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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

Source files