The design domain is a planar "ground structure": nodes on a 2D grid connected to every neighbor within one cell (axis and both diagonals — 4 unique directions, the 2D analogue of the 13-direction 3D ground structure), each acting as a linear spring.
Spring force: F = k · (‖xB − xA‖ − L0)
Stiffness: k = k0 · ρ(edge)^p (p = 3, SIMP-style penalization)
Strain energy: U = ½ · k · (‖xB − xA‖ − L0)²
Every frame the lattice is integrated forward with damped explicit dynamics (dynamic relaxation) — the load pulls the free nodes, the springs pull back, and viscous damping bleeds off kinetic energy until the shape settles into its static equilibrium, exactly like a physical model finding its resting deformation under load.
Periodically an evolutionary structural optimization step runs: every cell's sensitivity is the strain energy stored in the springs around it — cells carrying little strain energy are barely contributing to stiffness, so they are the first candidates to become void. The optimizer keeps exactly the top fraction of cells (by sensitivity) solid, ranked every step, and nudges that fraction toward your target by the evolution rate — this is a bi-directional scheme (BESO): raising the target regrows material in the highest-sensitivity void cells, lowering it removes more.
- Load magnitude — how hard the free end/midspan is pulled; higher load makes the surviving load path more visible.
- Target volume fraction — how much of the original block is allowed to remain once optimization converges.
- Evolution rate — how much volume fraction changes per optimization step (faster = coarser, more abrupt shapes).
- Displacement exaggeration — purely visual: multiplies the drawn deflection so the deformation is legible at a glance.
Real engineering relevance: this is the same family of algorithm (SIMP / BESO) used by generative-design tools in Fusion 360, Altair Inspire and nTopology to grow aircraft brackets and 3D-printed lattices that use the least material for a given stiffness — most classic BESO/SIMP demonstrations (the MBB beam, the L-bracket) are run in exactly this 2D plane-stress domain before ever being extruded to 3D.