第五章非线性有限元法.pdfVIP

5. FEM of material non-linearity 5.1 Solution of non-linear algebraic equations 5.2 弹塑性理论简介 5.3 Elastic-Plastic FE equations in increment form 5.4 应力增量的计算本构积分 5.5 动力学问题有限元法 1 Non-linear behaviour of solids: ◆ material non-linearity ◆ Geometric non-linearity ■Material non-linearity: ●the loading and unloading response of the material is different. ● Typical here is the case of classical elastic–plastic and viscoelastic behavior, non- linear ■ Finite deformation: Geometric non-linearity 大变形 2 5.1 Solution of non-linear algebraic equations [ ]T 方程 [k (u)]{u} = {f } u = u1 u2 u3 ...un T 初值 0 [ 0 0 0 0 ] u = u u u ...u 1 2 3 n 例如 ：  2 2 2 x1 + x2 + x3 −1.0 = 0 1      2x 2 + x 2 − 4x = 0 初值 1  1 2 3    2 2   1 3x − 4x + x = 0    1 2 3 K(u) x x x    x 1.0 1 2 3 1   与便利有关 