lecture 4

35

6.0 SOLID MODELLING AND ANSYS

Review of Simple Coursework ExercisesThree simple exercises were provided to give practice with the ANSYS finite elementprogram. The first, ‘The Simple Bracket’ introduced the ideas of preprocessing in PREP7 bycreating lines and areas, simplification to a 2D plane stress model, real constant input, elementtype PLANE42, element sizing, meshing, applying boundary conditions and loads. A solutionwas executed and output viewed using the post-processor POST1. Full listings are providedon the 16429 web page.

The second, ‘The Simple Bracket 2’ built on the first exercise by requiring the bracket to becreated by employing a symmetry reflection of the first (lower) half of the bracket andthereafter proceeding as per the first exercise.

The third exercise introduced beam elements in the form of a bicycle frame model. Theseelements require special consideration due to the extra input required to fully define the beamcross section and 'I' values in two directions, which are required for bending stress evaluation.Of course, if a pipe or cylindrical cross section is employed then these values are equal.Attention was also drawn to the idea of units selection with the user having to generate themodel and loading in a consistent set of units to ensure a satisfactory and meaningful result.The user was also required to select a pipe cross section suitable to ensure both stresses anddeflections were within some specified allowable limits.

Each of these exercises should have already been completed and have provided a goodintroduction into the use of the ANSYS system. These models will be used in later parts of thecourse.

3D Solid and Shell ElementsEarlier work has employed 2D solid element or beam (line) elements. However, theformulation of these elements means that some assumption has been made, normally constantor linear through thickness distributions, which reduces the real three dimensional problemdown to one of two dimensions. However, if through thickness variations are significant, e.g.in a large cast engine block or full turbine wheel, then 3D solid or brick elements (SOLID45 8noded brick or SOLID95 20 noded brick) must be employed.

36

In some engineering situations, where the geometry is three dimensional but the wall thicknessis thin with respect to the main leading dimensions of the component, then the assumption oflinear behaviour can be used for through thickness variations and 3D thin shell elements can beused (SHELL63 4 noded shell or SHELL93 8 noded shell).

4 noded shelllinear displacement

8 noded shellquadrat ic displacement

8 noded bricklinear displacement

20 noded brickquadrat ic displacement

It is worth recalling that the 4 noded shell and the 8 noded brick have a linear displacementformulation and the 8 noded shell and the 20 noded brick have a quadratic displacementformulation. The order of the interpolation function affects the variation of the function acrossthe element. This becomes even more important when considering stress results since these areessentially the derivative of displacement results, thus linear displacement become constantstress and quadratic displacement becoming a linear stress variation.

It is worth recalling that these elements require a numerical integration routine to enablecalculation of the displacements. The most common integration routine used in finite elementcodes is the Gaussian Quadrature rule and therefore the resultant values for the function arealways interior to the element nodal points. These locations are known as Gauss points. Thehigher the order of quadrature, the closer the result to the actual value at the node.

Gaussian Quadrature

37

These mathematical solutions have an important bearing on solid brick elements. Since theintegration routine calculates the result interior to the element, then surface results aresubsequently and extrapolation of those values calculated at the Gauss points. Therefore usersof brick elements must be careful when extracting outer surface results for their components.However, it is essential to note that 3D solid brick elements provide the most flexible elementsfor meshing complex geometries.

Some examples of complex 3D brick models

AN EXAMPLE - The Ball Valve BodyThe ball valve body shown below provides a good example of the use of three differentelement types (SHELL51, SHELL63, and SOLID45) together with the use of two types ofsymmetry (planar symmetry and axi-symmetry).Firstly, the mechanical problem must be evaluated. The aim of the analysis is the evaluation ofsuitable wall thicknesses for the specified loading. The valve body can be considered as asphere with two intersecting cylinders at the ends of which are located two flange rings, eachwith a number of bolt holes. The valve is subject to internal pressure and the bolts exert aforce which seals the gasket and in turn generates a ring bending moment resisted by thecylindrical portion of the valve body. If the valve spindle is neglected and it is assumed that theopening will be somehow reinforced, then the geometry has three possible planes of symmetry.Indeed it is possible to use an axi-symmetric model too. Therefore three models will becompared.

Model A: Axi-symmetric shell model with SHELL51 (File VALVE_A.INP)Model B: Eighth sector shell model with SHELL63 (File VALVE_B.INP)Model C: Eighth sector shell model with SOLID45 (File VALVE_C.INP)

38

The following dimensions are given: spherical diameter 200mm, cylindrical diameter 80mm,flange thickness 20mm, overall length between flange faces 400mm, internal pressure 20bar.

Model A is shown with elements as dotted lines withthe displaced plot shown as solid. The model iscreated by creating an arc for the sphere andintersecting with a line for the cylinder. This isperformed using the LCSL command. The flange iscreated by generating a point from the end of thecylinder. Thereafter pressure is applied using the SFEcommand.

Model B is shown, together with stress intensityresults for the top surface. Note the high degree of bending towards the shell intersections. Itis noted that both models are shell models and the assumption of linear through thicknessvariation is employed. A detailed examination of these stresses can be found using results fromModel C which uses SOLID45 brick elements as shown below.Model C is created from meshed volumes by using the areas from Model B and sweeping themaround 90o using the VDRAG command. Thereafter, the VMESH command is used to definethe mesh and suitable loads and boundary conditions are applied.

1

XYZ

Model A - Ball Valve Body using SHELL51

STEP=1SUB =1TIME=1SINT (AVG)TOPDMX =0.004385SMN =0.303311SMX =15.965SMXB=18.854

1

MN

MX

XY

Z

0.303311 2.044 3.784 5.524 7.264 9.004 10.745 12.485 14.225 15.965

1

XYZ

Model B - Ball Valve Body using SHELL63

1

XY

Z

Model C - using SOLID 45 elements

1

XYZ


39

Two meshes are shown: the first has an ESIZE of 10 whereas the second has an ESIZE of 5.This results in a more detailed mesh but also more expensive in terms of analysis time andcomputer resources. Recall from earlier, the main question is ‘Which is the better mesh?’Better for what? This is the most important part of FEA for engineers to establish why theanalysis is being undertaken and what is being expected from the results. The first mesh wouldprovide some information about the general stress levels away from the discontinuity but sincethe stress gradients vary quite markedly in this region, the more detailed mesh would bepreferable. However, the detailed mesh model has an excess of elements in regions locatedaway from the discontinuities and has too many elements defined in the circumferentialdirection. Four element through the thickness may also be too many, especially if the wallthickness is thin compared with the mean radius. Typical stress intensity plots are shownbelow.

For the ball valve subject to internalpressure, the maximum stress is located atthe inside surface ‘crotch’ corner. In caseswhere this stress dominates the design, a small fillet radius is often introduced to minimise thestress concentration effects in this region. One typical mesh design is shown, however, someof the element shapes are not quite ideal! In addition, there may be the requirement for moreelements through the wall thickness. These questions require further investigation.

Full listings for models VALVE_A, VALVE_B and VALVE_C are attached and can be foundon the 16429 web pages.

EXERCISE & COURSEWORK 1

ANSYS 5.0 AJAN 27 199515:12:15PLOT NO. 5NODAL SOLUTIONSTEP=1SUB =1TIME=1SINT (AVG)DMX =0.003993SMN =1.561SMNB=1.376SMX =17.681SMXB=18.959

1

MN

MX

X

YZ

1.561 3.352 5.143 6.934 8.726 10.517 12.308 14.099 15.89 17.681



1 MN

MX

XYZ

1.561 3.352 5.143 6.934 8.726 10.517 12.308 14.099 15.89 17.681



1

MX

1.562 3.277 4.991 6.706 8.42 10.135 11.85 13.564 15.279 16.994

Model D - with fillet

40

The first coursework exercise is to work from the VALVE_C.INP file and to introduce a filletof radius 5mm on the inside and outside surfaces of the spherical portion of the valve. This isfacilitated by using the LFILLT command.Read the on-line help for syntax and documentation for all commands.In addition, you are required to convince yourself that you have achieved a ‘suitable mesh’ inorder to provide you with a satisfactory result. (Hint: Use the LESIZE command to define avariable spacing mesh over your model.) A good check for the model is the use of thin shellexpressions (membrane) or thick shell expressions (Lame) depending on the wall thickness toleading radii ratios.

A brief report is required describing the main changes to the VALVE_C input file with one ortwo output pictures showing the mesh and the detail around the area of interest. Someverification calculations should be shown and brief conclusions should be noted. ANSYSlistings are not required.

This report should be typed and handed in no later than three weeks from date of issue.Marks will be deducted at the rate of 10% per day late with zero mark after one week.The report should not exceed ten pages in length.

41

File: VALVE_A.INP (c) DHN/PREP7

/TITLE,Model A - Ball Valve Body

using SHELL51 Elements

C*** Define Keypoints Parametrically

r_sphere=100

r_cyl=40

r_flange=60

t_flange=20

l_overal=200

cyl_thk=15

sph_thk=10

i_press=2

C*** Define keypoints

K,1,r_sphere

K,2,0,r_sphere

K,100

K,3,r_cyl

K,4,r_cyl,(l_overal-0.5*t_flange)

KGEN,2,4,4,1,(r_flange-r_cyl)

C*** Define Lines

LARC,1,2,100,r_sphere

L,3,4

L,4,5

C*** Perform boolean operation

BOPTN,YES

LCSL,1,2

C*** clear unwanted lines

LDEL,1,2

LDEL,5,6

C*** This completes the geometry

model

C*** Select element type

ET,1,51

ESIZE,SPH_THK/2

R,1,sph_thk

R,2,cyl_thk

R,3,t_flange

REAL,1

LMESH,4

REAL,2

LMESH,7

REAL,3

LMESH,3

SAVE

FINI

C*** Exit PREP7 and SAVE database

/SOLU

ANTYPE,STAT

C*** Define material properties

MP,EX,1,207000

MP,NUXY,1,0.3

C*** Select bottom node fixed in Y

NSEL,R,LOC,Y,0

D,ALL,UY,0

D,ALL,ROTZ,0

D,ALL,UZ,0

NALL

C*** Select lines 4 and 7

LSEL,R,LINE,,4

C*** Select elements lying on these

lines and apply pressure

SFE,ALL,2,PRES,,-I_press

LSALL

EALL

LSEL,R,LINE,,7

SFE,ALL,1,PRES,,-i_press

LSALL

EALL

SOLVE

FINI

42

File: VALVE_B.INP (c) DHN/PREP7

/TITLE,Model B - Ball Valve Body

using SHELL63 Elements

C*** Define Keypoints Parametrically

r_sphere=100

r_cyl=40

r_flange=60

t_flange=20

l_overal=200

sph_thk=10

cyl_thk=15

i_press=2


K,1,r_sphere

K,2,0,r_sphere

K,100

K,3,r_cyl

K,4,r_cyl,(l_overal-0.5*t_flange)

KGEN,2,4,4,1,(r_flange-r_cyl)

C*** Define Lines


L,3,4

L,4,5

C*** Perform boolean operation

BOPTN,YES

LCSL,1,2

c*** clear unwanted lines

LDEL,1,2

LDEL,5,6

C*** Create areas by rotating three

lines round 90 degrees

R,1,sph_thk

R,2,cyl_thk

R,3,t_flange

C*** Define material properties for

steel

MP,EX,1,207000

MP,NUXY,1,0.3

KGEN,2,100,100,1,,,-r_sphere

C*** Create line to drag areas around


C*** Drap lines 4, 7 and 3 round 1

ADRAG,4,7,3,,,,1

C*** Select element type

ET,1,63

ESIZE,SPH_THK

REAL,1

AMESH,1

REAL,2

AMESH,2

REAL,3

AMESH,3

FINI

c*** Exit PREP7 and SAVE database

/SOLU

ANTYPE,STAT

SFA,1,2,PRES,2

SFA,2,2,PRES,2

SFTRAN

NSEL,R,LOC,X,0

DSYM,SYMM,X

NALL

NSEL,R,LOC,Y,0

DSYM,SYMM,Y

NALL

NSEL,R,LOC,Z,0

DSYM,SYMM,Z

NALL

SOLVE

FINI

43

File: VALVE_C.INP (c) DHN/PREP7

/TITLE,Model C - using SOLID 45s

C*** Define parameters

cyl_ir=32.5

cyl_or=47.5

sph_ir=95

sph_or=105

r_flange=60

t_flange=20

l_overal=200

i_press=2


K,1,sph_ir

K,2,sph_or

K,3,0,sph_ir

K,4,0,sph_or

K,100

K,5,cyl_ir

K,6,cyl_or

KGEN,2,5,6,1,,l_overal

LARC,1,3,100,sph_ir

LARC,2,4,100,sph_or

L,5,7

L,6,8

C*** Perform Boolean Operation

BOPTN,YES

LCSL,1,3

LDEL,1,3,2

LDEL,6,7

LCSL,5,4

LDEL,1,7,6

LDEL,3,4LCSL,2,6LDEL,2,3LDEL,6,7C*** Form top FlangeKGEN,2,8,8,1,(r_flange-cyl_or)

KGEN,2,7,12,5,,-t_flange

L,13,14

LCSL,2,4

LDEL,2,4

C*** Define AREAS and VOLUMES

A,1,2,11,9

A,9,11,15,13

A,13,15,8,7

A,15,14,12,8

K,16,,,-sph_ir

LARC,1,16,100,sph_ir

VDRAG,1,2,3,4,,,15

C*** Select ELEM type and size

ET,1,45

ESIZE,10

VMESH,ALL

FINI

/SOLUT

ANTYPE,STAT

SFA,8,1,PRES,i_press



SFTRAN

C*** Apply symmetry conditions

NSEL,R,LOC,X,0

DSYM,SYMM,X

NALL

NSEL,R,LOC,Y,0

DSYM,SYMM,Y

NALL

NSEL,R,LOC,Z,0

DSYM,SYMM,Z

NALL

MP,EX,1,207000

MP,NUXY,1,0.3

SOLVE and FINI

lecture 4

Documents