Boundary Conditions

This section outlines the default boundary conditions used in the panl BEM solver and their impact on simulation results.

Overview

To simplify usage and ensure models are properly constrained against rigid-body motion (RBM), the BEMSolver.solve method implements a set of default boundary conditions when explicit values are not provided. These defaults are tailored for rectangular panel analysis under standard loading conditions (tension, shear).

Default Constraints (RBM Suppression)

BEM simulations require sufficient displacement constraints to prevent the model from “flying away” due to numerical or physical imbalances (Rigid-Body Motion). By default, the following pinning logic is applied to the outer boundary:

  • Lower-Left Corner: Fixed in both global X and Y directions ($u_x=0, u_y=0$).

  • Lower-Right Corner: Fixed in the global Y direction ($u_y=0$).

These constraints allow the panel to expand or contract freely in the X-direction while preventing translation and rotation.

Note

The solver identifies “corners” by searching for the elements closest to the geometric Extents (min/max X and Y) of the elements tagged as "outer".

Default Load Convention

When the qx, qy, or qxy parameters are used in solve(), the following running load (force per unit length) convention is adopted, matching standard in-plane element formulations (e.g., Nastran CQUAD4):

Load Parameter

Description

Boundary Application

qx

Uniaxial Tension in X

$+F_x$ on Max-X edge, $-F_x$ on Min-X edge

qy

Uniaxial Tension in Y

$+F_y$ on Max-Y edge, $-F_y$ on Min-Y edge

qxy

In-plane Shear

See Shear Convention below

Shear Convention (qxy)

The shear load qxy is applied as a balanced set of tractions on all four outer edges: - Right Edge (Max-X): $+t_y$ - Left Edge (Min-X): $-t_y$ - Top Edge (Max-Y): $+t_x$ - Bottom Edge (Min-Y): $-t_x$

Impact of Assumptions

  • Geometry Alignment: The default BC logic assumes the panel edges are aligned with the global X and Y axes. For rotated panels, the coordinate-based search for “horizontal” and “vertical” edges may yield unexpected results.

  • Homogeneity: The RBM suppression logic fixes single elements. In a perfectly balanced theoretical model, this has negligible impact on the internal stress field (Saint-Venant’s Principle). However, close to the pinned corners, local stress artifacts may be present.

  • Applicability: These defaults are highly applicable to standard coupon-level analysis (e.g., hole-in-plate problems). For complex built-up structures where the panel interfaces with other components, users should define explicit boundary conditions.

Future Refactor Path

The current implementation uses coordinate-based element identification. As the codebase evolves, we plan to move towards a more robust nodal or geometric set-based boundary condition system. Code comments in solver.py highlight these areas for ease of future refactoring.