Quad1PlaneStrain

Represents isoparametric four-node quadrilateral plane-strain finite element. Each node has 2 degrees of freedom. Structure should be defined in x,y plane. The nodes should be numbered anti-clockwise (positive rotation around z-axis).

**Figure 8:** Quad1PlaneStrain element. Node numbering, Side numbering and definition of local edge c.s.(a).
$\includegraphics[width=0.7\textwidth]{planestress2d.eps}$ $\begin{tikzpicture}[scale=6,>=stealth] \tikzstyle{elemnode} = [draw,circle,inne... ...}$}; \draw[->] (0,-0.05) - (0,0.5) node[right] {$y_{}$};}}}}; \end{tikzpicture}$

Keyword: quad1planestrain
Parameters: [ NIP(in) #]
Unknowns: Two dofs (u-displacement, v-displacement) are required in each node.

Approximation: Linear approximation of displacement and geometry.

Integration: Integration of membrane strain terms using gauss integration formula in 4 (the default), 9, or 16 integration points. The default number of integration point used can be overloaded using NIP parameter. Reduced integration for shear terms is employed. Shear terms are always integrated using 1 point integration rule.

Features: Nonlocal constitutive support, Adaptivity support.

CS properties: Thickness.

Loads: Body loads are supported. Boundary loads are supported and computed using numerical integration. The side numbering is following. Each i-th element side begins in i-th element node and ends on next element node (i+1-th node or 1-st node, in the case of side number 4). The local positive edge x-axis coincides with side direction, the positive local edge y-axis is rotated 90 degrees anti-clockwise (see fig. (8)).

Status: Reliable.

Borek Patzak 2011-12-29