Problems taken from “ANSYS Tutorial 11.0” by Kent L. Lawrence

(Worked With Femap and NeiNastran) by John R. Carr

10/2/2010

Lesson 1 – Trusses

The first model worked from the ANSYS Tutorial was a shelf model that was 3D

originally, but with applied symmetry for both the geometry and loads was modeled as a

2D model with rod elements. The total downward load was 1200 lb in the original

physical model, but was reduced to -600 lb with application of ½ symmetry which meant

that bending for the shelf was neglected. This -600 lb load was shared at the two

remaining nodes, applying -300 lb to each node in the y-direction. A generic steel was

used as the material for the rods with the following material properties: E = 30e6 psi and

poison’s ratio of 0.27. No tensile or compressive yield strength was given for the model,

but for maximum stress results comparison a value of 215,000 psi will be used, which

was taken from the AISI 4340 Steel Femap material library. The rod elements had a

rectangular cross sectional area of 0.50 x 0.25 (inches) so the area was inputted as 0.125

in2. Nodes 1 and 3 were modeled as pinned with no displacement in any of the three

linear directions. The model with nodes, elements, constraints and loading is given

below:

Figure 1 – FEA model of the shelf truss with 3 nodes, 2 elements, constraints and loads.

A linear elastic static analysis was performed giving the following results shown in

Figure 2:

Figure 2 – Contour plot of maximum rod equivalent stress of 4000 psi and a total

translation of 0.00867 inch.

ANSYS results: maximum total translation of 0.008667 inch downward and max

element stress of 4000 psi.

With the above NEi Nastran results of maximum stress of 4000 psi compared to a yield

strength of 215,000, no stress magnitudes or deflections are a safety issue for this model

and its intended and declared usage.

The second truss model worked was a modified truss where the steel rod of element 2 is

replaced by a composite tube. The material properties for the composite material used

were the following: E = 1.2e7 psi and poison’s ratio of 0.3, along with an area of 0.35

in2. We also include a prescribed displacement of 0.01 inch to the left of node 3 (in the –

x direction). This model with all constraints and loads prior to analysis is shown below:

Figure 3 – Modified truss model with a composite tube used for element 2 and a

prescribed displacement of -0.01 inch at node 3.

A linear elastic static analysis run produced the following results:

Figure 4 – Modified truss contour plot giving a maximum stress of 3200 psi and a

maximum displacement equal to the prescribed displacement at node 3 of -0.01 inch.

ANSYS results: No results were given for the modified truss.

Lesson 2 – Plane Stress Plane Strain

Model 1 – Plate With Central Hole

A plate with dimensions of 1.0 m x 0.4 m (length x width) and a thickness of 0.01 m has

a centrally located hole with a diameter of 0.2 m. It has a load applied to each end (RHS

and LHS) and due to geometry and loading symmetry can be modeled as a ¼ plate with

symmetry BCs applied at the cut planes The material is steel with the following

properties: E = 2.07e11 N/m2 and a poison’s ratio of 0.29. A load equivalent to a

pressure load of p = -1.0 N/m2 is applied to the RHS end of the ¼ symmetry model.

Because of problems loading a pressure load to a curve in Femap, the static loading of F

= p * A = (1.0) * (0.01) * (0.2) = 0.002 N was applied to the 9 nodes of the RHS, thus

each load was F/9 = 0.0002222 N for an equivalent static loading. On the LHS of the

model x-symmetry constraints were applied (T1 = R5 = R6 = 0) and along the bottom edge

y-symmetry constraints were applied (T2 = R4 = R6 = 0). To prevent a singularity error

while running NEi Nastran further constrains were added by setting T3 = 0 for all the

nodes, insuring a plane stress problem. The model with loads and constraints is given

below with a mesh density of esize = 0.025 m:

Figure 5 – Plate with central hole ¼ symmetry model with constraints and loading prior

to solution.

A linear elastic static analysis was performed giving the following results:

Figure 6: Plate with central hole FEA static analysis results (esize = 0.025) with give a

maximum total translation of 3.438e-12 m and a maximum shell von mises top stress of

4.029 Pa.

ANSYS results with a refined mesh give a total translation of 3.21e-12 and a maximum

stress of 4.386 Pa.

The mesh was refined to be esize = 0.0250/2 = 0.0125 m which gave 17 nodes and 16

elements around the central hole. This model, prior to analysis, is shown below:

Figure 7 – Refined mesh (esize = 0.0125 m) for the plate with central hole ¼ symmetry

model.

Figure 8 – Contour plot of the plate with central hole with a refined mesh of esize =

0.0125, giving total translation of 3.363e-12 m and maximum shell von mises top stress

of 4.236 Pa which agrees better with the ANSYS results.

Model 2 – Seatbelt Component

A seatbelt “tongue” was modeled with ½ symmetry with a horizontal cut plane giving the

upper portion of the tongue. Keypoints were designated to represent the geometry of the

model and curve-lines were drawn for the straight lines and arcs were drawn to represent

the 2 fillets on the inner portion of the slot. The left edge was constrained such that Ux

was zero and the lower two curves where constrained such that Uy = 0 was used to

represent y-axis symmetry. An element size of esize = 0.05 inch was used for the initial

mesh. The load on the RHS of the slot was 1000 lb for the full model and 500 lb for the

½ symmetry model. Using the 9 nodes along the slot face to evenly distribute the load

gave a nodal force of 500/9 = 55.56 lb for each of the 9 nodes. Also, to insure a planar

problem and avoid singularity errors with NEi Nastran, all nodes were constrained such

that Tz = 0. The model prior to the results is shown below:

Figure 9 – FEA model with esize = 0.05 inch used to model the seatbelt component

tongue.

A linear elastic static analysis was performed and gave the following results:

Figure 10 – Contour results for esize = 0.05 for the seatbelt tongue model giving a total

translation of 0.00174 inch and a max shell von mises top stress of 95631 psi.

Mesh refinement was performed on the model with an esize of 0.025 inch being used and

an equivalent nodal static load of 500/16 = 31.25 lb for each node on the slot. The

model, without constraints, is shown below:

Figure 11 – The seatbelt component tongue model with esize = 0.025 inch.

The results of a linear elastic static analysis for an esize of 0.025 inch is shown below:

Figure 12 – Contour plot of refined mesh (esize = 0.025) FEA model for the seatbelt

component tongue given a total translation of 0.00178 inch and max shell von mises top

stress of 111315 psi.

The mesh was further refined to esize = 0.0125 with the equivalent nodal static force on

the slot being = 500/31 = 16.129 lb and the following results from the second mesh

refinement are shown below:

Figure 13 – Contour plot of the seatbelt component tongue with esize = 0.0125 giving

total translation of 0.00178 inch and max shell von mises top stress of 138,090 psi.

The results shown in Figure 13 represent the converged results and agree well with the

ANSYS results of 140,000 psi.

Lesson 3 – Axisymmetric Problems

A steel pressure vessel with planar ends is subjected to an internal pressure of 35 MPa.

The vessel has an outer diameter of 200 mm with an overall length of 400 mm and a wall

thickness of 25 mm with an inside radius of 25 mm at the ends. Only the top or bottom

half need be considered and either half has axisymmetric symmetry in geometry and

loading, thus an axisymmetric “slice” is modeled. The cross section is created with

keypoints and lines along with a single arc with the appropriate dimensions. A very fine

mesh of 0.0025 was initially used to prevent the need for mesh refinement. The model

prior to solution is shown below:

Figure 14 – Cylindrical pressure vessel section cut that was modeling using a mesh of

esize = 0.0025 m.

A linear elastic static analysis was run and produced the following results.

Figure 15 – A full view of the contour plot for the cylindrical pressure vessel FEA results

giving a total translation of 0.0000997 m and max axisym von mises stress of 205.4 Pa.

Figure 15 – A zoom view of the contour plot for the cylindrical pressure vessel FEA

results giving a total translation of 0.0000997 m and max axisym von mises stress of

205.4 Pa.

Lesson 4 – 3D Problems

Model file – pressure_vessel_lesson4.mod

A 3D version of the previous axisymmetric model was created by revolving the cross

section 90° to create a solid. The same material was used with steel – SI units having the

following properties: E = 200 GPa, poison’s ratio is 0.3, and the yield strength = 330

MPa. A mesh size of 0.0025 was used in a tri mesh with midside nodes creating 1959

elements and 3397 nodes. Symmetry BCs were applied to the appropriate faces or

surfaces of the 3D model and an internal pressure load of 35e6 Pa was applied to the

three internal faces. The model prior to solution is shown below:

Figure 16 – FEA model for the 3D pressure vessel with loads and constraints.

The analysis was run for a linear elastic static load case and the following results were

obtained:

Figure 17 – Analysis results for the 3D pressure vessel model giving a total translation of

0.0000929 m and a max solid von mises stress of 210.2 MPa well within the yield

strength limit of the material.

Note that the 3D results are in good agreement with the axisymmetric results given in

Lesson 3.