts distributed loads to workequivalent loads 57 RayleighRitz Method gt RayleighRitz is a much older energy method 0 Relationship to FEA developed in 1960s similar to previous slides Assume 5L czy cWaL sluhan 6 a 701m 64M n 742me ml Unknown nQFAczCAi 741 g uLLJ v Z 4 quot L W A nc a u V07 Jpolihan Camuni Tab 71 75mquot gncian mus Ac ILJMLD39l a L MLer enemy Jigagngwf 5 qu CansI dru enema mtg 493 w a I 4 94 M unckw 1JS caAmzI 7 7 up disinamuk 1424 going 5 Wagon cammats a 7 1 7wa a rg 971 EL 0 DC 4 4 RayleighRitz Method Examples gt Consider several specific cases AXIU 34v MOO 1 J x L mil45441 PE am am 57 47 gram EndS L 7quot f 51quot a k 5 mar 5f 94M gt Work a detailed example 0 First derive the potential energy expression for a beam next slide Cantilever Beam Analysis via RayleighRitz Roger Bradshaw ME 512 mechanics This is Simiiav to me RayleigwRilZ memud discussed in EeCliO39i a a Lers do an COHSider a cantilever beam nown ax ngm n has iengm Li i3 iixed a a and a downward load iS applied at x L Assume the ioiiowmg displacement nmcnou descnbcs me displacement of Hi5 beam gtX L F39 59 Energy In Beam In Bending gt Equation for energy in a beam in bending easily derived 0 Return to first principles for relationship between Mx and vx Mx 6X and 8X integrate over volume to find energy U Need to recall thatI l y2 dA over section area Where y 0 at the centroid of the section in question ME 323 0 Also review handout describing the meaning of B matrix for beams r hon m 5min A 1cm v mam in smv 3 m 39H raw l Hana L U 531 L Canaan A a battl w M urih PM i 39 7 I 3 r Ag ct b J J Lce usuau s v a A 510 Generalized Finite Element Approach gt Potential energy approach is valid if energy function exists I Linear elasticity potential problems uids electrostatics etc gt Other classes of problems cannot express an energy function I Example 7 problems With energy loss such as plasticity friction etc I Need an alternate general apprth for nite element analysis I Many such approaches are available 7 consider one gt Galerkin s Method of Weighted Residuals I Only need governing differential equations to solve Exam3L1 EllIfICIb My my 7 A Why are these so 39 7 3 uwu m plMm toughtosolve Leads to 15 futHows stunMm Yum coupledpmial 6 744 lbw Juftau uh differentialequanons gt Solve using Galerkin s method 7 same result as PMIPE I Will always be identical if an energy method apprth is possible I Will consider further in ME 612 7 only need to be familiar With idea 5711

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