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Deformations

compute_internalforces(phi2l, q2) ¤

Recovery velocities in material frame.

Parameters:

Name Type Description Default
phi2l ndarray

Intrinsic force modes in local frame

 required
q2 ndarray

Force modal coordinate

 required

Returns:

Type Description
ndarray

Internal force field
Source code in feniax/intrinsic/postprocess.py 
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def compute_internalforces(phi2l: jnp.ndarray, q2: jnp.ndarray) -> jnp.ndarray:
    """Recovery velocities in material frame.

    Parameters
    ----------
    phi2l : jnp.ndarray
        Intrinsic force modes in local frame
    q2 : jnp.ndarray
        Force modal coordinate

    Returns
    -------
    jnp.ndarray
        Internal force field

    """

    X2 = jnp.tensordot(phi2l, q2, axes=(0, 1))  # 6xNnxNt
    return X2.transpose((2, 0, 1))

compute_strains(cphi2l, q2) ¤

Recovery strains in material frame.

Parameters:

Name Type Description Default
cphi2l ndarray

Intrinsic strain modes in local frame

 required
q2 ndarray

Force modal coordinate

 required

Returns:

Type Description
ndarray

Strain field
Source code in feniax/intrinsic/postprocess.py 
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def compute_strains(cphi2l: jnp.ndarray, q2: jnp.ndarray) -> jnp.ndarray:
    """Recovery strains in material frame.

    Parameters
    ----------
    cphi2l : jnp.ndarray
        Intrinsic  strain modes in local frame
    q2 : jnp.ndarray
        Force modal coordinate

    Returns
    -------
    jnp.ndarray
        Strain field

    """

    X3 = jnp.tensordot(cphi2l, q2, axes=(0, 1))  # 6xNnxNt
    return X3.transpose((2, 0, 1))

compute_velocities(phi1l, q1) ¤

Recovery velocities in material frame.

Parameters:

Name Type Description Default
phi1l ndarray

Intrinsic velocity modes in local frame

 required
q1 ndarray

Velocity modal coordinate

 required

Returns:

Type Description
ndarray

Velocity field
Source code in feniax/intrinsic/postprocess.py 
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def compute_velocities(phi1l: jnp.ndarray, q1: jnp.ndarray) -> jnp.ndarray:
    """Recovery velocities in material frame.

    Parameters
    ----------
    phi1l : jnp.ndarray
        Intrinsic velocity modes in local frame
    q1 : jnp.ndarray
        Velocity modal coordinate

    Returns
    -------
    jnp.ndarray
        Velocity field

    """

    X1 = jnp.tensordot(phi1l, q1, axes=(0, 1))  # 6xNnxNt
    return X1.transpose((2, 0, 1)) # Ntx6xNn

integrate_strains(ra_0n, Cab_0n, X3t, sol, fem) ¤

Function to integrate position from strains at a given time step

Source code in feniax/intrinsic/postprocess.py 
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def integrate_strains(ra_0n, Cab_0n, X3t, sol, fem):
    """
    Function to integrate position from strains at a given time step
    """

    ds = sol.data.modes.X_xdelta
    C0ab = sol.data.modes.C0ab  # 3x3xNn
    # TODO: make as fori loop
    Cab = jnp.zeros((3, 3, fem.num_nodes))
    ra = jnp.zeros((3, fem.num_nodes))

    comp_nodes = jnp.array(fem.component_nodes[fem.component_names[0]])[1:]
    numcomp_nodes = len(comp_nodes)
    Cab0_init = C0ab[:, :, 0]
    init = jnp.hstack([Cab_0n, Cab0_init, ra_0n.reshape((3, 1))])
    ds_i = ds[comp_nodes]
    ds_i = jnp.broadcast_to(ds_i, (3, ds_i.shape[0])).T.reshape((numcomp_nodes, 3, 1))
    strains_i = X3t[:3, comp_nodes].T.reshape((numcomp_nodes, 3, 1))
    kappas_i = X3t[3:, comp_nodes].T.reshape((numcomp_nodes, 3, 1))
    # import pdb; pdb.set_trace()
    C0ab_i = C0ab[:, :, comp_nodes].transpose((2, 0, 1))
    xs = jnp.concatenate([C0ab_i, strains_i, kappas_i, ds_i], axis=2)
    last_carry, Cra = jax.lax.scan(integrate_X3, init, xs)
    ra = ra.at[:, 0].set(ra_0n)
    Cab = Cab.at[:, :, 0].set(Cab_0n)
    ra = ra.at[:, comp_nodes].set(Cra[:, :, 3].T)
    Cab = Cab.at[:, :, comp_nodes].set(Cra[:, :, :3].transpose((1, 2, 0)))

    for ci in fem.component_names[1:]:
        comp_father = fem.component_father[ci]
        comp_nodes = jnp.array(fem.component_nodes[ci])
        numcomp_nodes = len(comp_nodes)
        if comp_father is None:
            node_father = 0
        else:
            node_father = fem.component_nodes[comp_father][-1]
        Cab_init = Cab[:, :, node_father]
        Cab0_init = C0ab[:, :, node_father]
        ra_init = ra[:, node_father]
        init = jnp.hstack([Cab_init, Cab0_init, ra_init.reshape((3, 1))])
        ds_i = ds[comp_nodes]
        ds_i = jnp.broadcast_to(ds_i, (3, ds_i.shape[0])).T.reshape(
            (numcomp_nodes, 3, 1)
        )
        strains_i = X3t[:3, comp_nodes].T.reshape((numcomp_nodes, 3, 1))
        kappas_i = X3t[3:, comp_nodes].T.reshape((numcomp_nodes, 3, 1))
        C0ab_i = C0ab[:, :, comp_nodes].transpose((2, 0, 1))
        xs = jnp.concatenate([C0ab_i, strains_i, kappas_i, ds_i], axis=2)
        last_carry, Cra = jax.lax.scan(integrate_X3, init, xs)
        ra = ra.at[:, comp_nodes].set(Cra[:, :, 3].T)
        Cab = Cab.at[:, :, comp_nodes].set(Cra[:, :, :3].transpose((1, 2, 0)))

    return Cab, ra

integrate_strainsl(ra_0n, Cab_0n, X3t, sol, fem) ¤

Function to integrate position from strains at a given time step

Source code in feniax/intrinsic/postprocess.py 
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def integrate_strainsl(ra_0n, Cab_0n, X3t, sol, fem):
    """
    Function to integrate position from strains at a given time step
    """

    ds = sol.data.modes.X_xdelta
    C0ab = sol.data.modes.C0ab  # 3x3xNn
    # TODO: make as fori loop
    Cab = jnp.zeros((3, 3, fem.num_nodes))
    ra = jnp.zeros((3, fem.num_nodes))

    comp_nodes = jnp.array(fem.component_nodes[fem.component_names[0]])[1:]
    numcomp_nodes = len(comp_nodes)
    Cab0_init = C0ab[:, :, 0]
    init = jnp.hstack([Cab_0n, Cab0_init, ra_0n.reshape((3, 1))])
    ds_i = ds[comp_nodes]
    ds_i = jnp.broadcast_to(ds_i, (3, ds_i.shape[0])).T.reshape((numcomp_nodes, 3, 1))
    strains_i = X3t[:3, comp_nodes].T.reshape((numcomp_nodes, 3, 1))
    kappas_i = X3t[3:, comp_nodes].T.reshape((numcomp_nodes, 3, 1))
    # import pdb; pdb.set_trace()
    C0ab_i = C0ab[:, :, comp_nodes].transpose((2, 0, 1))
    xs = jnp.concatenate([C0ab_i, strains_i, kappas_i, ds_i], axis=2)
    last_carry, Cra = jax.lax.scan(integrate_X3l, init, xs)
    ra = ra.at[:, 0].set(ra_0n)
    Cab = Cab.at[:, :, 0].set(Cab_0n)
    ra = ra.at[:, comp_nodes].set(Cra[:, :, 3].T)
    Cab = Cab.at[:, :, comp_nodes].set(Cra[:, :, :3].transpose((1, 2, 0)))

    for ci in fem.component_names[1:]:
        comp_father = fem.component_father[ci]
        comp_nodes = jnp.array(fem.component_nodes[ci])
        numcomp_nodes = len(comp_nodes)
        if comp_father is None:
            node_father = 0
        else:
            node_father = fem.component_nodes[comp_father][-1]
        Cab_init = Cab[:, :, node_father]
        Cab0_init = C0ab[:, :, node_father]
        ra_init = ra[:, node_father]
        init = jnp.hstack([Cab_init, Cab0_init, ra_init.reshape((3, 1))])
        ds_i = ds[comp_nodes]
        ds_i = jnp.broadcast_to(ds_i, (3, ds_i.shape[0])).T.reshape(
            (numcomp_nodes, 3, 1)
        )
        strains_i = X3t[:3, comp_nodes].T.reshape((numcomp_nodes, 3, 1))
        kappas_i = X3t[3:, comp_nodes].T.reshape((numcomp_nodes, 3, 1))
        C0ab_i = C0ab[:, :, comp_nodes].transpose((2, 0, 1))
        xs = jnp.concatenate([C0ab_i, strains_i, kappas_i, ds_i], axis=2)
        last_carry, Cra = jax.lax.scan(integrate_X3l, init, xs)
        ra = ra.at[:, comp_nodes].set(Cra[:, :, 3].T)
        Cab = Cab.at[:, :, comp_nodes].set(Cra[:, :, :3].transpose((1, 2, 0)))

    return Cab, ra