Introduction
This computes the summation of strain energy from each element as the response value and its gradient.
Formulation
Following formulation is used to compute the summation of strain energy from each element in the chosen model part where \(\underline{u}\) is the displacement vector for the element and \(\mathbf{K}\) is the stiffness matrix of the element.
$$ J = \frac{1}{2}\sum_{\forall \Omega_i \in \Omega} \underline{u}^T_i \mathbf{K}_i \underline{u}_i $$
Json settings
Following code snippet illustrates json settings used in this response function.
{
"name": "strain_energy",
"type": "linear_strain_energy_response_function",
"settings": {
"evaluated_model_part_names": [
"Structure"
],
"primal_analysis_name": "Structure_static",
"perturbation_size": 1e-8
}
}
Option | Allowed values |
---|---|
name | A unique string |
type | “linear_strain_energy_response_function” |
evaluated_model_part_names | List of model part names to compute strain energy |
primal_analysis_name | Name of the analysis from the list of analysis to be used for strain energy computation |
perturbation_size | Perturbation size to be used in the semi-analytic method |