ABSTRACT
Geometric mapping from the natural coordinate to the physical coordinate is
(6.1.17)
The Jacobian becomes
length.
Derivatives of the shape functions, Eqs. (6.1.13) through (6.1.15), are
dH1(C,) = _!_ dH1 = 2_(2(, _ 1) dx J dC, hi
(6.1.19)
(6.1.20)
QuadrilateralElements
Figure6.2.1BilinearElementintheNaturalCoordinate
dH3(0=_!_dH3=_!_( 2 ~+1) dxJd~h;
(6.1.21)
Theshapefunctionsforthebilinearisoparametricelementaregivenbelow:
(6.2.1)
1 H2(~,TJ)=4(1+0(1-TJ)(6.2.2)
1 Jfs(~,TJ)=4(1+~)(1+TJ)(6.2.3)
1 H4(~,TJ)=4(l-0(1+TJ)(6.2.4)
forthenodesshowninFig.6.2.1.Theseshapefunctionsaredefinedintermsofthe normalizednaturaldomain(i.e.-1:S~:S1and-1:::;TJ:S1).
