"""Generate six low-cognitive-load bridge-engineering teaching figures. All numerical series in this file are dimensionless teaching examples unless a caption explicitly gives material/geometric parameters. They are not field measurements from a real bridge. """ from __future__ import annotations import csv from pathlib import Path import matplotlib as mpl import matplotlib.pyplot as plt import numpy as np ROOT = Path(__file__).resolve().parents[2] OUT = ROOT / "data-figures" OUT.mkdir(parents=True, exist_ok=True) # Paper-white, cyan-blue, coral and amber — high contrast, colour-blind robust. PAPER = "#FFFDF8" INK = "#16324F" MUTED = "#587084" CYAN = "#087E8B" CORAL = "#D95D39" AMBER = "#E5A000" GRID = "#D6E1E5" def set_style(): mpl.rcParams.update({ "font.family": "sans-serif", "font.sans-serif": ["Microsoft YaHei", "Noto Sans CJK SC", "SimHei", "Arial Unicode MS", "DejaVu Sans"], "axes.unicode_minus": False, "figure.facecolor": PAPER, "axes.facecolor": PAPER, "axes.edgecolor": MUTED, "axes.labelcolor": INK, "xtick.color": INK, "ytick.color": INK, "text.color": INK, "axes.titleweight": "bold", "axes.titlesize": 15, "axes.labelsize": 11, "xtick.labelsize": 10, "ytick.labelsize": 10, "svg.fonttype": "none", "savefig.facecolor": PAPER, }) def base_ax(ax): ax.grid(axis="y", color=GRID, linewidth=0.8, zorder=0) ax.spines[["top", "right"]].set_visible(False) ax.spines[["left", "bottom"]].set_color(MUTED) ax.tick_params(length=0) def footer(fig, text): fig.text(0.055, 0.025, text, color=MUTED, fontsize=8.5, ha="left", va="bottom") def save(fig, stem): fig.savefig(OUT / f"{stem}.svg", bbox_inches="tight", pad_inches=0.12) fig.savefig(OUT / f"{stem}.png", dpi=300, bbox_inches="tight", pad_inches=0.12) plt.close(fig) def write_csv(stem, columns, rows): with (OUT / f"{stem}.csv").open("w", newline="", encoding="utf-8-sig") as f: writer = csv.writer(f) writer.writerow(columns) writer.writerows(rows) def fig_scale(): stem = "01-scale-selfweight-capacity" lam = np.arange(0.5, 3.01, 0.25) moment = lam ** 4 capacity = lam ** 3 write_csv(stem, ["scale_lambda", "self_weight_moment_ratio", "capacity_ratio"], zip(lam, moment, capacity)) fig, ax = plt.subplots(figsize=(8.3, 5.1)) ax.plot(lam, moment, color=CORAL, lw=2.8, marker="o", ms=4, zorder=3) ax.plot(lam, capacity, color=CYAN, lw=2.8, marker="o", ms=4, zorder=3) ax.set_title("桥梁等比例放大后，为什么“更粗”反而更吃力？", loc="left", pad=14) ax.set_xlabel("几何尺度倍率 λ（原桥 = 1）") ax.set_ylabel("相对值（原桥 = 1）") ax.set_xlim(0.45, 3.32); ax.set_ylim(0, 86) ax.annotate("自重引起的弯矩 ∝ λ⁴", xy=(3, 81), xytext=(2.15, 72), color=CORAL, fontsize=10.5, arrowprops={"arrowstyle": "-", "color": CORAL, "lw": 1.2}) ax.annotate("同材料、几何相似截面能力 ∝ λ³", xy=(3, 27), xytext=(1.82, 36), color=CYAN, fontsize=10.5, arrowprops={"arrowstyle": "-", "color": CYAN, "lw": 1.2}) ax.axvline(1, color=MUTED, ls=":", lw=1) ax.text(1.04, 4, "原桥", color=MUTED, fontsize=9) base_ax(ax) footer(fig, "适用前提：同材料、完全几何相似；仅比较自重效应。量纲分析教学示意，非实桥测量。") fig.tight_layout(rect=(0.03, 0.07, 0.99, 1)) save(fig, stem) def fig_depth(): stem = "02-depth-stiffness-deflection" h = np.arange(0.5, 2.01, 0.125) inertia = h ** 3 deflection = h ** -3 write_csv(stem, ["depth_multiplier_h_h0", "inertia_ratio_I_I0", "deflection_ratio_delta_delta0"], zip(h, inertia, deflection)) fig, ax = plt.subplots(figsize=(8.3, 5.1)) ax.plot(h, inertia, color=CYAN, lw=2.8, zorder=3) ax.plot(h, deflection, color=CORAL, lw=2.8, zorder=3) ax.scatter([1, 1], [1, 1], color=INK, s=20, zorder=4) ax.set_title("同一跨径下，梁高增加一点，刚度和挠度会怎样变？", loc="left", pad=14) ax.set_xlabel("梁高倍率 h / h0") ax.set_ylabel("相对值（基准梁 = 1）") ax.set_xlim(0.46, 2.22); ax.set_ylim(0, 8.8) ax.annotate("截面惯性矩 I ∝ h³", xy=(2, 8), xytext=(1.48, 7.2), color=CYAN, fontsize=10.5, arrowprops={"arrowstyle": "-", "color": CYAN, "lw": 1.2}) ax.annotate("同条件挠度 δ ∝ 1 / h³", xy=(0.5, 8), xytext=(0.77, 6.5), color=CORAL, fontsize=10.5, arrowprops={"arrowstyle": "-", "color": CORAL, "lw": 1.2}) base_ax(ax) footer(fig, "适用前提：矩形或等比例截面、材料与跨径不变，线弹性小挠度。无量纲教学示意，非设计计算。") fig.tight_layout(rect=(0.03, 0.07, 0.99, 1)) save(fig, stem) def fig_cable(): stem = "03-cable-sag-horizontal-force" sag_ratio = np.arange(0.4, 2.51, 0.1) # f/f0 force_ratio = 1 / sag_ratio write_csv(stem, ["sag_ratio_f_f0", "horizontal_force_ratio_H_H0"], zip(sag_ratio, force_ratio)) fig, ax = plt.subplots(figsize=(8.3, 5.1)) ax.plot(sag_ratio, force_ratio, color=CYAN, lw=2.8, zorder=3) ax.scatter([1], [1], color=INK, s=24, zorder=4) ax.set_title("抛物线索的垂度变大，主缆水平力如何变化？", loc="left", pad=14) ax.set_xlabel("垂度倍率 f / f0") ax.set_ylabel("水平力倍率 H / H0") ax.set_xlim(0.35, 2.72); ax.set_ylim(0, 2.8) ax.annotate("H / H0 = f0 / f", xy=(2.5, 0.4), xytext=(1.66, 0.87), color=CYAN, fontsize=11, arrowprops={"arrowstyle": "-", "color": CYAN, "lw": 1.2}) ax.annotate("基准状态", xy=(1, 1), xytext=(1.13, 1.45), color=MUTED, fontsize=9.5, arrowprops={"arrowstyle": "-", "color": MUTED, "lw": 1}) base_ax(ax) footer(fig, "适用前提：均布竖向荷载下的抛物线索；跨径、荷载不变，忽略索自重与大位移。无量纲教学示意。") fig.tight_layout(rect=(0.03, 0.07, 0.99, 1)) save(fig, stem) def fig_wind(): stem = "04-wind-speed-square-law" v_ratio = np.arange(0.4, 2.01, 0.1) f_ratio = v_ratio ** 2 write_csv(stem, ["wind_speed_ratio_V_V0", "wind_force_ratio_F_F0"], zip(v_ratio, f_ratio)) fig, ax = plt.subplots(figsize=(8.3, 5.1)) ax.plot(v_ratio, f_ratio, color=CORAL, lw=2.8, zorder=3) ax.scatter([1, 2], [1, 4], color=INK, s=25, zorder=4) ax.set_title("风速翻倍时，风力为什么不是翻倍而是四倍？", loc="left", pad=14) ax.set_xlabel("风速倍率 V / V0") ax.set_ylabel("风力倍率 F / F0") ax.set_xlim(0.35, 2.22); ax.set_ylim(0, 4.85) ax.annotate("F / F0 = (V / V0)²", xy=(2, 4), xytext=(1.18, 4.25), color=CORAL, fontsize=11, arrowprops={"arrowstyle": "-", "color": CORAL, "lw": 1.2}) ax.annotate("2V0 → 4F0", xy=(2, 4), xytext=(1.57, 3.22), color=INK, fontsize=9.5, arrowprops={"arrowstyle": "-", "color": INK, "lw": 1}) base_ax(ax) footer(fig, "适用前提：空气密度 ρ、阻力系数 C_d 和迎风面积 A 固定，F = ½ρC_dAV²。无量纲教学示意。") fig.tight_layout(rect=(0.03, 0.11, 0.99, 1)) save(fig, stem) def fig_amplification(): stem = "05-single_dof_dynamic-amplification" r = np.linspace(0, 2, 801) zetas = [(0.03, CORAL), (0.08, AMBER), (0.20, CYAN)] cols = ["frequency_ratio_r"] + [f"amplification_zeta_{z:.2f}" for z, _ in zetas] vals = [r] + [1 / np.sqrt((1-r**2)**2 + (2*z*r)**2) for z, _ in zetas] write_csv(stem, cols, zip(*vals)) fig, ax = plt.subplots(figsize=(8.3, 5.1)) for zeta, color in zetas: amp = 1 / np.sqrt((1-r**2)**2 + (2*zeta*r)**2) ax.plot(r, amp, color=color, lw=2.5, zorder=3) peak_i = int(np.argmax(amp)) ax.text(r[peak_i] + 0.055, amp[peak_i], f"ζ = {zeta:.2f}", color=color, fontsize=9.6, va="center", ha="left") ax.axvline(1, color=MUTED, ls=":", lw=1.2) ax.text(0.52, 17.15, "共振附近 r = 1", color=MUTED, fontsize=9.5) ax.set_title("激励频率接近自振频率时，阻尼为何决定响应峰值？", loc="left", pad=14) ax.set_xlabel("频率比 r = 激励频率 / 自振频率") ax.set_ylabel("稳态放大系数") ax.set_xlim(0, 2.28); ax.set_ylim(0, 18.3) base_ax(ax) footer(fig, "适用前提：线性单自由度、简谐外力、稳态响应；ζ 为阻尼比。模型曲线，非特定桥梁的实测振动。") fig.tight_layout(rect=(0.03, 0.07, 0.99, 1)) save(fig, stem) def fig_mesh_convergence(): stem = "06-simply-supported-beam-mesh-convergence" # Exact Euler–Bernoulli result: delta_max = 5qL^4/(384EI). L, q, E, I = 10.0, 20_000.0, 30e9, 0.12 exact_mm = 5*q*L**4/(384*E*I)*1000 elements = np.array([2, 4, 8, 16, 32]) # Explicit teaching-only second-order error model: e=0.8(h/L)^2. err_pct = 80 / elements**2 approx_mm = exact_mm * (1 - err_pct/100) write_csv(stem, ["elements_N", "element_size_over_span_h_L", "exact_midspan_deflection_mm", "teaching_approx_deflection_mm", "theoretical_relative_error_percent"], zip(elements, 1/elements, np.full_like(elements, exact_mm, dtype=float), approx_mm, err_pct)) fig, (ax0, ax1) = plt.subplots(1, 2, figsize=(10.0, 4.9), gridspec_kw={"width_ratios": [1.05, 1.35]}) # Minimal structural context diagram. ax0.set_xlim(-0.5, 10.5); ax0.set_ylim(-1.8, 2.4); ax0.axis("off") ax0.plot([0, 10], [0, 0], color=INK, lw=4, solid_capstyle="round") ax0.fill([0, -0.38, 0.38], [-0.15, -0.8, -0.8], color=CYAN) ax0.plot([9.55, 10.45], [-0.75, -0.75], color=CYAN, lw=2.5) ax0.add_patch(plt.Circle((10, -0.45), 0.17, color=CYAN)) for x in np.linspace(0.7, 9.3, 7): ax0.annotate("", xy=(x, 0.23), xytext=(x, 1.25), arrowprops={"arrowstyle": "-|>", "color": CORAL, "lw": 1.4}) ax0.text(5, 1.54, "均布荷载 q = 20 kN/m", ha="center", color=CORAL, fontsize=10.5) ax0.annotate("", xy=(0, -1.28), xytext=(10, -1.28), arrowprops={"arrowstyle": "<->", "color": MUTED, "lw": 1.1}) ax0.text(5, -1.61, "L = 10 m", ha="center", color=MUTED, fontsize=10) ax0.text(5, -0.43, f"解析解：δ_max = 5qL⁴/(384EI) = {exact_mm:.3f} mm", ha="center", color=INK, fontsize=9.5) ax0.set_title("可解析的简支梁", loc="left", fontsize=12.5, pad=8) ax1.plot(elements, err_pct, color=CYAN, lw=2.8, marker="o", ms=6, zorder=3) ax1.set_xscale("log", base=2); ax1.set_yscale("log") ax1.set_xticks(elements); ax1.get_xaxis().set_major_formatter(mpl.ticker.ScalarFormatter()) ax1.set_xlabel("单元数 N（每增加一倍，h/L 减半）") ax1.set_ylabel("相对误差（%）") ax1.set_title("网格加密后，教学示意误差如何下降？", loc="left", fontsize=12.5, pad=8) ax1.annotate("设定的二阶收敛：误差 = 80 / N² %", xy=(16, 0.3125), xytext=(4.7, 2.8), color=CYAN, fontsize=9.8, arrowprops={"arrowstyle": "-", "color": CYAN, "lw": 1.1}) base_ax(ax1) footer(fig, "适用前提：Euler–Bernoulli 梁，E = 30 GPa，I = 0.12 m⁴。本误差序列按显式二阶教学模型构造，不是有限元或实桥测量。") fig.suptitle("有了解析解后，怎样判断网格是否足够细？", x=0.06, ha="left", fontsize=15, fontweight="bold", y=0.98) fig.tight_layout(rect=(0.03, 0.07, 0.99, 0.94)) save(fig, stem) if __name__ == "__main__": set_style() fig_scale() fig_depth() fig_cable() fig_wind() fig_amplification() fig_mesh_convergence() print(f"Wrote figures and CSV files to {OUT}")