Finite Element Method with Applications in Engineering

8.3 EIGHT-NODE ISOPARAMETRIC ELEMENT FOR THREE-DIMENSIONAL STRESS ANALYSIS

Formulation presented for 4-node isoparametric element presented in the previous chapter for two-dimensional stress analysis has been extended here to 8-node element for three-dimensional stress analysis. A typical element from the discretized domain is shown in Figure 8.6. Intrinsic co-ordinates ξ, η and ζ are also shown in this Figure. Note that regardless of the size or shape of the element, the intrinsic co-ordinates always vary from –1 to +1. Thus, a given 8-node element is effectively mapped into a cube in the natural co-ordinate system. At each ith node, U_i, V_i and W_i are degrees of freedom, where i = 1,2, …, 8.

 

 

Figure 8.6 Eight-node element in the X-Y-Z ...