绪论

• 研究对象：强度、刚度、稳定性
• 连续性假设、均匀性假设、各向同性假设

外力分类

• 静载荷、动载荷
• 应力

基本概念

• Strain \[\begin{align} \varepsilon=\lim_{\Delta x\rightarrow0}\frac{\Delta s}{\Delta x} \end{align} \]
• 切应变 \[\begin{align} \gamma=\lim_{ML、MN\rightarrow0}(\frac{\pi}{2}-\angle L'M'N') \end{align}\]
• 名义应力(工程应力)
• 真实应力

拉伸、压缩

Method of sections

Sign convention for axial force

• Tensile force
• Compressive force

Deformation phenomenon

• Plane assumption

• 弹性模量 modulus of elasticity \[\begin{align}E=\frac{\sigma}{\varepsilon} \end{align}\]

• Formula for normal stress \[\begin{align}\sigma=\frac{F_N}{A} \end{align}\]

• Stress on an inclined plane Mechanical properties of materials in axial tension and compression

• Tension diagram

• Stress-strain diagram

• 塑形材料 Ductile material \(\delta \geq5\%\)

• 冷却硬化

  • Elastic strain\(\varepsilon_e\)
  • Plastic strain\(\varepsilon_p\)

• 脆性材料 Brittle material \(\delta <5\%\)

• 比例极限 Proportional limit \(\sigma_p\)

• 卸载定律 Unloading law yielding

• 屈服极限 Yielding Strength \(\sigma_s\)

hardening

• 强度极限 Ultimate Strength \(\sigma_b\)

necking

• 伸长率 Percent elongation
• 断面收缩率 Percent reduction in area
• 蠕变 creeping&relaxation

Axial deformation

\[\begin{align} \Delta l=\frac{F_Nl}{EA} \end{align}\] \(E\) is the modulus of elasticity
And we call \(EA\) rigidity - Poisson's ratio \[\begin{align} \mu=-\frac{\varepsilon'}{\varepsilon} \end {align}\] \(\varepsilon'\) is Lateral strain

• Allowable stress\(\left[ \sigma \right]\)
  \(\left[ \sigma \right]=\frac{\sigma_u}{n}\)
  \(n\) is factor of safety

• 理论应力集中因数 Stress concentration factor \[\begin{align}\kappa=\frac{\sigma_{max}}{\sigma}\end{align}\]

• 应变能 \[\begin{align}V&=W=\frac{1}{2}F\Delta l\\&=\frac{F^2l}{2EA} \end{align}\] 多用于难以找几何条件的题目

超静定

• 列变形协调方程 温度应力和装配应力