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

考虑一端固定的杆，在自由端承受轴向力，该力会引发应力并导致杆件伸长。&#160;
随着轴向力的增加，伸长量也随之增加。轴向力与伸长量的关系曲线呈现出典型的载荷-变形曲线。
当杆件发生微小伸长时，轴向力所做的功等于轴向力与相应伸长量的乘积。
该功等于变形曲线下的面积，其宽度等于微小变形。
总功可以通过在伸长限度内对上述方程进行积分来计算，其值等于在相同伸长限度内载荷-变形曲线下的面积。
作用在杆上的总功代表输入系统的能量，称为应变能。
在弹性限度内，轴向力与伸长量成正比。因此，应变能与伸长量的平方成正比。

应变能

Strain Energy

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 应变能是材料科学和结构工程领域中的一个基本概念，用来描述材料或结构在荷载的作用下发生变形时所吸收的能量。
 
 假设有一根一端固定并在自由端承受轴向力的杆。该轴向力在杆内能够产生应力，从而导致其伸长。随着轴向力的逐渐增加，杆伸长的长度也会随之增加，这说明了所施加的力与产生的变形之间的直接关系。这种行为可以通过荷载-变形曲线来进行图形化表示。
 
 轴向力使杆发生伸长所做的功等于力与相应伸长量的乘积。从图形上来看，其中的功相当于给定伸长量中荷载-变形曲线下的面积。为了计能够算任何给定伸长量在杆上所做的总功，必须对伸长极限上对力-伸长方程来进行积分。总功表示了输入到系统的能量，该能量被存储为应变能。在材料的弹性极限内，由于弹性变形而储存在材料中的应变能 U 与伸长率的平方是成正比的。
 
 <img alt="Equation 1" src="/files/ftp_upload/15682/15682_Equation_1.svg" style="text-align: center; height: 52px;">
 应变能的概念使得工程师能够量化材料或部件中的能量吸收能力，这对于评估其承受载荷而不发生永久变形或失效的能力是至关重要的。应变能在各种工程应用中也发挥着关键作用，例如减震器、储能装置的设计以及对冲击力的分析。
 
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应变能是材料科学与结构工程领域的一个基本概念，描述材料或结构在受力变形过程中所吸收的能量。

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JoVE Core

Mechanical Engineering

机械工程

Unit 1

第一单元

Energy Methods

能量法

KEY TERMS AND CONCEPTS

关键术语与概念

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

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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...

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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 Mechanical Engineering offers concise, easy-to-understand animated videos covering key topics such as equilibrium, forces, truss analysis, and structural mechanics. Explore their real-world applications, and witness these concepts in action through scientist-led experiments.

mechanical engineering

Load-Deformation and Stored Strain Energy

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