Core Shape Optimization Using Homeomorphic Nonlinear Mapping
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Solution Overview
Problem
Existing core design methods struggle to find a shape that improves device performance using a wide search range while avoiding excessively complex or impractically simple shapes.
Innovation Solution
A core design apparatus and method that includes a basic shape acquisition part, a core shape determination part, and a program to calculate and determine the shape of a core by applying nonlinear mapping to a design target element using deformation patterns and application parameters, ensuring a homeomorphic mapping relationship.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If nonlinear mapping is applied to the basic shape of the design target element to widen the search range, then the ability to improve device performance is enhanced, but the shape may become excessively complex or practically impossible to fabricate
Solution Approach 1:
The patent applies parameter changes by using homeomorphic nonlinear mapping to transform the basic shape parameters while preserving topological properties. This allows the shape to be optimized within a wider search range while ensuring the transformed shape remains within feasible fabrication limits through the homeomorphic constraint that maintains continuous deformation without self-intersection or topology changes.
Solution Approach 2:
The patent performs preliminary action by pre-defining the homeomorphic mapping relationship before the shape optimization process. This preliminary establishment of mapping constraints ensures that subsequent nonlinear transformations will not produce impossible shapes, as the homeomorphic property guarantees the transformed shape remains topologically equivalent to the original basic shape.
2Ease of manufacture
If the shape obtained by applying nonlinear mapping is too simple, then fabrication is easy, but it may be impossible to design the shape of a core that sufficiently improves the performance of the device
Solution Approach 1:
The patent uses parameter changes through homeomorphic nonlinear mapping to transform the basic shape into an optimized shape that improves device performance. The mapping allows sufficient geometric complexity to be introduced while maintaining topological equivalence, enabling performance optimization without sacrificing fabrication feasibility.
Solution Approach 2:
The patent employs copying by creating a transformed copy of the basic shape through homeomorphic mapping. This copied shape retains the topological properties of the original (ensuring fabrication feasibility) while having modified geometric parameters that improve device performance, thus resolving the contradiction between simplicity and performance.
3Ease of manufacture
If homeomorphic mapping is enforced to maintain feasible shapes, then fabrication feasibility is preserved, but the search range for optimal shapes is constrained
Solution Approach 1:
The patent applies parameter changes by using homeomorphic nonlinear mapping, which transforms shape parameters while preserving topological properties. This approach expands the search range within the feasible domain by allowing continuous deformation of the basic shape parameters without violating topological constraints, thus maintaining fabrication feasibility while exploring a broader design space.
Solution Approach 2:
The patent employs dynamics by implementing a dynamic optimization process that operates within the homeomorphic mapping framework. The optimization algorithm dynamically adjusts shape parameters through homeomorphic transformations, enabling the search to explore a wide range of feasible shapes adaptively while always maintaining the homeomorphic property that ensures fabrication feasibility.
Data Source
AI summary
A core design device (100) acquires an application parameter including a parameter indicating an application method of a deformation pattern (310a, 310b). The core device (100) changes a shape of a design target element by applying the deformation pattern (310a, 310b) to the design target element according to the application method included in the application parameter. The core design apparatus (100) determines a shape of a core based on a value indicating a characteristic of a device when the device including the core in which the shape of the design target element has been changed is operated.