Peridynamic Boundary Mirroring Node for Numerical Analysis
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Solution Overview
Problem
The existing peridynamic method produces inaccurate numerical analysis results at the boundary of a structure due to incomplete horizon regions, leading to complex calculations and prolonged analysis times.
Innovation Solution
The method incorporates a mirroring node technique, where a mirroring node is added to the boundary, mirroring existing nodes outside the horizon region to complete the interaction calculations, using shape tensors and force state vectors to improve accuracy and reduce the number of nodes required.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the existing peridynamic method is used without mirroring nodes, then the calculation process is simpler, but the numerical analysis result accuracy at the boundary deteriorates
Solution Approach 1:
The patent applies the copying principle by creating mirroring nodes that replicate existing nodes across the boundary. These mirroring nodes are virtual copies that allow the horizon region to be completed without adding physical complexity to the actual structure. The mirroring nodes copy the positional and interaction properties of nodes outside the domain, enabling accurate boundary calculations while maintaining a manageable computational model.
2Measurement precision
If more nodes are added to improve boundary accuracy, then the numerical analysis result accuracy improves, but the numerical analysis time increases
Solution Approach 1:
Instead of adding numerous physical nodes to improve boundary accuracy, the patent uses mirroring nodes that are virtual copies. These mirroring nodes provide the necessary computational information for accurate boundary analysis without increasing the actual number of discrete elements in the model, thus avoiding the time penalty associated with processing more nodes.
Solution Approach 2:
The patent changes the parameter representation by introducing mirroring nodes with specific symmetry properties. Rather than increasing node density, it transforms the problem by using parameter symmetry (origin-symmetrical positioning) to complete the horizon region, achieving accuracy through parameter transformation rather than quantity increase.
3Measurement precision
If the horizon region is completed at the boundary, then the numerical analysis result accuracy improves, but the number of nodes increases
Solution Approach 1:
The patent uses mirroring nodes as virtual copies to complete the horizon region at the boundary. These mirroring nodes are not additional physical entities but rather computational constructs that replicate the necessary interaction information. This approach completes the horizon region for accurate boundary analysis without actually increasing the number of discrete nodes in the peridynamic model.
Data Source
AI summary
A peridynamic method having an added mirroring node according to embodiments of the present invention includes: a first step of calculating a shape tensor of a first node; a second step of calculating force state vectors of the first node and each of a plurality of second nodes by using the shape tensor; and a third step of calculating a peridynamic motion equation of the first node by using the force state vectors. The first node is a node located on a boundary of a structure and has a predetermined size horizon region, the plurality of second nodes is nodes in the horizon region, the plurality of second nodes includes one or more third nodes, and the third node is a second node having no node at a point which is origin-symmetrical based on the first node among the plurality of second nodes. In the first step, the shape tensor is calculated by using a position value in which the third node is origin-symmetrical based on the first node.