| What Is Optimization Module? |
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The optimization module decides a search direction and finds the optimal point using the result of design sensitivity analysis. It determines whether the objective function and constraints are satisfied. If the module concludes that recalculation is required, it updates the design variables and returns them to the FEM solver. |
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| Optimization
Method |
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CLAY OPERA uses mathematical programming for optimization. As a mathematical programming method, we chose the sequential second order programming and sequential programming that have relatively stable convergent property and require no experience factors (e.g. penalty factor and extended Lagrange variable). |
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| What Is Objective Function? |
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An objective function provides a condition (i.e. objective) that is literally optimized, such as a weight or stress to be minimized. It basically tries to bring the variable that is set as an objective function to the target defined by the user. (The target is called "expected value" in CLAY OPERA.) However, for natural oscillation, the optimization tries to bring the variable as far as possible from the expected value. (In this case, the target is called "non-expected value" in CLAY OPERA.) The latter is useful avoiding resonance at a certain frequency. CLAY OPERA currently supports the following objective functions.
- Structural Weight
Optimization(Expected Value)
- Stress Distribution Optimization (Expected Value)
- Natural Oscillation Optimization
(Expected Value, Non-expected Value) |
- Structural Deformation Optimization
- Constraint Reverse Force Optimization (Expected Value) |
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| What Is a Design Variable? |
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A design variable is
a candidate variable that indicates how a shape can
be changed by optimization. Currently board thickness
(for shell only elements) and basis vector can be
specified as design variables. (For details of basis
vector, see"Technical
Background") It is necessary to set the
allowable range for changing the variable.
| - Shell Element Board Thickness |
- Basis Vector |
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| What Is a Restriction? |
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In some optimization cases, it is necessary to suppress changes in the design variable even within the allowable range unless certain conditions are not satisfied. For example, suppose that minimizing structural weight has been defined as an objective function and some design variables have been set up. In this case, it is estimated that the volume will be minimized no matter whether the design variable is board thickness or basis vector. However, such optimization reduces stiffness, which may lead to increased deformation and stress. Such improper change in the design variable can be avoided by defining upper limits in deformation and stress as constrains. The restriction specifies a lower limit as well as an upper limit. And either or both limits can be applied. Currently the restrictions are supported:
- Structural Weight Restriction
(Upper limit or lower limit, or both)
- Deformation Restriction (Upper limit or lower
limit, or both)
- Stress Restriction (Upper limit or lower limit,
or both)
- Constraint Reverse Force Restriction (Upper
limit or lower limit, or both)
- Natural Oscillation Restriction (Upper limit
or lower limit, or both) |
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| Multiple Load Cases Optimization |
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CLAY OPERA performs optimization in single load cases. If there are more than one load cases (called "Multiple Load Cases" or "Multiple Cases" in CLAY OPERA), a set of optimization condition must be defined individually for each load case. For example, the reference for evaluating safety of a pressure vessel is different between under static stress by pressure load and under heat stress. To cope with such a case, CLAY OPERA supports multiple load cases optimization. In this optimization, a different set of objective functions, design variables, and restrictions can be provided for each load case. (The type of objective function is fixed.) The optimization tries to satisfy all of these conditions simultaneously. |
