はりの大たわみの近似式に基づくヤング率測定法（片持ちはりおよび3 点曲げの場合）

たわみやすいはりが大変形の下にあるときのヤング率測定法を提案する．特に，片持ちはりと3点曲げのたわみをヤング率の測定に利用する．本手法は，大たわみの厳密解を簡単で高精度な多項式で近似することに基づいている．この多項式を用いれば，複雑な楕円関数を用いることなく大たわみのもとでの荷重と変位の関係を得ることができ，ヤング率の測定が容易である．本手法の有効性を確認するために，ピアノ線を用いた実験を行う．本手法は，可撓性薄板やほかのたわみやすい材料のヤング率の測定にも適用可能である．

A measurement method is established to determine the elastic modulus of slender, flexible beams when they are subjected to the large deflections. Specifically, the deflections of cantilever beam and simply supported beam is used to determine the modulus of elasticity, Young's modulus. Present method is based on approximate formulas for the nonlinear relation between deflection and load under large deflection. By using the approximate formulas, we can easily obtain the dimensionless load parameters corresponding to the deflection without employing elliptical functions. The approach is validated with experiments using a steel piano wire. While this approximation formulas are easy to use and simple, it
has high-precise approximation to the exact solution, consisting from elliptic integrals. Present method is also applicable to flexible thin plates and extremely delicate materials in order to obtain a quick estimate of the material's elastic modulus.

Large deflection, Cantilever, Three point bending, Young's modulus, Material testing