Beam-to-Surface Contact Detection in Finite Element Analysis
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Solution Overview
Problem
Existing methods for simulating beam-to-surface contacts in finite element analysis are inadequate, particularly when dealing with surface meshes of varying sizes and curvatures, and beam elements of longer lengths, as they fail to accurately detect contacts beyond the end nodes, leading to inefficient simulations.
Innovation Solution
The proposed solution involves calculating a minimum characteristic length for the surface mesh, defining interior points for beam elements longer than this length, and using distributed nodal masses to calculate stiffness values and compensational forces for initial penetration, along with a global and local search scheme to detect and manage contacts along the beam element, ensuring accurate contact force calculations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If prior art approaches use only end nodes for contact detection, then the simulation is computationally simple, but contact accuracy is insufficient for long beam elements
Solution Approach 1:
The beam element is segmented into multiple sections by introducing interior points along its length. These interior points divide the single long beam element into smaller segments, allowing contact detection at multiple locations rather than just at the two end nodes. This segmentation enables accurate detection of contacts occurring at any position along the beam element, resolving the inaccuracy problem while maintaining computational efficiency through systematic division.
Solution Approach 2:
The contact detection approach transitions from a one-dimensional endpoint check to a continuous along-element search. By parameterizing the beam element position with a parameter t ranging from 0 to 1, the method searches for contacts across the entire length of the beam element, not just at discrete endpoints. This dimensional expansion in the detection space ensures that contacts at any position along the beam are captured.
2Reliability
If prior art approaches detect only two contacts at end nodes, then the computational efficiency is maintained, but contact detection completeness fails for beams with multiple contact points
Solution Approach 1:
Interior points are predefined and positioned along the beam element before the contact simulation begins. This preliminary placement of detection points ensures that potential contact locations are identified in advance, allowing the simulation to efficiently check for contacts at these predetermined positions without requiring complex real-time calculations during the contact detection phase.
Solution Approach 2:
The mechanical contact detection process is replaced with a mathematical parameterization approach. Instead of physically testing for contacts at multiple points along the beam, the method uses parametric equations to describe the beam position and systematically evaluates contact conditions along its length. This substitution transforms a potentially computationally intensive mechanical search into an efficient mathematical evaluation process.
3Measurement precision
If prior art approaches ignore interior portion contacts, then the model simplicity is preserved, but simulation accuracy deteriorates for complex surface geometries
Solution Approach 1:
The contact detection model incorporates dynamic positioning of interior points along the beam element. Rather than using fixed static points, the interior points are positioned to adaptively capture contact locations that may occur at different positions along the beam during deformation. This dynamic approach ensures accurate contact detection even as the beam geometry changes during the simulation, maintaining precision without requiring excessive model complexity.
Data Source
AI summary
Methods and systems for simulating beam-to-surface contacts in finite element analysis (FEA) are disclosed. A FEA model contains at least one beam element and at least one surface mesh. Surface mesh comprises a plurality of two-dimensional finite elements having arbitrary mesh density. A minimum characteristic length (CL) of the surface mesh is calculated. One or more interior points are defined for those beam elements with length longer than CL. For every nodal point (i.e., end nodes and interior points if any), a parametric coordinate between 0 and 1 inclusive is established and kept constant throughout the FEA analysis. Distributed nodal masses are used for calculating a stiffness value for calculating nodal force to resist penetration. Initial penetration with the surface mesh at each nodal point along the beam element is compensated with a set of displacements subtracting from the initial nodal displacements, such that the compensational forces remain at zero as the nodal point's initial interpenetration decreases.