Optimization Methodology

Local sizing optimization refers to the process of finding the weight minimum panel cross-section. The problem as implemented in HyperSizer can be formally defined as:

   Minimize: W(x)

   Subject to: MS_i(x) > 0

W is the panel weight, MS_i are the margins of safety constraints, and x is the vector of design variables that make up the panel. The lightest panel design that passes are margin of safety checks is the optimum panel. Note that panel minimum stiffness/deformation constraints are implemented as margin of safety checks.

The design variables x are the collection of dimensions and materials that fully defined a panel cross-section. All design (sizing) variables are defined as discrete variables. Cross-section dimension variables are specified using a minimum bound, maximum bound, and a number of permutations. The statistical optimization feature automatically refines the user defined bounds based on the observed trends during analysis. See Statistical Optimization.

For detailed sizing, HyperSizer uses a direct search algorithm to find the weight minimum panel. The candidate panels are sorted by weight and analyzed sequentially until the lightest candidate that passes all margin checks is found. Most stress and failure analyses are closed-form so analyzing hundreds of thousands of candidates takes seconds.

Before any optimization is performed on any component, a design space must be defined. The optimization is constrained to search within this space.

The design space is defined by:

• Sizing variables
• Material selections
• Panel/beam concepts

These data are defined for each component.

Sizing Variables

Sizing variables define the dimensions of the panel or beam cross section. Sizing variables are specified using a minimum bound, maximum bound, and a number of permutations. The range specified by the bounds is divided by the number of permutations to give an evenly spaced range of candidate dimensions.

For example, if the geometric bounds on the skin thickness are defined as:

• Maximum = 0.5
• Minimum = 0.1
• Permutations = 5

Then the range of skin thickness in the design space are 0.1, 0.2, 0.3, 0.4, 0.5.

Material Selections

Material selections define the candidate materials used in the panel or beam cross section. If multiple materials are selected, the lightest combination that passes all margin of safety checks is returned. See About Material Selections.

Concepts

A concept is a panel or beam type within a family. For example, the open beam family has the I, C, and Z beam concepts. Concepts are grouped into families. Each panel/beam concept belongs to only one family. See Panel and Beam Families.

Multiple panel/beam concepts can be sized simultaneously if they are in the same family. The lightest weight option that passes all margin of safety checks will be returned.

Candidates

The sizing variables, material selections, and concepts are combined to generate a discrete pool of candidate designs. If the number of candidates is one, then technically speaking no sizing (optimization) is performed, only an analysis.

The number of candidate designs is computed each time the project is saved. If the sizing variable information is incomplete or the dimensions are in conflict, HyperSizer will return a warning indicating that no workable sections were generated. Typically, this is due to incomplete material assignments.

To find the optimum design, the pool of candidate designs is sorted by unit weight and analyzed sequentially. The first candidate that passes all margin of safety checks is selected as the optimum panel.

This method is in contrast to global optimization based on formal approaches such as gradient-based search algorithms. Traditional formal optimization software is rich in numerical sophistication, however, with the hundreds of dissimilar potential failure modes and the many different design variables, formal optimization is unable to resolve the hundreds of local minimums that occur in the process of evaluating a panel’s cross-sectional shape.

HyperSizer’s sizing optimization is solidly based on detailed and accurate analyses that include the complete potential failure modes that are required for final design certification and margin of safety reporting. Because the failure analyses are efficient, optimization takes seconds per component.

Margin of safety checks are performed for:

• Material strength
• Local and global instability
• Crippling
• Deformation limit
• Required stiffness
• Required natural frequency
• Manufacturability

Rapid sizing is similar to detailed sizing in terms of problem definition and failure modes used to check margins of safety. The key difference is that rapid sizing is non-parametric in terms of user input. Detail sizing requires input of min, max, and permutations for design variables to populate the design space to be explored. Rapid sizing, however, only needs general stiffener information to be defined: cross section ratios, material selection, and ply angle rules (if composite). These inputs to rapid sizing allow for concise application of domain-specific knowledge to reduce the design space without restricting the potential for weight minimization. The rapid sizing algorithm intelligently works through the design space to find an optimum solution without any active user input. This entire process finds optimum designs for stiffened panels much more quickly than detailed sizing.

See Fabrication Criteria Form and Ply Angle Rules for information on the inputs into the rapid sizing process.