CLAY OPERA 構造最適化CAEソフトウェア for WindowsNT4.0/Windows2000

Technical Background
Software Configuration
Preprocessor
Postprocessor
FEM Solver
Sensitivity
Module
Optimaization
Module
Main Functions
Technical Background
Basis Vector
Method
Operating Enviroument
Basis Vector Method
Basic Principle
The basis vector method determines the optimal shape by combining possible basic shape candidates (called basis vectors) that the designer imagines for the original shape. Each basis vector has its weight factor. Applying weight factors change the shape of basis vectors. The final optimal shape is represented as the union (logical sum) of the basis vector with different weight factors.
A basis vector is sometimes indicated by acronym as "BV". In CLAY OPERA, any number of basis vectors can be defined. Therefore, usually a number is appended to each basis vector. Suppose we create two shapes (original and basis) as shown in the above figure. In CLAY OPERA, the initial value for the weight factor of the basis vector is "1.0" when it is created. For example, BV1 is defined as follows:
The optimal shape can be defined by using a relationship represented by the following formula:
Opt=Org+{(Org−BV1)*W1+(Org−BV2)*W2 . . . +(Org−BVn)*Wn}
Opt: Coordinate of the optimal shape BV: Coordinate of the basis vector Org: Coordinate of the original shape W: Weight factor of the basis vector
The above formula indicates that "the final optimal shape is represented as the union (logical sum) of the basis vector with different weight factors" as described in above. For this relationship to be established, there must be vertex coordinate data for the original shape and basis vectors. This means that it is impossible to change the element configuration (topology). This is a distinctive feature of the basis vector method. Since weight factors are signed, the vertex coordinates could be inverted against the original shape.

The following figures show how the optimal shape changes according to the weight factor of the basis vector.
 

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