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Chapter 27

Energy Methods

应变能
应变能
Consider a rod fixed at one end and subjected to an axial force at the free end, which induces stress and leads to elongation in the rod.  As the ...
应变-能量密度
应变-能量密度
An axial load causes a rod to elongate, and store strain energy in it. The strain energy density in the rod is the energy per unit volume. Here, the ratio ...
法向应力的弹性应变能
法向应力的弹性应变能
When a material is subjected to an axial loading, it experiences normal stress, leading to strain energy generation. This equation is valid for uniformly ...
剪切应力的弹性应变能
剪切应力的弹性应变能
When the material is subjected to a shearing stress, the strain energy density can be expressed in integral form as the product of the shearing stress and ...
冲击载荷
冲击载荷
Consider a rod of uniform cross-sectional area fixed at one end. When another moving object hits the free end of the rod, the rod deforms, and stress is ...
悬臂梁上的冲击载荷
悬臂梁上的冲击载荷
Consider a cantilever beam fixed at one end, having a circular cross-section. If an object is dropped on the free end of the cantilever from a height h, ...
卡斯蒂利亚诺定理
卡斯蒂利亚诺定理
Castigliano's theorem is useful for determining displacements and rotations in structures undergoing elastic deformations. It states that the partial ...
Castigliano 定理:解决问题
Castigliano 定理:解决问题
Consider a simply supported beam PQ of length L, carrying a point load F at the center. What will be the deflection at the center of the beam? Here, the ...
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