有限元方法 绪论 有限单元法 有限元法：基于近代计算机快算发展而发展出的求解偏微分方程边值问题近似解的数值技术 核心思想：离散化+数值近似 固体力学控制微分方程 梁弯曲问题, 挠度ω(x)\omega(x)ω(x) EJd4ω(x)dx4−q=0EJ\frac{\mathrm{d}^4\omega(x)}{\mathrm{d}x^4}-q=0 EJdx4d4ω(x)​−q=0 悬臂梁边界条件, 固定端挠度转角为零，自由端弯矩剪力为零 {x=0: ω=0,ω′(x)=0x=l: ω′′(x)=0,ω′′′(x)=0\begin{cases} x=0: \ \omega=0,\omega\prime(x)=0 \\ x=l: \ \omega\prime\prime(x)=0,\omega\prime\prime\prime(x)=0 \end{cases} {x=0: ω=0,ω′(x)=0x=l: ω′′(x)=0,ω′′′(x)=0​ 薄板弯曲问题, 挠度 D∇4ω(x,y)=q(x,y)D \nabla^4 \omega(x,y)=q(x,y) D∇ ...

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