## Example 19

0. Example 19

1. Steps to prepare this example in BI (before analysis)

2. Prepare for Point Estimation Analysis

3. Prepare for Optimization Analysis

0. Example 19

This example has a linear limit state function in physical space as Eq. (1) .

Table 1 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

TRSQP Method

SLSQP Method

COBYLA Method

3.3 Run this Optimization object.

3.4 Show Plot and Text result of each method:

TRSQP Method

SLSQP Method

COBYLA Method

4. References

 SCHMIT LA, FARSHI B. Some Approximation Concepts for Structural Synthesis. AIAA J 1974;12:692–9. https://doi.org/10.2514/3.49321.