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NPTEL

Course On

STRUCTURAL

RELIABILITY Module # 09

Lecture 1

Course Format: Web

Instructor:

Dr. Arunasis Chakraborty

Department of Civil Engineering

Indian Institute of Technology Guwahati

Course Instructor: Dr. Arunasis Chakraborty

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1. Lecture 01: MATLAB – ANSYS

Combination

Limit state for real life problems are often implicit in nature. Mostly they involve finite element

analysis using commercially available software. With this in view this module is dedicated to

demonstrate the reliability analysis of implicit limit states involving structural analysis using

commercially available FE packages (e.g. ANSYS). The reliability analysis is carried out in

MATLAB platform which invokes ANSYS for evaluations of limit states in each iteration. The

example considered in this module is given below.

Problem Statement

A five storey portal frame consists of three bays as shown in the Figure 9.1.1. The element types

as shown in the figure corresponds to geometrical properties – modulus of elasticity, moment of

inertia and cross-section area (see Table 9.1.1). The probability distributions and statistical

parameters of the geometrical properties as well as loadings are illustrated in the Table 9.1.2.

Table 9.1.1 Cross–sectional parameters

Element–type Modulus of Elasticity Moment of Inertia Cross–section Area

1 𝐸1 𝐼5 𝐴5

2 𝐸1 𝐼6 𝐴6

3 𝐸1 𝐼7 𝐴7

4 𝐸1 𝐼8 𝐴8

5 𝐸2 𝐼1 𝐴1

6 𝐸2 𝐼2 𝐴2

7 𝐸2 𝐼3 𝐴3

8 𝐸2 𝐼4 𝐴4

Table 9.1.2 Statistical properties of random variables

Lecture 01: MATLAB – ANSYS Combination


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Variable Type of Distribution Units Mean Value Standard Deviation

𝑃1 Gumbel kN 133.454 40.04

𝑃2 Gumbel kN 88.97 35.59

𝑃3 Gumbel kN 71.175 28.47

𝐸1 Normal kN/m2 2.173752 × 107 1.9152 × 106

𝐸2 Normal kN/m2 2.379636 × 107 1.9152 × 106

𝐼1 Normal m4 8.134432 × 10–3

1.038438 × 10–3

𝐼2 Normal m4 1.150936 × 10–2 1.298048 × 10–3

𝐼3 Normal m4

2.137452 × 10–2 2.59609 × 10–3

𝐼4 Normal m4 2.596095 × 10–2 3.028778 × 10–3

𝐼5 Normal m4

1.081706 × 10–2 2.596095 × 10–3

𝐼6 Normal m4

1.410545 × 10–2 3.46146 × 10–3

𝐼7 Normal m4 2.327852 × 10–2 5.624873 × 10–3

𝐼8 Normal m4 2.596095 × 10–2 6.490238 × 10–3

𝐴1 Normal m2 0.3126 0.0558

𝐴2 Normal m2 0.3721 0.0744

𝐴3 Normal m2 0.5061 0.0930

𝐴4 Normal m2 0.5582 0.1116

𝐴5 Normal m2 0.2530 0.0930

𝐴6 Normal m2 0.2912 0.1023

𝐴7 Normal m2 0.3730 0.1209

𝐴8 Normal m2 0.4186 0.1395

Thus, the structure has 21 design variables reflecting different properties of the structural

components. Additionally, some basic variables were assumed to be correlated. This can be

expressed directly in form of correlation matrix 𝜌 (see next page).

The reliability analysis for the given portal frame is confined to the serviceability limit state

defined as the exceedance of top floor displacement (point A, see Figure 9.1.1) by ℎ/320, where

ℎ is the height of building from base. The limit state performance function, 𝑔(𝑋) is defined as

𝑔 𝑋 = 0.061 − 𝑟 𝑋 9.1.1

where, 𝑟(𝑋) denotes the actual horizontal displacement (in meters) as a function of all basic

variables. This displacement is calculated using finite element software package ANSYS where

the mechanical model of proposed example is characterized with given 21 random variables as

discussed above. The ANSYS model of the structure is given below in the Figure 9.1.2. The



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𝑃1 𝑃2 𝑃3 𝐸1 𝐸2 𝐼1 𝐼2 𝐼3 𝐼4 𝐼5 𝐼6 𝐼7 𝐼8 𝐴1 𝐴2 𝐴3 𝐴4 𝐴5 𝐴6 𝐴7 𝐴8

𝜌 =

10.130.130.130.130.130.130.130.130.130.130.130.130.130.130.13

00000

0.131

0.130.130.130.130.130.130.130.130.130.130.130.130.130.13

00000

0.130.13

10.130.130.130.130.130.130.130.130.130.130.130.130.13

00000

0.130.130.13

10.130.130.130.130.130.130.130.130.130.130.130.13

00000

0.130.130.130.13

10.130.130.130.130.130.130.130.130.130.130.13

00000

0.130.130.130.130.13

10.130.130.130.130.130.130.130.130.130.13

00000

0.130.130.130.130.130.13

10.130.130.130.130.130.130.130.130.13

00000

0.130.130.130.130.130.130.13

10.130.130.130.130.130.130.130.13

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0.130.130.130.130.130.130.130.13

10.130.130.130.130.130.130.13

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0.130.130.130.130.130.130.130.130.13

10.130.130.130.130.130.13

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0.130.130.130.130.130.130.130.130.130.13

10.130.130.130.130.13

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0.130.130.130.130.130.130.130.130.130.130.13

10.130.130.130.13

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0.130.130.130.130.130.130.130.130.130.130.130.13

10.130.130.13

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0.130.130.130.130.130.130.130.130.130.130.130.130.13

10.130.13

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0.130.130.130.130.130.130.130.130.130.130.130.130.130.13

10.13

00000

0.130.130.130.130.130.130.130.130.130.130.130.130.130.130.13

100000

00000000000000001

0.950.95

00

0000000000000000

0.951

0.9500

0000000000000000

0.950.95

100

00000000000000000001

0.9

0000000000000000000

0.91

𝑃1

𝑃2

𝑃3

𝐸1 𝐸2 𝐼1 𝐼2 𝐼3 𝐼4 𝐼5 𝐼6 𝐼7 𝐼8 𝐴1 𝐴2 𝐴3 𝐴4 𝐴5 𝐴6 𝐴7 𝐴8



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structural analysis is performed by use of ANSYS which was iteratively called by MATLAB

program as explained later.

Figure 9.1.1 Structural system of the portal frame (dimensions in meters) with element

type numbers



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Figure 9.1.2 ANSYS Model of the portal frame

A series of stepwise procedure in discussed below in how to solve such complex problems. The

following steps are:

Step 1. First, model the structure with appropriate structural properties as per illustration given

above using ANSYS [preferably, Mechanical APDL (ANSYS) in GUI mode]. After

completing the finite element modelling, one have to save its log file (*.lgw, kind of

batch mode script file used by ANSYS). This can be done by following: File >> Write

DB log file ... >> Ok. A typical glimpse of this log file is presented in Figure 9.1.3.

/BATCH

/input,menust,tmp,'',,,,,,,,,,,,,,,,1

! /GRA,POWER

! /GST,ON

⋮

/PREP7

K,1,0,0,0,

K,2,7.625,0,0,

K,3,16.775,0,0,

K,4,24.4,0,0,

FLST,3,4,3,ORDE,2

FITEM,3,1

FITEM,3,-4

KGEN,2,P51X, , , ,4.88, , ,0

FLST,3,4,3,ORDE,2

FITEM,3,5

FITEM,3,-8

KGEN,2,P51X, , , ,3.66, , ,0

FLST,3,4,3,ORDE,2

FITEM,3,9

FITEM,3,-12

KGEN,2,P51X, , , ,3.66, , ,0

FLST,3,4,3,ORDE,2

FITEM,3,13

FITEM,3,-16

KGEN,2,P51X, , , ,3.66, , ,0

FLST,3,4,3,ORDE,2

FITEM,3,17

FITEM,3,-20

KGEN,2,P51X, , , ,3.66, , ,0

⋮

R,1,0.312564,0.008134432, , , , ,

!*

! /REPLOT,RESIZE

R,2,0.3721,0.01150936, , , , ,

!*

R,3,0.50606,0.02137452, , , , ,

!*

R,4,0.55815,0.02596095, , , , ,

!*

R,5,0.253028,0.01081706, , , , ,

!*

R,6,0.29116825,0.01410545, , , , ,

!*

R,7,0.37303,0.02327852, , , , ,

!*



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R,8,0.4186,0.02596095, , , , ,

⋮

Figure 9.1.3 A typical log file created from ANSYS

Step 2. This log file is then modified according to a numerical computation software (like

MATLAB). The modification is done, so that new random values can be feed in for

every evaluation of 𝑟 𝑋 at places where structural parameters are defined. These places

are highlighted in Figure 9.1.3. In case of MATLAB these places in the log file are

replaced by an inbuilt function, num2str(.)as shown below

⋮

R,1,' num2str(A1) ',' num2str(I1) ', , , , ,

!*

! /REPLOT,RESIZE


!*


!*


!*


!*


!*


!*


⋮

Figure 9.1.4 A modified ANSYS log file with respect to MATLAB

where, A1, A2, ..., A8, I1, I2, ... and I8 are 𝐴1, 𝐴2, ..., 𝐴8, 𝐼1, 𝐼2, ... and 𝐼8 as shown

in Table 9.1.1, 9.1.2 and Figure 9.1.1. Similarly, other random variables are also

replaced at their corresponding places. Additionally, a pair of apostrophes with the

inbuilt function (' num2str(.) ') is also used as MATLAB reads this file as string

matrix and thus, these apostrophes separates these sub-matrixes. The command

num2str(.) transforms the numerical values of random variables into strings. Thus,

a new log file with modified random values is created with an extension *.inp (means

input file in batch mode). For ease, one can create a template function file in MATLAB

which will create the input file when appropriate random values are given.

Step 3. At the bottom of log file, one has to include a set of APDL commands for extracting the

desired results in a separate output file (say, output.txt) . A series of such relevant

commands used in the above example are demonstrated as

*get,<parameter>(<node number>)

/OUTPUT,<output file name>,<output file extension>

*VWRITE,<parameter>(<node number>)

<format descriptor>

/OUTPUT,TERM

for example,



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*get,ux(32)

/OUTPUT,output,txt

*VWRITE,ux(32)

%G

/OUTPUT,TERM

where, ux(32) gives the displacement of node 32 (node position of A in Figure 9.1.1

as per ANSYS model) in X direction. First line extracts the desired displacement

whereas second line creates an output file named output.txt. Third line command

writes the displacement in that file. Next line defines the format of output result to be

written, in this case %G means double precision data is used. The last evades writing rest

of results in output.txt. This addition enables the ANSYS to extract the desired

result of structural system in a separate and easy readable file by MATLAB.

Step 4. In next step, after creating the input file, one have to run the ANSYS in batch mode for

solving the structural system. This is done via DOS command prompt (in case of

Windows OS). The MATLAB executes DOS commands by calling dos(.) function

as shown below

dos( ' "< Path of ANSYS Extension >" -b -i "< Name of Input File and Extension

>" -o "< Name of Output File and Extension >"')

for example,

dos( ' "C:\Program Files\ANSYS Inc\v130\ansys\bin\win32\ANSYS130" -b -i

"input.inp" -o "outp.out"')

but the output result is not stored in this output file, it is stored in the file stated in log

file. In the above command, -b refers to execution of ANSYS in batch mode, -i and

-o are related to input and output files.

Now, if one call the ANSYS file for solving the 𝑟(𝑋) value, the MATLAB will generate a new

input log file, run the batch mode and store the desired output result in file stated in the input file.

This output result is read by MATLAB as the 𝑟(𝑋) value.

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