Plane Strain Elements

Plane Strain Elements

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). The element features are summarized in Table 15.

Fig. 9 Quad1PlaneStrain element. Node numbering, Side numbering and definition of local edge c.s.(a).

Table 15 quad1planestrain element summary

Keyword	quad1planestrain
Description	2D linear quadrilateral plane-strain element
Specific parameters	[NIP (in)]
Parameters	NIP: allows to set the number of integration points for integration of membrane terms.
Unknowns	Two dofs (u-displacement, v-displacement) are required in each node.
Approximation	Linear approximation of displacements 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 points 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	Cross section thickness is required.
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. (Quad1PlaneStrain element. Node numbering, Side numbering and definition of local edge c.s.(a).)).
Nlgeo
Status	Reliable
Tests/Examples	sm/DruckerPrager_01.in, sm/ogden1.in, sm/ogden2.in, sm/mooneyrivlin1.in, sm/timestepreduction.in, sm/mooneyrivlin2.in, sm/contact2d_sliding.in, sm/contact2d_generalized_vertex_direct.in, sm/contact2d_projection_outside.in, sm/contact2d_projection_boundary.in (and 9 more)

TrplaneStrain

Implements an triangular three-node constant strain plane-strain finite element. Each node has 2 degrees of freedom. The node numbering is anti-clockwise. The element features are summarized in Table 16.

Fig. 10 TrplaneStrain element - node and side numbering.

Table 16 trplanestrain element summary

Keyword	trplanestrain
Description	2D linear triangular plane-strain element
Parameters	NIP: allows to set the number of integration points for integration of membrane terms.
Unknowns	Two dofs (u-displacement, v-displacement) are required in each node.
Approximation	Linear approximation of displacements and geometry.
Integration	Integration of membrane strain terms using one point gauss integration formula.
Features	Nonlocal constitutive support. Edge load support, Adaptivity support.
CS properties	Cross section thickness is required.
Loads	Body loads are supported. Boundary loads are supported and are 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 3). The local positive edge x-axis coincides with side direction, the positive local edge y-axis is rotated 90 degrees anti-clockwise (see fig. (TrplaneStrain element - node and side numbering.)).
Nlgeo
Status	Reliable
Tests/Examples	sm/patch107.in