Three Rod-examples

examples/CantileverDistributedLoad/cantilever_conservative_distributed_load.py

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+# from charset_normalizer.legacy import ResultDict
+from matplotlib import pyplot as plt
+import numpy as np
+import elastica as ea
+from cantilever_distrubuted_load_postprecessing import (
+    plot_video_with_surface,
+    Find_Tip_Position,
+    adjust_square_cross_section,
+)
+
+
+def Conservative_Force_Simulator(load, Animation=False):
+    class StretchingBeamSimulator(
+        ea.BaseSystemCollection, ea.Constraints, ea.Forcing, ea.Damping, ea.CallBacks
+    ):
+        pass
+
+    stretch_sim = StretchingBeamSimulator()
+    final_time = 10
+
+    # Options
+    PLOT_FIGURE = True
+    SAVE_FIGURE = False
+    SAVE_RESULTS = False
+    # setting up test params
+    n_elem = 100
+    start = np.zeros((3,))
+    direction = np.array([1.0, 0.0, 0.0])
+    normal = np.array([0.0, 1.0, 0.0])
+    base_length = 0.5
+    base_radius = 0.01 / (
+        np.pi ** (1 / 2)
+    )  # The Cross-sectional area is 1e-4(we assume its equivalent to a square cross-sectional surface with same area)
+    base_area = np.pi * base_radius**2
+    density = 1000  # nomilized with conservative case F=15
+    youngs_modulus = 1.2e7
+    dl = base_length / n_elem
+    dt = 0.1 * dl / 50
+    I = (0.01**4) / 12
+    end_force_x = (youngs_modulus * I * load) / (density * base_area * (base_length**3))
+    # For shear modulus of 1e4, nu is 99!
+    poisson_ratio = 0.0
+    shear_modulus = youngs_modulus / (2 * (poisson_ratio + 1.0))
+
+    rendering_fps = 30
+
+    stretchable_rod = ea.CosseratRod.straight_rod(
+        n_elem,
+        start,
+        direction,
+        normal,
+        base_length,
+        base_radius,
+        density,
+        youngs_modulus=youngs_modulus,
+        shear_modulus=shear_modulus,
+    )
+
+    adjust_section = adjust_square_cross_section(
+        n_elem,
+        direction,
+        normal,
+        base_length,
+        base_radius,
+        density,
+        youngs_modulus=youngs_modulus,
+        shear_modulus=shear_modulus,
+        rod_origin_position=start,
+        ring_rod_flag=False,
+    )
+
+    stretchable_rod.mass_second_moment_of_inertia = adjust_section[0]
+    stretchable_rod.inv_mass_second_moment_of_inertia = adjust_section[1]
+    stretchable_rod.bend_matrix = adjust_section[2]
+
+    stretch_sim.append(stretchable_rod)
+    stretch_sim.constrain(stretchable_rod).using(
+        ea.OneEndFixedBC, constrained_position_idx=(0,), constrained_director_idx=(0,)
+    )
+
+    Conservative_Load = np.array([0.0, -end_force_x, 0.0])
+
+    stretch_sim.add_forcing_to(stretchable_rod).using(
+        ea.GravityForces, acc_gravity=Conservative_Load
+    )
+
+    # add damping
+
+    damping_constant = 0.1
+
+    stretch_sim.dampen(stretchable_rod).using(
+        ea.AnalyticalLinearDamper,
+        damping_constant=damping_constant,
+        time_step=dt,
+    )
+
+    # Add call backs
+    class AxialStretchingCallBack(ea.CallBackBaseClass):
+        def __init__(self, step_skip: int, callback_params: dict):
+            ea.CallBackBaseClass.__init__(self)
+            self.every = step_skip
+            self.callback_params = callback_params
+
+        def make_callback(self, system, time, current_step: int):
+            if current_step % self.every == 0:
+                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["com"].append(
+                    system.compute_position_center_of_mass()
+                )
+                self.callback_params["radius"].append(system.radius.copy())
+                self.callback_params["velocity"].append(
+                    system.velocity_collection.copy()
+                )
+                self.callback_params["avg_velocity"].append(
+                    system.compute_velocity_center_of_mass()
+                )
+
+                self.callback_params["center_of_mass"].append(
+                    system.compute_position_center_of_mass()
+                )
+                self.callback_params["velocity_magnitude"].append(
+                    (
+                        stretchable_rod.velocity_collection[-1][0] ** 2
+                        + stretchable_rod.velocity_collection[-1][1] ** 2
+                        + stretchable_rod.velocity_collection[-1][2] ** 2
+                    )
+                    ** 0.5
+                )
+
+    recorded_history = ea.defaultdict(list)
+    stretch_sim.collect_diagnostics(stretchable_rod).using(
+        AxialStretchingCallBack, step_skip=200, callback_params=recorded_history
+    )
+
+    stretch_sim.finalize()
+    timestepper = ea.PositionVerlet()
+    # timestepper = PEFRL()
+
+    total_steps = int(final_time / dt)
+    print(stretch_sim)
+    print("Total steps", total_steps)
+    ea.integrate(timestepper, stretch_sim, final_time, total_steps)
+
+    relative_tip_position = np.zeros(
+        2,
+    )
+    relative_tip_position[0] = (
+        Find_Tip_Position(stretchable_rod, n_elem)[0] / base_length
+    )
+    relative_tip_position[1] = (
+        -Find_Tip_Position(stretchable_rod, n_elem)[1] / base_length
+    )
+
+    print(relative_tip_position)
+
+    if Animation:
+        plot_video_with_surface(
+            [recorded_history],
+            video_name="cantilever_conservative_distributed_load.mp4",
+            fps=rendering_fps,
+            step=1,
+            # The following parameters are optional
+            x_limits=(-0.0, 0.5),  # Set bounds on x-axis
+            y_limits=(-0.5, 0.0),  # Set bounds on y-axis
+            z_limits=(-0.0, 0.5),  # Set bounds on z-axis
+            dpi=100,  # Set the quality of the image
+            vis3D=True,  # Turn on 3D visualization
+            vis2D=False,  # Turn on projected (2D) visualization
+        )
+
+    relative_tip_position = np.zeros(
+        2,
+    )
+    relative_tip_position[0] = (
+        Find_Tip_Position(stretchable_rod, n_elem)[0] / base_length
+    )
+    relative_tip_position[1] = (
+        -Find_Tip_Position(stretchable_rod, n_elem)[1] / base_length
+    )
+
+    print(relative_tip_position)
+    return relative_tip_position
+
+
+Conservative_Force_Simulator(15, Animation=True)
+
+x_tip_experiment = []
+y_tip_experiment = []
+x_tip_paper = [
+    0.9912,
+    0.9309,
+    0.8455,
+    0.7613,
+    0.6874,
+    0.6249,
+    0.5724,
+    0.5281,
+    0.4906,
+    0.4584,
+    0.4306,
+    0.4064,
+    0.3851,
+]
+y_tip_paper = [
+    0.1241,
+    0.3411,
+    0.4976,
+    0.6031,
+    0.6745,
+    0.7243,
+    0.7603,
+    0.7871,
+    0.8077,
+    0.8239,
+    0.8370,
+    0.8478,
+    0.8568,
+]
+load_on_rod = np.arange(1, 26, 2)
+for i in load_on_rod:
+    x_tip_experiment.append(Conservative_Force_Simulator(i)[0])
+    y_tip_experiment.append(Conservative_Force_Simulator(i)[1])
+
+
+plt.plot(
+    load_on_rod,
+    x_tip_paper,
+    color="black",
+    marker="*",
+    linestyle="--",
+    label="Theoretical_x",
+)
+plt.plot(
+    load_on_rod,
+    y_tip_paper,
+    color="black",
+    marker="*",
+    linestyle=":",
+    label="Theoretical_y",
+)
+plt.scatter(
+    load_on_rod,
+    x_tip_experiment,
+    color="blue",
+    marker="s",
+    linestyle="None",
+    label="x_tip/L",
+)
+plt.scatter(
+    load_on_rod,
+    y_tip_experiment,
+    color="red",
+    marker="s",
+    linestyle="None",
+    label="y_tip/L",
+)
+
+plt.title("Conservative-Load Elastica Simulation Results")
+# Title
+plt.xlabel("Load")  # X-axis label
+plt.ylabel("x_tip/L and y_tip/L")  # Y-axis label
+plt.grid()
+plt.legend()  # Optional: Add a grid
+plt.show()  # Display the plot