structure shell recover command

Syntax

structure shell recover keyword <range>

Primary keywords:

resultants    stress    surface

Stress-recovery for shell elements. The stress-recovery procedure can be applied to all elements to compute both the stress resultants and the stresses acting at a specified depth. The range keyword identifies the patch of elements to which the command will apply. Note that the recovered quantities will depend upon the range of elements over which these quantities are being recovered, because nodal averaging only occurs for elements within this range.

resultants <range>

recover the eight stress resultants for all elements in the optional range. The stress resultants are expressed in terms of the surface coordinate system. This command assumes that a consistent surface coordinate system has been established for the group of elements in the range (see the surface keyword). The bending and membrane stress resultants (\(M_x\), \(M_y\), \(M_{xy}\), \(N_x\), \(N_y\), and \(N_{xy}\)) vary linearly over each element, whereas the transverse-shear stress resultants (\(Q_x\) and \(Q_y\) ) are constant over each element. The recovery procedure first computes the average values of bending and membrane stress resultants (by averaging, at the nodes, the contributions from each element in the range), and then spatially differentiates this average bending field over each element to obtain the transverse-shear stress resultants.

Stress resultants can be queried after recovery with the command structure shell list resultant and the FISH function struct.shell.resultant. The validity of the stress resultants for a particular element can be queried with the FISH function struct.shell.resultant.valid.

stress <depth-factor f >

recover a stress tensor (expressed in global coordinate system) at a specified depth in all elements in the optional range. The depth equals \(v\) times \(t\)/2, where \(t\) is shell thickness. The depth factor, \(v\), must be in the range [-1, +1]. \(v\) equal to +1 / -1 corresponds with the outer/inner shell surface (outer surface defined by positive surface system \(z\)-direction), and \(v\) equal to zero corresponds with the shell mid-surface. If \(v\) is not specified, it defaults to +1.

Stresses are recovered at the three nodal points and centroid of each element. If we designate the shell mid-surface by \(xy\)-axes, then 1) stress components \(σ_{xx}\), \(σ_{yy}\), and \(σ_{xy}\) vary linearly over each element, 2) stress components \(σ_{zy}\) and \(σ_{zx}\) are constant over each element, and 3) \(σ_{zz}\) = 0 over each element. The stresses are derived from the internal element forces (see structure shell list force-node). If the stress resultants are not valid when this command is executed, then an attempt is first made to recover them. If this attempt fails, then an error message is displayed indicating the problem—usually the inconsistency of the surface system, which then must be established manually using the structure shell recover surface command (see next keyword).

Stresses and principal stresses can be queried after recovery with the commands structure shell list stress and structure shell list stress-principal, and with the FISH functions struct.shell.stress and struct.shell.stress.prin. The depth at which these stresses have been recovered can be queried with the structure shell list depth-factor and the FISH function struct.shell.depth.factor. The validity of the stresses and principal stresses for a particular element can be queried with the FISH function struct.shell.stress.valid.

surface v

The vector v enables a surface coordinate system to be generated for all nodes used by the elements in the optional range. The surface coordinate system, \(x\)ʹ \(y\)ʹ \(z\)ʹ, has the following properties: 1) \(z\)ʹ is normal to the surface; 2) \(x\)ʹ is the projection of the given vector onto the surface; and 3) \(y\)ʹ is orthogonal to \(x\)ʹ and \(z\)ʹ. The \(z\)ʹ-direction is found at each node by taking the average normal direction of all elements in the range. If surface v is aligned with \(z\)ʹ at any node, then processing stops and an error message is displayed. To proceed, designate a different v, or restrict the range of elements considered.

The surface coordinate system can be queried with structure shell list system-local and the FISH function struct.node.system.surface. It can also be set for an individual node with the FISH function struct.node.system.local. It can be visualized with the Shell plot item by choose the corresponding System attribute.

The surface system at a node automatically becomes invalid under the following conditions: 1) large-strain update; or 2) creation or deletion of a element that uses the node. Validity must be re-established with the command structure shell recover surface.