hermit.outputs

Postprocess a hermit.ShellState into scalar and field outputs.

Every function here takes the solved state and nothing else – the state back-references its domain, geometry, material, loads and boundary conditions. Scalar outputs return csdl.Variables; field outputs return hermit.Fields. All of them are differentiable in reverse mode, including with respect to the mesh coordinates when the solve was given a live geometry.

Functions

`aggregated_stress`(state, *[, rho, m, region, surface, ...])	Smooth aggregate of isotropic von Mises stress, `(1/m) * pnorm**(1/rho)`.
`center_of_gravity`(state)	Mass-weighted centre of gravity, in global Cartesian coordinates.
`compliance`(state)	Work done by the applied loads on the solution.
`displacement_field`(state)	Mid-surface displacement as a field.
`elastic_energy`(state)	Stored shell strain energy.
`failure_field`(state, *[, sampling])	Per-cell, per-ply-face Tsai-Wu failure indices.
`failure_index`(state, *[, rho, sampling])	KS-aggregated Tsai-Wu failure index over the whole laminate.
`mass`(state)	Structural mass, `int density * thickness dx`.
`nodal_displacement`(state)	Displacements at the mesh vertices.
`nodal_rotation`(state)	Director rotations at the mesh vertices.
`pnorm_stress`(state, *[, rho, m, region, surface, ...])	Area-normalized p-norm stress integral, `(1/A) int (mvm)*rho dx`.
`rotation_field`(state)	Director rotation as a field.
`strain_fields`(state, *[, space, method, frame])	Membrane strain, bending curvature and transverse shear.
`stress_field`(state, *[, space, method, surface])	Isotropic von Mises stress field.
`stress_scaling`(state, *[, surface, space, method])	Suggest the stress scaling `m = 1 / max\|von Mises\|` for the aggregates.

Module Contents

hermit.outputs.aggregated_stress(state, *, rho=100, m=1e-06, region=None, surface='top', quadrature_degree=None)

Smooth aggregate of isotropic von Mises stress, (1/m) * pnorm**(1/rho).

A differentiable stand-in for the peak stress, suitable as an optimizer constraint.

Parameters:

stateShellState
rhofloat, optional: Aggregation exponent. Default 100.
mfloat, optional: Stress scaling; see pnorm_stress(). Default 1e-6.
regionstr or int, optional: Restrict to a mesh-tagged region.
surface{‘top’, ‘bottom’, ‘mid’}, optional: Through-thickness station. Default 'top'.
quadrature_degreeint, optional: Overrides the domain’s degree for this integral.

Returns:

csdl.Variable: Scalar, in stress units.

Warns:

UserWarning: If m is degenerate for this problem, which would otherwise return a number that barely depends on the solution.

Notes

Approaches max(vm) from below as rho grows: this is the area-averaged integral p-norm, bounded above by the pointwise maximum, unlike the discrete log-sum-exp aggregate failure_index() uses.

Examples

>>> m = hm.stress_scaling(state)
>>> peak = hm.aggregated_stress(state, m=m)

hermit.outputs.center_of_gravity(state)

Mass-weighted centre of gravity, in global Cartesian coordinates.

Parameters:

stateShellState

Returns:

csdl.Variable: Shape (3,).

hermit.outputs.compliance(state)

Work done by the applied loads on the solution.

Parameters:

stateShellState

Returns:

csdl.Variable: Scalar. Conjugate to the exact Loads object that was solved, including edge and point terms.

hermit.outputs.displacement_field(state)

Mid-surface displacement as a field.

Parameters:

stateShellState

Returns:

Field: (3,) vector field on the displacement subspace of the element, in global Cartesian components.