3d_shellexample_s04

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March 13-15, 2001 FEM/Ansys 1

3D Structural Analysis

Deformation of a cylindrical barrel vaultunder weight and pressure impact

K. Nema

Y. Liu and H.U. Akay

Department of Mechanical Engineering,

Indiana University-Purdue University

Indianapolis

Indianapolis, Indiana 46202


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Problem Description

R=7.62 m

Supported by

rigid diaphragm7.62 m

t = 0.076 m

40oFree edge

Material Properties

E = 3e6 lb/in2 = 2.068e10 N/m2

v= 0.0

= 90 lb/ft2 = 439.7 kg/m2


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Approach and Assumptions

Because the geometry is symmetric, only 1/4th portion is analyzed.

Element types tried:

Shell63 (4 nodes, 6 DOF)

Solid45 (8 nodes, 3 DOF)



Note: 3 DOF are: , 6 DOF are: Analysis

Static

Modal

Transient analysis under impact pressure

Option 1. Full analysis

Option 2. Mode superposition (five modes)

, ,u v w , , , , ,y zu v w


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Basic steps

Preprocessing

Create solid model

Option 1. Solid model for shell element mesh

Option 2. Solid model for solid element mesh Create finite element model

Apply boundary conditions

Apply loads (gravity, pressure, etc.) Solve

Postprocessing


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Preprocessing: Step 1. Create solid model (for Shell63 Element)

1.Create a partial cylinder


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Preprocessing : Step 1. Create solid model (for Shell63 Element)

2. Delete volume only


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3. Plot areas


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Preprocessing: Step 1. Create solid model (for Shell63 Element)

4. Front view of areas model


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5. Delete areas and below

Turn on Box Pick

Box select the unnecessary areas


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6. The solid model (for Shell63 Element)


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Preprocessing: Step 1. Create solid model (for Solid Element)


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Preprocessing : Step 2. Mesh with Shell63 Element


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Preprocessing : Step 2. Mesh with Solid Element


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Preprocessing: Step 3. Apply boundary conditions

1. Apply symmetric B. C.

Pick the two highlighted

symmetric lines


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Preprocessing: Step 3. Apply boundary conditions

2. Apply B. C. on support edge

Pick the support edge


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Preprocessing: Step 4. Apply gravity


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Postprocessing for static analysis Path Operation

1. Define path by nodes (a. Pick nodes in order)

Pick nodes in order


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1. Define path by nodes (b. Define Path specification)


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2. Map results onto path (Displacement on Z direction)


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3. Plot path results on geometry (Displacement on Z direction)

P t i f t ti l i P th O ti


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3. Plot path results on geometry (Displacement on Z direction)

Comparison of results from different element models


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(Longitudinal displacement of support)

-2.00E-03

-1.00E-03

0.00E+00

1.00E-03

2.00E-03

3.00E-03

4.00E-03

5.00E-03

6.00E-03

0 5 10 15 20 25 30 35 40

Angle f rom vertical direction ( o)

Longitudinaldisplacementofsupport(m

shell63

solid45(3 DOF, 8 nodes)-top

solid45(3 DOF, 8 nodes)-bottom


solid95(3 DOF, 20 nodes)-middle






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(Vertical displacement of central section)

-1.00E-01

-8.00E-02

-6.00E-02

-4.00E-02

-2.00E-02

0.00E+00

2.00E-02

0 5 10 15 20 25 30 35 40

Angle from vertical direction (o)

Verticaldisplacemen

tofcentralsection(m)

shell63




solid95(3 DOF, 20 nodes)-middle





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Modal analysis: Step 1. Define analysis type

Turn on Modal

M d l l i St 2 D fi d t ti th d


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Modal analysis: Step 2. Define mode extraction method

Five modes will be extracted

M d l l i St 3 D fi ti f S b th d


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Modal analysis: Step 3. Define options for Subspace method

Postprocessing for Modal analysis(Shell63)


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p g y ( )

(Frequencies (Hz) for first five modes)

Postprocessing for Modal analysis (Solid95, 20 nodes)


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p g y ( , )

(Frequencies (Hz) for first five modes)

Transient analysis (Full method)


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y ( )

Step 1. Define analysis type

Turn on Transient



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Step 2. Apply pressure on the area

Apply downward pressure of

1000 Pa on the area



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Step 3. Define time step (Impact pressure)



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Step 4. Define time integration method

Use unconditionally stable scheme



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Step 5. Define output controls

Time History Postprocessing for Transient analysis

St 1 D fi lt i bl ( )


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Step 1. Define result variables (a)


St 1 D fi lt i bl (b)


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Step 1. Define result variables (b)

Pick the node


St 1 D fi lt i bl ( )


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Step 1. Define result variables (c)

Vertical displacement

Time History Postprocessing for Full Transient analysis

Step 2 Graph the variables


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Step 2. Graph the variables

Transient vertical displacement of vault bottom edge centerunder pressure impact (1000 Pa) (no damping, t=0.03)


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p p ( ) ( p g )

(Full transient analysis)

Shell63



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Solid95 (20 nodes, 3 DOF), middle node



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Shell63

Transient vertical displacement of vault bottom edge centerunder pressure impact (1000 Pa) (with damping, t=0.03)


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Shell63

Transient analysis (Mode Superposition method)

Step 1 Define analysis type


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Step 1. Define analysis type

Turn on Transient

Note: Modal analysis should be done

before using Mode Superposition,


Step 2. Define analysis option


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Step 2. Define analysis option

Define the maximum mode number for superposition


Step 3. Delete pressure applied earlier in the modal analysis


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Step 3. Delete pressure applied earlier in the modal analysis


Step 4. Apply the load vector obtained from the modal analysis


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p pp y y


Step 5. Define the first time step


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p p

Note: Only define the time step size


Step 6. Solve


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p


Step 7. Define the second time step, then solve again


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Note: Only define the time at end of load step

Time History Postprocessing for Mode Superposition Transientanalysis

Step 1 Set result file


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Step 1. Set result file

Select the result file with extension .rdsp

Time History Postprocessing for Mode Superposition Transientanalysis

Step 2 Define result variables (a)


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Step 2. Define result variables (a)

Time History Postprocessing for Mode Superposition Transient analysis

Step 2. Define result variables (b)


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Pick the node

Transient vertical displacement of vault bottom edge center

under pressure impact (1000 Pa) (no damping, t=0.001)

M d iti t i t l i fi d


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-- Mode superposition transient analysis, five modes

-- Unconditionally stable scheme

Shell63



M d iti t i t l i fi d


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-- Unconditionally stable scheme

Shell63



Mode s perposition transient anal sis fi e modes


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-- Conditionally stable scheme

Shell63



Mode superposition transient analysis five modes


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-- Conditionally stable scheme

Shell63


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Summary

Shell element and solid elements can be used for this problem

Solid95 (20 nodes, 3 DOF) can give the same results of verticaldisplacement of central section as shell63

For the longitudinal displacement of support, solid95 (20 nodes,

3 DOF) is slightly different from shell63

Solid45 (8 nodes, 3 DOF) and solid73 (8 nodes, 6 DOF) give the

same results as solid95 (20 nodes, 3 DOF)

Mode superposition transient analysis uses much less time than

full transient analysis, while providing almost the same results Numerical damping occurs when large time step size is applied

3d_shellexample_s04

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