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Merge pull request GazzolaLab#335 from Ali-7800/230_dev_catenary
Catenary curve validation
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| Original file line number | Diff line number | Diff line change |
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| @@ -0,0 +1,129 @@ | ||
| import numpy as np | ||
| from elastica import * | ||
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| from post_processing import ( | ||
| plot_video, | ||
| plot_catenary, | ||
| ) | ||
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| class CatenarySimulator(BaseSystemCollection, Constraints, Forcing, Damping, CallBacks): | ||
| pass | ||
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| catenary_sim = CatenarySimulator() | ||
| final_time = 10 | ||
| damping_constant = 0.3 | ||
| time_step = 1e-4 | ||
| total_steps = int(final_time / time_step) | ||
| rendering_fps = 20 | ||
| step_skip = int(1.0 / (rendering_fps * time_step)) | ||
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| n_elem = 500 | ||
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| start = np.zeros((3,)) | ||
| direction = np.array([1.0, 0.0, 0.0]) | ||
| normal = np.array([0.0, 0.0, 1.0]) | ||
| binormal = np.cross(direction, normal) | ||
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| # catenary parameters | ||
| base_length = 1.0 | ||
| base_radius = 0.01 | ||
| base_area = np.pi * (base_radius ** 2) | ||
| volume = base_area * base_length | ||
| mass = 0.2 | ||
| density = mass / volume | ||
| E = 1e4 | ||
| poisson_ratio = 0.5 | ||
| shear_modulus = E / (poisson_ratio + 1.0) | ||
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| base_rod = CosseratRod.straight_rod( | ||
| n_elem, | ||
| start, | ||
| direction, | ||
| normal, | ||
| base_length, | ||
| base_radius, | ||
| density, | ||
| youngs_modulus=E, | ||
| shear_modulus=shear_modulus, | ||
| ) | ||
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| catenary_sim.append(base_rod) | ||
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| # add damping | ||
| catenary_sim.dampen(base_rod).using( | ||
| AnalyticalLinearDamper, | ||
| damping_constant=damping_constant, | ||
| time_step=time_step, | ||
| ) | ||
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| # Add gravity | ||
| catenary_sim.add_forcing_to(base_rod).using( | ||
| GravityForces, acc_gravity=-9.80665 * normal | ||
| ) | ||
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| # fix catenary ends | ||
| catenary_sim.constrain(base_rod).using( | ||
| FixedConstraint, constrained_position_idx=(0, -1), constrained_director_idx=(0, -1) | ||
| ) | ||
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| # Add call backs | ||
| class CatenaryCallBack(CallBackBaseClass): | ||
| """ | ||
| Call back function for continuum snake | ||
| """ | ||
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| def __init__(self, step_skip: int, callback_params: dict): | ||
| CallBackBaseClass.__init__(self) | ||
| self.every = step_skip | ||
| self.callback_params = callback_params | ||
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| def make_callback(self, system, time, current_step: int): | ||
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| if current_step % self.every == 0: | ||
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| self.callback_params["time"].append(time) | ||
| self.callback_params["step"].append(current_step) | ||
| self.callback_params["position"].append(system.position_collection.copy()) | ||
| self.callback_params["radius"].append(system.radius.copy()) | ||
| self.callback_params["internal_force"].append(system.internal_forces.copy()) | ||
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| return | ||
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| pp_list = defaultdict(list) | ||
| catenary_sim.collect_diagnostics(base_rod).using( | ||
| CatenaryCallBack, step_skip=step_skip, callback_params=pp_list | ||
| ) | ||
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| catenary_sim.finalize() | ||
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| timestepper = PositionVerlet() | ||
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| integrate(timestepper, catenary_sim, final_time, total_steps) | ||
| position = np.array(pp_list["position"]) | ||
| b = np.min(position[-1][2]) | ||
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| SAVE_VIDEO = True | ||
| if SAVE_VIDEO: | ||
| # plotting the videos | ||
| filename_video = "catenary.mp4" | ||
| plot_video( | ||
| pp_list, | ||
| video_name=filename_video, | ||
| fps=rendering_fps, | ||
| xlim=[0, base_length], | ||
| ylim=[-0.5 * base_length, 0.5 * base_length], | ||
| ) | ||
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| PLOT_RESULTS = True | ||
| if PLOT_RESULTS: | ||
| plot_catenary( | ||
| pp_list, | ||
| xlim=(0, base_length), | ||
| ylim=(b, 0.0), | ||
| ) |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,76 @@ | ||
| import numpy as np | ||
| import matplotlib | ||
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| matplotlib.use("Agg") # Must be before importing matplotlib.pyplot or pylab! | ||
| from matplotlib import pyplot as plt | ||
| from tqdm import tqdm | ||
| import scipy as sci | ||
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| def plot_video( | ||
| plot_params: dict, | ||
| video_name="video.mp4", | ||
| fps=15, | ||
| xlim=(0, 4), | ||
| ylim=(-1, 1), | ||
| ): | ||
| import matplotlib.animation as manimation | ||
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| positions_over_time = np.array(plot_params["position"]) | ||
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| print("plot video") | ||
| FFMpegWriter = manimation.writers["ffmpeg"] | ||
| metadata = dict(title="Movie Test", artist="Matplotlib", comment="Movie support!") | ||
| writer = FFMpegWriter(fps=fps, metadata=metadata) | ||
| fig = plt.figure(figsize=(10, 8), frameon=True, dpi=150) | ||
| ax = fig.add_subplot(111) | ||
| ax.set_xlim(*xlim) | ||
| ax.set_ylim(*ylim) | ||
| ax.set_xlabel("x [m]", fontsize=16) | ||
| ax.set_ylabel("y [m]", fontsize=16) | ||
| # plt.axis("equal") | ||
| with writer.saving(fig, video_name, dpi=150): | ||
| rod_lines_2d = ax.plot(positions_over_time[0][2], positions_over_time[0][0])[0] | ||
| for time in tqdm(range(1, len(plot_params["time"]))): | ||
| rod_lines_2d.set_xdata(positions_over_time[time][0]) | ||
| rod_lines_2d.set_ydata(positions_over_time[time][2]) | ||
| writer.grab_frame() | ||
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| # Be a good boy and close figures | ||
| # https://stackoverflow.com/a/37451036 | ||
| # plt.close(fig) alone does not suffice | ||
| # See https://github.com/matplotlib/matplotlib/issues/8560/ | ||
| plt.close(plt.gcf()) | ||
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| def plot_catenary(plot_params: dict, xlim=(0, 1), ylim=(-0.5, 0.5), base_length=1.0): | ||
| """ | ||
| Catenary analytical solution from Routh, Edward John (1891). "Chapter X: On Strings". A Treatise on Analytical Statics. University Press. | ||
| """ | ||
| matplotlib.use("TkAgg") | ||
| position = np.array(plot_params["position"]) | ||
| lowest_point = np.min(position[-1][2]) | ||
| x_catenary = np.linspace(0, base_length, 100) | ||
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| def f_non_elastic_catenary(x): | ||
| return x * (1 - np.cosh(1 / (2 * x))) - lowest_point | ||
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| a = sci.optimize.fsolve(f_non_elastic_catenary, x0=1.0) # solve for a | ||
| y_catenary = a * np.cosh((x_catenary - 0.5) / a) - a * np.cosh(1 / (2 * a)) | ||
| plt.plot(position[-1][0], position[-1][2], label="Simulation", linewidth=3) | ||
| plt.plot( | ||
| x_catenary, | ||
| y_catenary, | ||
| label="Catenary (Analytical Solution)", | ||
| linewidth=3, | ||
| linestyle="dashed", | ||
| ) | ||
| plt.xlim(xlim) | ||
| plt.ylim(ylim) | ||
| plt.title("Catenary Final Shape") | ||
| plt.grid() | ||
| plt.legend() | ||
| plt.xlabel("x [m]", fontsize=16) | ||
| plt.ylabel("y [m]", fontsize=16) | ||
| plt.savefig("plot.png", dpi=300) | ||
| plt.show() |
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