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20250204123422.png differ diff --git a/Pasted image 20250204124026.png b/Pasted image 20250204124026.png new file mode 100644 index 0000000..a8063c6 Binary files /dev/null and b/Pasted image 20250204124026.png differ diff --git a/Pasted image 20250204124109.png b/Pasted image 20250204124109.png new file mode 100644 index 0000000..f9c999b Binary files /dev/null and b/Pasted image 20250204124109.png differ diff --git a/Pasted image 20250204124240.png b/Pasted image 20250204124240.png new file mode 100644 index 0000000..9640966 Binary files /dev/null and b/Pasted image 20250204124240.png differ diff --git a/补课/材料力/笔记.md b/补课/材料力/笔记.md new file mode 100644 index 0000000..4586b43 --- /dev/null +++ b/补课/材料力/笔记.md @@ -0,0 +1,130 @@ + +刚度 -- 抵抗**变形**的能力 + +材料力学研究构件的 强度 刚度 稳定性 + +孙训方《材料力学》一二 + +# 基本假设 + +1 连续性假设，材料是连续分布的 +2 均匀性假设，材料是均匀分布的 +3 各向同性假设，材料再各个方向上的力学性能相同 + +小变形问题： +1 材料力学要研究变形、计算变形 +2 变形与构件的原始尺寸相比很小 +3 受力分析按照构件的原始尺寸计算 + +基本变形 4种 +拉压 扭转 弯曲 剪切 + +# 轴向拉伸和压缩 + + +拉压 弯 剪 扭 + +## 拉压 +变形特点 轴线方向伸长或缩短，横向缩短或伸长 +几何形状 等直杆：轴线是笔直的 +横截面的形状和尺寸不变，可以分段等直 + +![[Pasted image 20250124172148.png]] + +受力特点：外力或合力的作用线与轴线重合 + +## 内力、截面法、轴力及轴力图 + +集中力及其作用点 +分布载荷及其集度 + +轴力 沿着轴的内力 拉为正，压为负 +外力只有方向，没有正负 + +![[Pasted image 20250124174502.png]] + +![[Pasted image 20250124174629.png]] + +## 应力 拉（压）杆内的应力 + +![[Pasted image 20250124181513.png]] +杆件两端收拉，截面横截面各处都有轴力 +横截面每个点受到的力 称为应力，应力与其作用面垂直 称为正应力normal stress σ +正应力的正 只表示与作用面垂直 + +![[Pasted image 20250124182138.png]] + +正应力计算公式：轴力除以面积 +$$ +σ = F_N / A +$$ +使用条件 +- 拉压变形的平面假设成立 +- 在集中载荷作用区附近和截面发生剧烈变化的区域，横截面上的应力情况复杂，上述公式不再正确 计算时不考虑应力集中 +- 对工程中大多数横截面形状都适用；但对于平面假设不成立的某些特定截面，上述公式不适用 + +单位 N/m2 帕 Pa +轴力 = 正应力 乘 面积 +$$ +F_N = σ A +$$ + +圣维南原理： +力作用于杆端方式的不同，只会使与杆端距离不大于杆的横向尺寸的范围内受到影响 + +变截面杆件 变截面部分，打孔杆件孔的周围易出现应力集中现象 +![[Pasted image 20250124190040.png]] + +## 强度条件 安全系数 许用应力 + +强度条件 最大的正应力小于许用正应力 +$$ +σ_{max} ≤ [σ] +$$ +控制住整个杆件最大的正应力，整个杆件就安全了 + + +## 拉（压）杆的变形-胡克定律 + +刚度问题 弹性变形问题 +### 拉（压）杆的纵向变形 + +拉压胡克定律 + +![[Pasted image 20250204103838.png]] + +Δl 正比于 Fl/A +引入一个系数E - 弹性模量，将正比写成等式 +弹性模量表示材料的属性软硬，EA - 拉压刚度，表示杆件的属性 + +![[Pasted image 20250204105436.png]] + +小变形：变形量较主尺度非常小 千分之一？ + +![[Pasted image 20250204114310.png]] + +线应变 + +![[Pasted image 20250204114538.png]] +线应变 因Δl有正负而有正负 + +轴力/面积 Fn/A 为正应力 + +### 拉（压）杆的横向变形 +材料横向、纵向变形线应变的比值是定值 - 泊松比 +![[Pasted image 20250204115538.png]] +![[Pasted image 20250204115635.png]] +![[Pasted image 20250204120006.png]] + +## 材料在拉伸和压缩时的力学性能 + +![[Pasted image 20250204121642.png]] + +![[Pasted image 20250204122335.png]]![[Pasted image 20250204122801.png]]![[Pasted image 20250204122958.png]] + +波动段，应力上下波动，第一个波动最低点不稳定，取第二个及以后波动取最小的数值作为应力最低点 -- 作为屈服极限 + +![[Pasted image 20250204123254.png]]![[Pasted image 20250204123422.png]] +从强化阶段开始卸载，总应变包含两个部分 -- 弹性应变（可以恢复）+ 塑性应变（不可恢复） + +![[Pasted image 20250204124026.png]]![[Pasted image 20250204124109.png]]![[Pasted image 20250204124240.png]] \ No newline at end of file