Scordelis–Lo Roof Shell Benchmark

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Scordelis–Lo Roof Shell Benchmark

In the following example you build and solve a 3D shell model using the Shell interface. This example is a widely used benchmark model called the Scordelis–Lo roof. The computed maximum z-deformation is compared with the value given in Ref. 1.

Model Definition

The geometry consists of a curved face as shown in Figure 1. Only one quarter is analyzed due to symmetry.

Figure 1: The Scordelis-Lo roof shell benchmark geometry.

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Roof length 2L = 50 m

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Roof radius R = 25 m.

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Isotropic material with Young’s modulus set to E = 4.32·108 N/m2.

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Poisson’s ratio set to ν = 0.0.

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The outer straight edge is free.

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The outer curved edge is constrained against translation in the y and z directions.

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The straight edge on the top of the roof has symmetry edge constraints.

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The curved inner edge also has symmetry constraints.

A force per area unit of −90 N/m2 in the z direction is applied on the surface.

Results and Discussion

The maximum deformation in the global z direction with the default mesh settings is shown in Figure 2. The computed value is −0.303 m.

Figure 2: z-displacement with 176 triangular elements.

When changing to a mapped mesh, the more efficient quadrilateral elements are used. The result is −0.301 m as shown in Figure 3. With a very fine mesh, the value converges to −0.302 m, Figure 4. The reference solution quoted in Ref. 1 for the midside vertical displacement is −0.3086 m. The value −0.302 m is in fact observed in other published benchmark results treating this problem as the value that this problem converges toward. A summary of the performance for different element types and mesh densities is given in Table 1. As can be seen, the results are good even with rather coarse meshes.

Figure 3: z-displacement with 70 quadrilateral elements.

Figure 4: z-displacement with 580 quadrilateral elements.

Table 1: Convergence of midpoint vertical displacement.
Mesh size setting	Element type	Number of elements	Midpoint displacement
Coarser	Triangle	64	-0.304
Coarser	Quadrilateral	24	-0.300
Normal	Triangle	176	-0.303
Normal	Quadrilateral	70	-0.301
Extra fine	Triangle	1384	-0.302
Extra fine	Quadrilateral	580	-0.302

1. R.H. MacNeal and R.L. Harder, Proposed Standard Set of Problems to Test Finite Element Accuracy, Finite Elements in Analysis and Design, 1, 1985.

Structural_Mechanics_Module/Verification_Examples/scordelis_lo_roof

Modeling Instructions

From the menu, choose .

In the window, click

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In the window, click

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In the tree, select .

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In the tree, select .

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Work Plane 1 (wp1)

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In the toolbar, click

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In the window for , click

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Work Plane 1 (wp1)>Plane Geometry

In the window, click .

Work Plane 1 (wp1)>Polygon 1 (pol1)

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In the toolbar, click

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In the window for , locate the section.

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In the table, enter the following settings:


xw (m)	yw (m)
0	25
25	25

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Right-click and choose .

Revolve 1 (rev1)

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In the window, under right-click and choose .

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In the window for , locate the section.

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Click the button.

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In the text field, type 90.

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In the text field, type 90+40.

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Locate the section. Find the subsection. In the text field, type 1.

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In the text field, type 0.

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button in the toolbar.

Form Union (fin)

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In the window, click .

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In the window for , click

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Thickness and Offset 1

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In the window, under click .

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In the window for , locate the section.

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In the d text field, type 0.25.

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In the toolbar, click

and choose .

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Select Edges 3 and 4 only.

Prescribed Displacement/Rotation 1

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In the toolbar, click

and choose .

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Select Edge 1 only.

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In the window for , locate the section.

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Select the check box.

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Select the check box.

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In the toolbar, click

and choose .

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Select Boundary 1 only.

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In the window for , locate the section.

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Specify the FA vector as


0	x
0	y
-90	z

Material 1 (mat1)

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In the window, under right-click and choose .

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In the window for , locate the section.

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In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Young’s modulus	E	4.32e8	Pa	Basic
Poisson’s ratio	nu	0	1	Basic
Density	rho	1	kg/m³	Basic

First, compute the results with the default triangular mesh.

Free Triangular 1

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In the toolbar, click

and choose .

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In the window for , locate the section.

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From the list, choose .

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Study 1: Tri Normal

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In the window, click .

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In the window for , type Study 1: Tri Normal in the text field.

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In the toolbar, click

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Vertical displacement

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In the window for , type Vertical displacement in the text field.

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button in the toolbar.

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In the window, expand the node, then click .

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In the window for , click in the upper-right corner of the section. From the menu, choose .

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Locate the section. Select the check box.

Vertical displacement

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In the window, click .

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In the toolbar, click

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In the window, expand the node, then click .

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In the window for , type Tri Normal in the text field.

Switch to the more effective quadrilateral mesh elements.

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In the window, under click .

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In the window for , type Tri Normal in the text field.

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In the toolbar, click

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In the window for , type Quad Normal in the text field.

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In the toolbar, click

and choose .

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In the window for , locate the section.

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From the list, choose .

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In the toolbar, click

to open the window.

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Go to the window.

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Find the subsection. In the tree, select .

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Click in the window toolbar.

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In the toolbar, click

to close the window.

Study 2: Quad Normal

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In the window, click .

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In the window for , type Study 2: Quad Normal in the text field.

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Locate the section. Clear the check box.

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In the toolbar, click

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Vertical displacement

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In the window, under click .

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In the window for , locate the section.

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From the list, choose .

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In the toolbar, click

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In the window, under click .

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In the window for , type Quad Normal in the text field.

Examine a well converged result with a fine quadrilateral mesh.

In the window, under right-click and choose .

Quad Extra fine

In the window for , type Quad Extra fine in the text field.

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In the window, expand the node, then click .

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In the window for , locate the section.

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From the list, choose .

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In the toolbar, click

to open the window.

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Go to the window.

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Find the subsection. In the tree, select .

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Click in the window toolbar.

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In the toolbar, click

to close the window.

Study 3: Quad Extra fine

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In the window, click .

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In the window for , type Study 3: Quad Extra fine in the text field.

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Locate the section. Clear the check box.

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In the toolbar, click

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Vertical displacement

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In the window, under click .

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In the window for , locate the section.

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From the list, choose .

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In the toolbar, click

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Quad Extra fine

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In the window, under click .

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In the window for , type Quad Extra fine in the text field.

Examine a well converged result with a triangular mesh.

In the window, under right-click and choose .

In the window for , type Tri Extra Fine in the text field.

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In the window, expand the node, then click .

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In the window for , locate the section.

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From the list, choose .

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In the toolbar, click

to open the window.

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Go to the window.

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Find the subsection. In the tree, select .

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Click in the window toolbar.

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In the toolbar, click

to close the window.

Study 4: Tri Extra fine

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In the window, click .

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In the window for , type Study 4: Tri Extra fine in the text field.

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Locate the section. Clear the check box.

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In the toolbar, click

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Vertical displacement

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In the window, under click .

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In the window for , locate the section.

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From the list, choose .

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In the toolbar, click

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In the window, under click .

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In the window for , type Tri Extra fine in the text field.

Investigate how well the elements perform with a very coarse mesh.

In the window, under right-click and choose .

In the window for , type Tri Coarser in the text field.

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In the window, expand the node, then click .

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In the window for , locate the section.

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From the list, choose .

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In the toolbar, click

to open the window.

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Go to the window.

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Find the subsection. In the tree, select .

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Click in the window toolbar.

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In the toolbar, click

to close the window.

Study 5: Tri Coarser

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In the window, click .

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In the window for , type Study 5: Tri Coarser in the text field.

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Locate the section. Clear the check box.

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In the toolbar, click

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Vertical displacement

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In the window, under click .

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In the window for , locate the section.

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From the list, choose .

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In the toolbar, click

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In the window, under click .

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In the window for , type Tri Coarser in the text field.

In the window, under right-click and choose .

In the window for , type Quad Coarser in the text field.

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In the window, expand the node, then click .

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In the window for , locate the section.

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From the list, choose .

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In the toolbar, click

to open the window.

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Go to the window.

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Find the subsection. In the tree, select .

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Click in the window toolbar.

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In the toolbar, click

to close the window.

Study 6: Quad Coarser

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In the window, click .

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In the window for , type Study 6: Quad Coarser in the text field.

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Locate the section. Clear the check box.

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In the toolbar, click

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Vertical displacement

1

In the window, under click .

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In the window for , locate the section.

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From the list, choose .

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In the toolbar, click

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In the window, under click .

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In the window for , type Quad Coarser in the text field.

The following section compares the maximum deformation of the midpoint, in the vertical direction, for different element types and mesh densities.

Point Evaluation 1

1

In the toolbar, click

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Select Point 3 only.

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In the window for , locate the section.

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In the table, enter the following settings:


Expression	Unit	Description
w	m	Midpoint displacement, Tri Normal

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Point Evaluation 2

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Right-click and choose .

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In the window for , locate the section.

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From the list, choose .

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Locate the section. In the table, enter the following settings:


Expression	Unit	Description
w	m	Midpoint displacement, Quad Normal

5

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Point Evaluation 3

1

Right-click and choose .

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In the window for , locate the section.

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From the list, choose .

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Locate the section. In the table, enter the following settings:


Expression	Unit	Description
w	m	Midpoint displacement, Quad Extra fine

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Point Evaluation 4

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Right-click and choose .

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In the window for , locate the section.

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From the list, choose .

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Locate the section. In the table, enter the following settings:


Expression	Unit	Description
w	m	Midpoint displacement, Tri Extra fine

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Point Evaluation 5

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Right-click and choose .

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In the window for , locate the section.

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From the list, choose .

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Locate the section. In the table, enter the following settings:


Expression	Unit	Description
w	m	Midpoint displacement, Tri Coarser

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Point Evaluation 6

1

Right-click and choose .

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In the window for , locate the section.

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From the list, choose .

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Locate the section. In the table, enter the following settings:


Expression	Unit	Description
w	m	Midpoint displacement, Quad Coarser

5

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