0. Example 20
This example has a linear limit state function in physical space as Eq. (1) [1,2].
A ten-story building with a mass damper attached on the top floor under the seismic excitation (El Centro, 1940) has been investigated. The properties of this building are shown in Table 1.
Table 2 shows correlation matrix, the number and statistical moment of random variables for this example.
The probability density function for random variables is in accordance with Eq. (2).
1. Steps to prepare this example in BI (before analysis):
1.1 Generate Random Variable object: Define > Variable > RandomVariable
1.2 Generate Model object: Define > Model
1.3 Generate Response object: Define > Response
1.4 Generate Limit State Function object: Define > Limit State Function
2. Prepare for FORM Analysis
2.1 Generate Nataf Transformation object: Analysis > Transformer
2.2 Generate Convergence Checker object: Analysis > Convergence Checker
2.3 Generate Step Direction Searcher object: Analysis > Step Direction Searcher
2.4 Generate Merit Checker object: Analysis > Merit Checker
2.5 Generate Step Size Searcher object: Analysis > Step Size Searcher
In this part, you need to insert name of previous object, which is created in steps 2.4.
2.6 Generate Solver object: Analysis > Solver
In this part, you need to insert names of previous objects, which are created in steps 2.1, 2.2, 2.3, and 2.5.
2.7 Generate Output object: Analysis > Output
2.8 Generate FORM Analysis object: Analysis > FORM Analysis
2.9 Run this FORM Analysis object.
2.10 Show Plot result:
2.11 Show text result:
3. Prepare for Optimization Analysis
3.1 Generate Output object: Analysis > Output
3.2 Generate Optimization Analysis object: Analysis > Optimization
3.3 Run this Optimization object.
3.4 Show Plot and Text result of each method:
 Hadi MNS, Arfiadi Y. Optimum Design of Absorber for MDOF Structures. J Struct Eng 1998;124:1272–80. https://doi.org/10.1061/(asce)0733-9445(1998)124:11(1272).
 Kaveh A, Mohammadi S, Khadem Hosseini O, Keyhani A, Kalatjari VR. Optimum parameters of tuned mass dampers for seismic applications using charged system search. Iran J Sci Technol – Trans Civ Eng 2015;39:21–40.