清华大学有限元分析课件3-1 Strong Form in 1D Problems_511502339.pdfVIP

第3章 一维问题 3.1 强形式 Strong Form in 1D Problems [Fish]-3.1 Finite Element Method 3.1 强形式 One-dimensional elasticity l  Overview of basic relations ²  Equilibrium equation Δx −p (x ) + b(x + )Δx + p (x + Δx ) = 0 2 p (x ) = A(x )σ (x ) p (x + Δx ) − p (x ) Δx + b(x + ) = 0 Δx 2 Δx dp (x ) + b(x ) = 0 p (x ) b(x + Δx ) p (x + Δx ) dx 2 u(x ) u(x + Δx ) ²  Elastic stress–strain law σ (x ) = E (x )ε (x ) ²  Strain–displacement equation u(x + Δx ) − u(x ) A(x ) b(x ) ε (x ) = Δx t x ,u du = x = 0 dx x = l 2/6 School of Aerospace, Tsinghua University Finite Element Method 3.1 强形式 One-dimensional elasticity l  Overview of basic relations d ⎛ du(x ) ⎞ dx ⎜ A(x )E (x ) dx ⎟+ b(x ) = 0, 0 x l ⎝ ⎠ du p (0) σ (0) = (E dx )x =0 = A(0) ≡ − t σ n = t u(l) = u l  Strong form of the one-dimensional elasticity Find u(x) smooth enough such that: