def _local_stiffness(self): k = np.zeros((6,6)) # Standard beam stiffness matrix (axial, bending) # ... (implementation omitted for brevity) return k

def _mass_matrix(self): M = lil_matrix((self.ndof, self.ndof)) # Assemble consistent mass matrix return M.tocsc()

def solve(self, dt, t_final, actuation_func): t = 0.0 u = np.zeros(self.ndof) v = np.zeros(self.ndof) a = np.zeros(self.ndof) while t < t_final: # Newmark prediction u_pred = u + dt * v + dt**2 * (0.5 - self.beta) * a v_pred = v + dt * (1 - self.gamma) * a # Nonlinear solve for a_new # ... Newton-Raphson using residual = M*a + F_int - F_ext # Update u, v, a t += dt return u, v, a The full implementation (~500 lines) is available in the supplementary material.

def nonlinear_force(self, u_e, x0_e): # Compute local deformations, then rotate to global # Returns internal force vector (6,) and tangent stiffness (6,6) pass class SnakeFEModel: def (self, n_elements, length, E, rho, radius=0.005): self.n_elements = n_elements self.n_nodes = n_elements + 1 self.ndof = 3 * self.n_nodes self.E = E self.rho = rho A = np.pi * radius 2 I = np.pi * radius 4 / 4 self.beam = CorotationalBeam(E, A, I, length) self.M = self._mass_matrix()