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 _mass_matrix(self): M = lil_matrix((self.ndof, self.ndof)) # Assemble consistent mass matrix return M.tocsc()
def _local_stiffness(self): k = np.zeros((6,6)) # Standard beam stiffness matrix (axial, bending) # ... (implementation omitted for brevity) return k
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 _mass_matrix(self): M = lil_matrix((self.ndof, self.ndof)) # Assemble consistent mass matrix return M.tocsc()
def _local_stiffness(self): k = np.zeros((6,6)) # Standard beam stiffness matrix (axial, bending) # ... (implementation omitted for brevity) return k