{
  "assumptions": [
    "杆件为直径恒定的圆形实心截面。",
    "材料处于线弹性范围，采用均匀单轴拉伸模型。"
  ],
  "calculationType": "轴向拉伸应力与伸长量计算",
  "inputs": {
    "diameter_mm": 20,
    "elastic_modulus_GPa": 200,
    "force_N": 10000,
    "length_mm": 1000
  },
  "method": "圆形实心截面按 A=πd²/4；轴向应力按 σ=F/A；将 E 从 GPa 换算为 N/mm²（1 GPa=1000 N/mm²），伸长量按 δ=FL/(AE)。",
  "result": {
    "axial_stress": 31.830988618379067,
    "cross_sectional_area": 314.1592653589793,
    "elongation": 0.15915494309189535
  },
  "units": {
    "axial_stress": "MPa",
    "cross_sectional_area": "mm²",
    "elongation": "mm"
  },
  "warnings": []
}