补充:关于离散 About discretization In reality elements are connected together along their common boundaries. Here it is assumed that these elements are only interconnected at their nodes 实际:单元间相连定:只结点相连 徐汉忠第一版2000/7 弹性力学第六章有限元 16
徐汉忠第一版2000/7 弹性力学第六章有限元 16 补充：关于离散 About Discretization • In reality Elements are connected together along their common boundaries. Here it is assumed that these elements are only interconnected at their nodes. 实际：单元间相连----假定：只结点相连
关于离散-2 However in the finite element method the individual elements are constrained to deform in specific patterns. 然而,单元变形按指定模式 徐汉忠第一版2000/7 弹性力学第六章有限元
徐汉忠第一版2000/7 弹性力学第六章有限元 17 关于离散-2 • However,in the finite element method, the individual elements are constrained to deform in specific patterns. 然而，单元变形按指定模式
关于离散-3 Hence, although continuity is onl specified at the nodal points, the choice of a suitable pattern of deflection for the elements can lead to the satisfaction of some, if not all, of the continuity requirements along the sides of adjacent elements 位移模式使相连单元位移连续得某些满 足 徐汉忠第一版2000/7 弹性力学第六章有限元
徐汉忠第一版2000/7 弹性力学第六章有限元 18 关于离散--3 • Hence, although continuity is only specified at the nodal points, the choice of a suitable pattern of deflection for the elements can lead to the satisfaction of some,if not all,of the continuity requirements along the sides of adjacent elements. 位移模式使相连单元位移连续得某些满 足
关于离散-4 Hence, as stated by Clough, finite elements are not merely pieces cut from the original structure, but are special types of elastic elements constrained to deform in specific patterns such that the overall continuity of the assemblage tends to be maintained? 徐汉忠第一版2000/7 弹性力学第六章有限元
徐汉忠第一版2000/7 弹性力学第六章有限元 19 关于离散--4 • Hence, as stated by Clough, ‘finite elements are not merely pieces cut from the original structure, but are special types of elastic elements constrained to deform in specific patterns such that the overall continuity of the assemblage tends to be maintained’
6.3 Displacement pattern and convergence criteria 63位移模式和收敛性 Element with nodes numbered单元的结点编号 Fig. I shows the typical triangular element with nodes ijm numbered in an anti-clockwise order. m 图1为一典型的三角形单元, 结点im逆钟向编号-x正向到 y正向。 X 徐汉忠第一版2000/7 弹性力学第六章有限元
徐汉忠第一版2000/7 弹性力学第六章有限元 20 6.3 Displacement pattern and convergence criteria 6.3 位移模式和收敛性 • Fig. 1 shows the typical triangular element with nodes ijm numbered in an anti-clockwise order. Y m 图1为一典型的三角形单元， i 结点 ijm 逆钟向编号--x正向到 j y正向。 Fig..1 x Element with nodes numbered 单元的结点编号