Internal Node Spring for FEA Surface Constraints
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Solution Overview
Problem
Existing methods for resolving surface-based constraints in finite element modeling often fail when node swapping is restricted by conditions such as displacement boundary conditions or joint elements associated with Lagrange Multipliers, leading to over-constrained conditions and instability in solution convergence.
Innovation Solution
The introduction of an internal node based on the pilot node, with a numerical spring connecting the pilot node and the internal node, allows for the modification of the model to resolve node dependency by limiting relative movements within a tolerance, thereby avoiding over-constrained conditions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If node swapping is used to resolve node dependency in elimination method, then the constraint resolution is simplified, but node swapping cannot be performed when both pilot node and surface node are subject to other constraints and/or boundary conditions
Solution Approach 1:
An internal node is introduced as an intermediary between the pilot node and surface nodes. The internal node serves as a mediator that allows constraint equations to be applied without requiring direct node swapping, thus resolving the contradiction between simplifying constraint resolution and maintaining adaptability when nodes are subject to other constraints
Solution Approach 2:
The constraint system is segmented by separating the pilot node from the surface nodes through the introduction of an internal node. This segmentation allows the constraint equations to be applied in a structured manner without requiring node swapping, enabling the system to handle cases where nodes are subject to multiple constraints
2Stability of the object's composition
If rigid constraint is applied with pilot node as independent and surface nodes as dependent, then kinematic coupling is achieved, but over-constraint condition occurs when nodes are subject to multiple constraints
Solution Approach 1:
The internal node acts as an intermediary that decouples the direct dependency relationship between pilot nodes and surface nodes. This allows rigid constraints to maintain kinematic coupling stability while avoiding over-constraint conditions that would compromise solution convergence reliability
Solution Approach 2:
The constraint hierarchy is segmented into multiple levels: pilot nodes connected to internal nodes, and internal nodes connected to surface nodes. This segmentation distributes the constraint relationships, maintaining kinematic coupling stability while preventing over-constraint situations
3Stability of the object's composition
If force-distributed constraint is applied with pilot node as dependent and surface nodes as independent, then kinetic coupling is achieved, but over-constraint condition occurs when nodes are subject to multiple constraints
Solution Approach 1:
The internal node serves as a mediator that enables force-distributed constraints to achieve kinetic coupling stability without creating over-constraint conditions. By routing forces through the internal node, the system maintains reliability in solution convergence
4Reliability
If internal node is created and numerical spring is added to connect pilot node and internal node, then model complexity increases, but node dependency is resolved and solution convergence improves
Solution Approach 1:
The internal node and numerical spring together form an intermediary mechanism that resolves node dependency issues. While this increases model structure complexity, it significantly improves solution convergence reliability by eliminating over-constraint conditions
Solution Approach 2:
The numerical spring introduces a controllable stiffness parameter that allows flexible adjustment of the connection between pilot node and internal node. This parameter change enables resolution of node dependency while managing model complexity through tunable properties
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach improves solution convergence and stability in simulations by allowing for effective resolution of node dependency in surface-based constraints, even when node swapping is restricted, while maintaining physical characteristics within a specified tolerance.
Implementation Method 1
a numerical spring connecting the pilot node and the internal node, wherein the numerical spring is configured for limiting relative movements between the pilot node and the internal node within a tolerance
Data Source
AI summary
A model representing a physical object is received. The model contains a pilot node, one or more surface nodes, and a constraint for coupling displacements/movements of the pilot node with the one or more surface nodes via a set of constraint equations. The pilot node is subject to a condition that restricts node swapping for resolving node dependency in elimination method. An internal node is created based on the pilot node. The internal node and the pilot node occupy a same location initially. The internal node and the one or more surface nodes are constrained via the set of constraint equations. The model is modified with the internal node and a numerical spring connecting the pilot node and the internal node. The numerical spring is configured for limiting relative movements between the pilot node and the internal node. Physical behaviors of the physical object are simulated using the modified model.