Name: load-deformation and stored strain energy
Uploaded: 2025-05-22T09:06:18.000Z
Duration: 1 min 13 s
Channel: JoVE

ロッドが一端に固定され、自由端で軸方向の力を受けると、応力が誘発され、ロッドが伸びると考えてください。
軸力が大きくなると、伸びが増加します。軸力と伸びの関係をプロットすると、特性荷重-変形プロットが得られます。
ロッドがわずかに伸びるときに軸力によって行われる仕事は、軸力と対応する伸びの積です。
この作業は変形プロットの下の面積に等しく、その幅は小さな変形に等しくなります。
行われた総仕事量は、伸び限界内で方程式を積分することによって計算でき、同じ伸び限界内の荷重-変形曲線の下の面積に等しくなります。
ロッドで行われた合計作業は、ひずみエネルギーと呼ばれるシステムへの入力エネルギーを表します。
弾性限界内では、軸力は伸びの量に比例します。したがって、ひずみエネルギーは伸びの2乗に比例します。

ひずみエネルギー

Strain Energy

ひずみエネルギーは、材料科学および構造工学の分野における基本概念であり、荷重を受けて変形したときに材料または構造によって吸収されるエネルギーを表します。

一端が固定され、自由端で軸方向の力を受ける棒を考えてみましょう。この軸力により棒内に応力が生じ、棒の伸びが生じます。軸力が増加すると棒の伸びも増加し、加えられる力と結果として生じる変形との直接的な関係がわかります。この動作は、荷重-変形プロットによってグラフで表すことができます。

棒を少量だけ伸ばすために軸方向の力によって行われる仕事は、力と対応する伸びの積に等しくなります。グラフ的には、この作業は、特定の伸びに対する荷重変形曲線の下の領域に対応します。任意の伸びに対して棒に加えられた総仕事量を計算するには、伸びの限界にわたって力と伸びの方程式を積分する必要があります。この合計仕事量は、装置へのエネルギー入力を表し、ひずみエネルギーとして保存されます。材料の弾性限界内では、弾性変形によって材料に蓄えられるひずみエネルギー U は伸びの 2 乗に比例します。

<img alt="Equation 1" src="/files/ftp_upload/15682/15682_Equation_1.svg" style="height: 52px;">

ひずみエネルギーの概念により、エンジニアは材料や部品のエネルギー吸収能力を定量化できます。これは、永久変形や破損を起こすことなく荷重に耐える能力を評価するために不可欠です。ひずみエネルギーは、ショックアブソーバーやエネルギー貯蔵装置の設計、衝撃力の解析など、さまざまな工学用途でも重要な役割を果たします。

ロッドが一端に固定され、自由端で軸方向の力を受けると、応力が誘発され、ロッドが伸びると考えてください。
として...

Education

JoVE Core

Mechanical Engineering

機械工学

Unit 1

ユニット1

Energy Methods

エネルギー法

KEY TERMS AND CONCEPTS

主要用語と概念

load-deformation and stored strain energy

Strain energy is the energy stored in a material when it deforms under load. It is a key idea in materials science and structural engineering. A loaded rod fixed at one end shows this clearly. When an axial force pulls on the free end, the rod stretches and stress builds inside it.

As the axial force increases, the rod elongates more. This creates a direct link between the applied force and the amount of deformation. Engineers can show this relationship with a load-deformation plot. The plot makes it easier to see how much the rod stretches at each load.

The work done by the axial force over a small elongation is the force multiplied by that elongation. On the graph, this work appears as the area under the load-deformation curve for a given elongation. To find the total work for any elongation, the force-elongation equation is integrated over the elongation limits. That total work is the energy put into the system, and it is stored as strain energy.

Within the elastic limit of the material, the strain energy stored in the rod is proportional to the square of the elongation. This means the stored energy rises as the deformation increases, as long as the material still behaves elastically. Knowing strain energy helps engineers judge how much energy a material or component can absorb before permanent deformation or failure. It is also useful in shock absorbers, energy storage devices, and impact force analysis.

Load-Deformation and Stored Strain Energy

load-deformation-and-stored-strain-energy

strain energy

Strain energy is the energy stored in a material when it deforms under load. It is a key idea in materials science and structural engineering. A loaded rod fixed at one end shows this clearly. When an axial force pulls on the free end, the rod stretches and stress builds inside it. As the axial force increases, the rod elongates more. This creates a direct link between the applied force and the amount of deformation. Engineers can show this relationship with a load-deformation plot. The plot...

strain-energy density

Energy Stored in Loaded Rods

Energy stored in a rod under axial load helps show how a material will respond to stretching and breaking. When the rod elongates, it stores strain energy as potential energy inside the material. Strain energy density is the amount of that energy per unit volume. In the elastic region, stress and strain have a linear relationship that follows Hooke's Law. The strain energy density in this region is found from the area under the stress-strain curve up to the elastic limit. This recoverable...

elastic strain energy for normal stresses

elastic-strain-energy-for-normal-stresses

Strain Energy in Stressed Materials

Strain energy in stressed materials describes the energy stored when a material deforms under load. It is an important idea in materials science and engineering. For axial loading with a uniform stress distribution, the stress is the internal force divided by the cross-sectional area, and the strain follows from the stress through the modulus of elasticity. When the stress is uniform, the strain energy density can be found from the product of stress and strain. That density is then integrated...

elastic strain energy for shearing stresses

elastic-strain-energy-for-shearing-stresses

Shear Energy Stored in Twisted Shafts

Shear energy stored in twisted shafts depends on elastic strain energy in a material. This energy is stored when a solid is deformed within its elastic limit. It comes from internal work done against the cohesive forces inside the material. When a material carries shearing stress, it also develops shearing strain. The strain energy density is the energy stored per unit volume. Within the elastic limit, stress is proportional to strain through the modulus of rigidity, so the strain energy...

impact loading

Impact Loading on a Fixed Rod

Impact loading on a fixed rod happens when a moving object strikes a stationary rod that has a uniform cross-sectional area and is fixed at one end. The impact makes the rod deform and begin to develop stress. This setup shows how a sudden hit can store energy in a structure. As the rod moves back toward its original shape, the stress rises to a maximum. At that point, the energy from the moving object has changed from kinetic energy into strain energy. Kinetic energy is the energy of motion,...

impact loading on a cantilever beam

Dropped-Weight Bending of a Cantilever Beam

Dropped-weight bending of a cantilever beam shows how impact loading changes a beam’s shape and stress. The beam has a circular cross-section and is fixed at one end. An object is dropped on the free end from a height h, so its potential energy from gravity becomes kinetic energy at impact. After the object hits the beam, the beam bends and develops a bending moment along its length. The bending is not uniform. The fixed end carries the highest strain energy, which is the energy stored in the...

castigliano&#39;s theorem

Using Strain Energy to Find Deflection

Castigliano's theorem uses strain energy to find deflection and rotation in elastic structures. Strain energy is the work done by external loads during elastic deformation. The theorem links that energy to the movement caused by the load. The key idea is simple. The partial derivative of the total strain energy with respect to a specific force gives the displacement at the point where that force acts. The same method also works for a moment, where the derivative gives the rotation at the point...

castigliano&#39;s theorem: problem solving

Beam Deflection from Central Load

Beam deflection from a central load can be found with Castigliano's theorem. The method applies to a simply supported beam with a point load at the center. It links the deflection at the load point to the strain energy stored in the beam. For this beam, the supports share the load equally. Each support carries half of the force. The bending moment at any point along the beam comes from these reactions and is written using the distance from the nearest support. Castigliano's theorem says the...

key terms and concepts

Explore how load creates deformation in a rod, how work becomes stored strain energy, and why this matters in shock absorbers and impact analysis.

Load-Deformation and Stored Strain Energy | JoVE K12

JoVE Core 機械工学は、平衡、力、トラス解析、構造力学などの重要なトピックをカバーする簡潔でわかりやすいアニメーション ビデオを提供します。実際のアプリケーションを探索し、科学者主導の実験を通じてこれらのコンセプトが実際に動作しているのを目撃してください。

mechanical engineering

Load-Deformation and Stored Strain Energy

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