Source code for pyNastran.bdf.cards.elements.beam_connectivity

# pylint: disable=C0326
"""
Defines the faces for representing the PBARL/PBEAML cards as 3D objects
instead of just 1D elements.

These functions intentionally do not handle offsets.
Node 1/2 should be the offset/actual coordinates.

The following shapes are fully supported:
 - ROD
 - TUBE
 - BAR
 - BOX
 - L
 - H
 - I1  (I1 is handled correctly because it's doubly symmetric)
 - T
 - T1
 - T2
 - Z
 - HEXA

The following shapes don't do the shear center correctly:
 - CHAN
 - CHAN1
 - I
 - HAT

The following shapes aren't supported:
 - CROSS
 - TUBE2
 - CHAN2 (will be a shear center issue)
 - BOX1  (will be a shear center issue)
 - HAT1  (will be a shear center issue)
 - DBOX  (will be a shear center issue)

"""
from typing import Tuple, List
import numpy as np
from pyNastran.nptyping import NDArray3float, NDArray33float, NDArrayN3float
from pyNastran.bdf.cards.aero.utils import elements_from_quad, tri_cap

Faces = List[List[int]]

def _transform_points(n1: NDArray3float, n2: NDArray3float,
                      points1: NDArrayN3float, points2: NDArrayN3float,
                      xform: NDArray33float) -> NDArrayN3float:
    points_list = []
    for nid, points in [(n1, points1), (n2, points2)]:
        pointsi = points @ xform + nid
        points_list.append(pointsi)
    return np.vstack(points_list)

[docs]def rod_setup(dim1: Tuple[float], dim2: Tuple[float]) -> Faces: # validated """defines points in a circle with triangle based end caps""" # 4,8,12,16,... becomes 5,9,13,17,... ntheta = 17 thetas = np.radians(np.linspace(0., 360., ntheta)) nfaces = 0 all_faces = [] points_list = [] x = np.zeros(ntheta) for dim in (dim1, dim2): radius, = dim y = radius * np.cos(thetas) z = radius * np.sin(thetas) xyz = np.vstack([x, y, z]).T assert xyz.shape == (ntheta, 3), xyz.shape # the tri_cap buils triangles that fan out from the first node tris = tri_cap(ntheta) # we need to use the tolist because we're going to # combine quads and tris (the elements have different # lengths) all_faces += (nfaces + tris).tolist() nfaces += tris.shape[0] points_list.append(xyz) # the main cylinder uses the points defined independent # of the points n1/n2 faces = elements_from_quad(2, ntheta) all_faces += faces.tolist() return all_faces, points_list[0], points_list[1]
[docs]def rod_faces(n1: NDArray3float, n2: NDArray3float, xform: NDArray33float, dim1: Tuple[float], dim2: Tuple[float]): # validated """defines points in a circle with triangle based end caps""" faces, points1, points2 = rod_setup(dim1, dim2) points_array = _transform_points(n1, n2, points1, points2, xform) return faces, points_array, points_array.shape[0]
[docs]def tube_setup(dim1: Tuple[float, float], dim2: Tuple[float, float]) -> Tuple[Faces, NDArrayN3float, NDArrayN3float]: # validated """defines a rod with a hole""" # 4,8,12,16,... becomes 5,9,13,17,... ntheta = 17 thetas = np.radians(np.linspace(0., 360., ntheta)) npoints = ntheta * 2 x = np.zeros(ntheta) points = [] #points_list_in = [] #points_list_out = [] for dim in (dim1, dim2): radius_out, radius_in = dim # inner rod y = radius_in * np.cos(thetas) z = radius_in * np.sin(thetas) xyz2 = np.vstack([x, y, z]).T #points_list_in.append(xyz2) # outer rod y = radius_out * np.cos(thetas) z = radius_out * np.sin(thetas) xyz1 = np.vstack([x, y, z]).T #points_list_out.append(xyz1) xyz = np.vstack([xyz1, xyz2]) points.append(xyz) # the main cylinder uses the points defined independent # of the inner/outer faces faces_n1 = elements_from_quad(2, ntheta) faces_n2 = faces_n1 + npoints #faces_n1 #[[ 0 17 18 1] #[ 1 18 19 2] #[ 2 19 20 3] #[ 3 20 21 4] #[ 4 21 22 5] #[ 5 22 23 6] # we use slicing to link the outer surface to the # inner surface using quads # # we'd like to hstack the column arrays, but hstack and a # transpose is easier. Presumably, a "newaxis" index would work... faces_out = np.vstack([ faces_n1[:, 0], faces_n1[:, 3], faces_n2[:, 3], faces_n2[:, 0]]).T faces_in = np.vstack([ faces_n1[:, 1], faces_n1[:, 2], faces_n2[:, 2], faces_n2[:, 1]]).T # combine everything together all_faces = np.vstack([faces_n1, faces_n2, faces_out, faces_in]) return all_faces, points[0], points[1]
[docs]def tube_faces(n1: NDArray3float, n2: NDArray3float, xform: NDArray33float, dim1: Tuple[float, float], dim2: Tuple[float, float]): # validated """defines a rod with a hole""" faces, points1, points2 = tube_setup(dim1, dim2) points_array = _transform_points(n1, n2, points1, points2, xform) return faces, points_array, points_array.shape[0]
[docs]def bar_setup(dim1: Tuple[float, float], dim2: Tuple[float, float]) -> Tuple[Faces, NDArrayN3float, NDArrayN3float]: # validated """ ^y | 0-----3 | | | |----> z | | 1-----2 """ faces = [ # front/back [0, 1, 2, 3], [4, 5, 6, 7], # 4-sides [0, 1, 5, 4], [1, 2, 6, 5], [2, 3, 7, 6], [3, 0, 4, 7], ] points = [] for dim in (dim1, dim2): w, h = dim pointsi = np.array([ [0., h/2, -w/2], # 0 [0., -h/2, -w/2], # 1 [0., -h/2, w/2], # 2 [0., h/2, w/2], # 3 ]) # 16 x 3 points.append(pointsi) return faces, points[0], points[1]
[docs]def bar_faces(n1: NDArray3float, n2: NDArray3float, xform: NDArray33float, dim1: Tuple[float, float], dim2: Tuple[float, float]): # validated """builds the BAR faces""" unused_faces, points1, points2 = bar_setup(dim1, dim2) points_array = _transform_points(n1, n2, points1, points2, xform) return points_array
[docs]def box_setup(dim1: Tuple[float, float, float, float], dim2: Tuple[float, float, float, float]) -> Tuple[Faces, NDArrayN3float, NDArrayN3float]: """ ^ y | 0---------3 | | | 4---7 | | | + | |---> z | 5---6 | | | 1---------2 """ faces = [ # front face [0, 1, 5, 4], [1, 2, 6, 5], [2, 3, 7, 6], [3, 0, 4, 7], # back face [8, 9, 13, 12], [9, 10, 14, 13], [10, 11, 15, 14], [11, 8, 12, 15], # outer # around the box (counter-clockwise) [0, 8, 9, 1], [1, 9, 10, 2], [2, 10, 11, 3], [3, 11, 8, 0], # inner # backwards - I don't think this matters [4, 12, 13, 5], [5, 13, 14, 6], [6, 14, 15, 7], [7, 15, 12, 4], ] points = [] for dim in (dim1, dim2): wbox, hbox, th, tw = dim hbox_in = hbox - 2*th wbox_in = wbox - 2*tw pointsi = np.array([ [0., -hbox/2., wbox/2], # 0 [0., -hbox/2, -wbox/2], # 1 [0., hbox/2, -wbox/2], # 2 [0., hbox/2, wbox/2], # 3 [0., -hbox_in/2., wbox_in/2], # 4 [0., -hbox_in/2, -wbox_in/2], # 5 [0., hbox_in/2, -wbox_in/2], # 6 [0., hbox_in/2, wbox_in/2], # 7 ]) points.append(pointsi) return faces, points[0], points[1]
[docs]def box_faces(n1: NDArray3float, n2: NDArray3float, xform: NDArray33float, dim1: Tuple[float, float, float, float], dim2: Tuple[float, float, float, float]): # validated """builds the BOX faces""" faces, points1, points2 = box_setup(dim1, dim2) points_array = _transform_points(n1, n2, points1, points2, xform) return faces, points_array
[docs]def i_setup(dim1: Tuple[float, float, float, float, float, float], dim2: Tuple[float, float, float, float, float, float]): # validated """ ^y | 0----------11 - y3 | | 1---2 9---10 - y2 | | | | | | 4---3 8---7 - y1 | | 5-----+----6-----> z """ faces = [ # around the I (counter-clockwise) [0, 12, 13, 1], [1, 13, 14, 2], [2, 14, 15, 3], [3, 15, 16, 4], [4, 16, 17, 5], [5, 17, 18, 6], [6, 18, 19, 7], [7, 19, 20, 8], [8, 20, 21, 9], [9, 21, 22, 10,], [10, 22, 23, 11,], [11, 23, 12, 0], # front face [0, 1, 2, 9, 10, 11], [2, 3, 8, 9], [4, 5, 6, 7, 8, 3], # back face [12, 13, 14, 21, 22, 23], [14, 15, 20, 21], [16, 17, 18, 19, 20, 15], ] points = [] for dim in (dim1, dim2): hall, bflange_btm, bflange_top, tweb, tflange_btm, tflange_top = dim hweb = hall - tflange_top - tflange_btm ysc = -hall / 2. # TODO: fix the shear center formula y0 = ysc y1 = y0 + tflange_btm y2 = y1 + hweb y3 = y2 + tflange_top pointsi = np.array([ [0., y3, -bflange_top/2], # 0 [0., y2, -bflange_top/2], # 1 [0., y2, -tweb/2, ], # 2 [0., y1, -tweb/2, ], # 3 [0., y1, -bflange_btm/2], # 4 [0., y0, -bflange_btm/2], # 5 [0., y0, bflange_btm/2], # 6 [0., y1, bflange_btm/2], # 7 [0., y1, tweb/2, ], # 8 [0., y2, tweb/2, ], # 9 [0., y2, bflange_top/2], # 10 [0., y3, bflange_top/2], # 11 ]) # 24 x 3 points.append(pointsi) return faces, points[0], points[1]
[docs]def i_faces(n1: NDArray3float, n2: NDArray3float, xform: NDArray33float, dim1: Tuple[float, float, float, float, float, float], dim2: Tuple[float, float, float, float, float, float]): # validated """builds the I faces""" faces, points1, points2 = i_setup(dim1, dim2) points_array = _transform_points(n1, n2, points1, points2, xform) return faces, points_array
[docs]def i1_setup(dim1: Tuple[float, float, float, float], dim2: Tuple[float, float, float, float]) -> Tuple[Faces, NDArrayN3float, NDArrayN3float]: """builds the I1 faces""" """ ^y | 0----------11 - y3 | | 1---2 9---10 - y2 | | | | | | 4---3 8---7 - y1 | | 5-----+----6-----> z """ faces = [ # around the I (counter-clockwise) [0, 12, 13, 1], [1, 13, 14, 2], [2, 14, 15, 3], [3, 15, 16, 4], [4, 16, 17, 5], [5, 17, 18, 6], [6, 18, 19, 7], [7, 19, 20, 8], [8, 20, 21, 9], [9, 21, 22, 10,], [10, 22, 23, 11,], [11, 23, 12, 0], # front face [0, 1, 2, 9, 10, 11], [2, 3, 8, 9], [4, 5, 6, 7, 8, 3], # back face [12, 13, 14, 21, 22, 23], [14, 15, 20, 21], [16, 17, 18, 19, 20, 15], ] points = [] for dim in (dim1, dim2): bfoot_2x, tweb, hin, hall = dim bflange = bfoot_2x + tweb bflange_top = bflange bflange_btm = bflange tflange_top = (hall - hin) / 2. tflange_btm = tflange_top hweb = hall - tflange_top - tflange_btm ysc = -hall / 2. # TODO: fix the shear center formula y0 = ysc y1 = y0 + tflange_btm y2 = y1 + hweb y3 = y2 + tflange_top pointsi = np.array([ [0., y3, -bflange_top/2], # 0 [0., y2, -bflange_top/2], # 1 [0., y2, -tweb/2, ], # 2 [0., y1, -tweb/2, ], # 3 [0., y1, -bflange_btm/2], # 4 [0., y0, -bflange_btm/2], # 5 [0., y0, bflange_btm/2], # 6 [0., y1, bflange_btm/2], # 7 [0., y1, tweb/2, ], # 8 [0., y2, tweb/2, ], # 9 [0., y2, bflange_top/2], # 10 [0., y3, bflange_top/2], # 11 ]) # 24 x 3 points.append(pointsi) return faces, points[0], points[1]
[docs]def i1_faces(n1: NDArray3float, n2: NDArray3float, xform: NDArray33float, dim1: Tuple[float, float, float, float], dim2: Tuple[float, float, float, float]): """builds the I1 faces""" """ ^y | 0----------11 - y3 | | 1---2 9---10 - y2 | | | | | | 4---3 8---7 - y1 | | 5-----+----6-----> z """ faces, points1, points2 = i1_setup(dim1, dim2) points_array = _transform_points(n1, n2, points1, points2, xform) return faces, points_array
[docs]def h_setup(dim1: Tuple[float, float, float, float], dim2: Tuple[float, float, float, float]): """ ^y | 0----11 | 8----7 | | | | | | 10----9 | | | | | | | | +--|----|---> z | | | | | 3-----4 | | | | | | | | | 1----2 5----6 <---> dim1 <----> 0.5*dim2 <---------------> w_all """ faces = [ # front face [0, 1, 2, 3, 10, 11], [3, 4, 9, 10], [4, 5, 6, 7, 8, 9], # back face [12, 13, 14, 15, 22, 23], [15, 16, 21, 22], [16, 17, 18, 19, 20, 21], # around the H (counter-clockwise) [0, 12, 13, 1], [1, 13, 14, 2], [2, 14, 15, 3], [3, 15, 16, 4], [4, 16, 17, 5], [5, 17, 18, 6], [6, 18, 19, 7], [7, 19, 20, 8], [8, 20, 21, 9], [9, 21, 22, 10,], [10, 22, 23, 11,], [11, 23, 12, 0], ] points = [] for dim in (dim1, dim2): winner, wouter, hall, hinner = dim w_all = winner + wouter pointsi = np.array([ [0., hall/2, -w_all/2], # 0 - upper far left [0., -hall/2, -w_all/2], # 1 - lower far left [0., -hall/2, -winner/2], # 2 - lower near left [0., -hinner/2, -winner/2], # 3 - lower H left [0., -hinner/2, winner/2], # 4 - lower H right [0., -hall/2, winner/2], # 5 - lower near right [0., -hall/2, w_all/2], # 6 - lower far right [0., hall/2, w_all/2], # 7 - upper far right [0., hall/2, winner/2], # 8 - upper near right [0., hinner/2, winner/2], # 9 - upper H right [0., hinner/2, -winner/2], # 10 - upper H left [0., hall/2, -winner/2], # 11 - upper near left ]) # 24 x 3 points.append(pointsi) return faces, points[0], points[1]
[docs]def h_faces(n1: NDArray3float, n2: NDArray3float, xform: NDArray33float, dim1: Tuple[float, float, float, float], dim2: Tuple[float, float, float, float]): # validated """builds the H faces""" faces, points1, points2 = h_setup(dim1, dim2) points_array = _transform_points(n1, n2, points1, points2, xform) return faces, points_array
[docs]def chan_setup(dim1: Tuple[float, float, float, float], dim2: Tuple[float, float, float, float]): """ ^y | 0--------7 | | | | | 5-----6 | | | +--|--|-------> z | | | 4-----3 | | 1--------2 <----> e/zsc <--------> bflange """ faces = [ # front face [0, 5, 6, 7], [0, 1, 4, 5], [1, 2, 3, 4], # back face [8, 13, 14, 15], [8, 9, 12, 13], [9, 10, 11, 12], # around the C (counter-clockwise) [0, 8, 9, 1], [1, 9, 10, 2], [2, 10, 11, 3], [3, 11, 12, 4], [4, 12, 13, 5], [5, 13, 14, 6], [6, 14, 15, 7], [7, 15, 8, 0], ] points = [] for dim in (dim1, dim2): bflange, hall, tweb, tflange = dim # distance from shear center to neutral axis #zsc_na = 3 * bflange ** 2 / (6 * bflange + h) # per msc 2018 refman zsc = 0. ## TODO: consider the shear center #if 0: # pragma: no cover # msc 2018 refman; p.670 #h = hall - tflange #tw = tweb #tf = tflange #b = bflange - tw / 2. #bf = bflange - tw #hw = hall - 2. * tf #A = 2 * tf * bf + (h + tf) * tw #zc = bf * tf * (bf + tw) / A #zsc = b**2 * tf / (2*b*tw + 1/3. * h * tf) #E = zs - tw / 2. #zna = zc + zsc pointsi = np.array([ [0., hall/2, zsc], # 0 [0., -hall/2, zsc], # 1 [0., -hall/2, zsc + bflange], # 2 [0., -hall/2 + tflange, zsc + bflange], # 3 [0., -hall/2 + tflange, zsc + tweb], # 4 [0., hall/2 - tflange, zsc + tweb], # 5 [0., hall/2 - tflange, zsc + bflange], # 6 [0., hall/2, zsc + bflange], # 7 ]) # 16 x 3 points.append(pointsi) return faces, points[0], points[1]
[docs]def chan_faces(n1: NDArray3float, n2: NDArray3float, xform: NDArray33float, dim1: Tuple[float, float, float, float], dim2: Tuple[float, float, float, float]): # validated """builds the CHAN faces""" faces, points1, points2 = chan_setup(dim1, dim2) points_array = _transform_points(n1, n2, points1, points2, xform) return faces, points_array
[docs]def chan1_setup(dim1: Tuple[float, float, float, float], dim2: Tuple[float, float, float, float]) -> Tuple[Faces, NDArrayN3float, NDArrayN3float]: """ ^y | 0--------7 ^ hall | | | | | | 5-----6 | ^ | | | | | hweb +--|--|-------> z | | | | | v | 4-----3 | ^ | | | | tflange 1--------2 v v <--> tweb <-----> bflange_out <--------> bflange """ faces = [ # front face [0, 5, 6, 7], [0, 1, 4, 5], [1, 2, 3, 4], # back face [8, 13, 14, 15], [8, 9, 12, 13], [9, 10, 11, 12], # around the C (counter-clockwise) [0, 8, 9, 1], [1, 9, 10, 2], [2, 10, 11, 3], [3, 11, 12, 4], [4, 12, 13, 5], [5, 13, 14, 6], [6, 14, 15, 7], [7, 15, 8, 0], ] zsc = 0. # TODO: consider the shear center points = [] for dim in (dim1, dim2): bflange_out, tweb, hin, hall = dim bflange = bflange_out + tweb tflange = (hall - hin) / 2. pointsi = np.array([ [0., hall/2, zsc], # 0 [0., -hall/2, zsc], # 1 [0., -hall/2, zsc + bflange], # 2 [0., -hall/2 + tflange, zsc + bflange], # 3 [0., -hall/2 + tflange, zsc + tweb], # 4 [0., hall/2 - tflange, zsc + tweb], # 5 [0., hall/2 - tflange, zsc + bflange], # 6 [0., hall/2, zsc + bflange], # 7 ]) # 16 x 3 points.append(pointsi) return faces, points[0], points[1]
[docs]def chan1_faces(n1: NDArray3float, n2: NDArray3float, xform: NDArray33float, dim1: Tuple[float, float, float, float], dim2: Tuple[float, float, float, float]): """builds the CHAN1 faces""" faces, points1, points2 = chan1_setup(dim1, dim2) points_array = _transform_points(n1, n2, points1, points2, xform) return faces, points_array
[docs]def z_setup(dim1: Tuple[float, float, float, float], dim2: Tuple[float, float, float, float]) -> Tuple[Faces, NDArrayN3float, NDArrayN3float]: """ ^ y | 0--------7 ^ hall | | | | 1----2 | | | ^ | | | z | | hin | +-|---> | | | | | v | 6-----5 | | | | 3---------4 v <---> tweb <-----> bfoot <-----------> bflange """ faces = [ # front face [0, 1, 2, 7], [2, 3, 6, 7], [3, 4, 5, 6], # back face [8, 9, 10, 15], [10, 11, 14, 15], [11, 12, 13, 14], # around the C (counter-clockwise) [0, 8, 9, 1], [1, 9, 10, 2], [2, 10, 11, 3], [3, 11, 12, 4], [4, 12, 13, 5], [5, 13, 14, 6], [6, 14, 15, 7], [7, 15, 8, 0], ] points = [] for dim in (dim1, dim2): bfoot, tweb, hin, hall = dim wall = bfoot * 2. + tweb tflange = (hall - hin) / 2. pointsi = np.array([ [0., hall/2, -wall/2], # 0 [0., hall/2 - tflange, -wall/2], # 1 [0., hall/2 - tflange, -tweb/2], # 2 [0., -hall/2, -tweb/2], # 3 [0., -hall/2, wall/2], # 4 [0., -hall/2 + tflange, wall/2], # 5 [0., -hall/2 + tflange, tweb/2], # 6 [0., hall/2, tweb/2], # 7 ]) # 16 x 3 points.append(pointsi) return faces, points[0], points[1]
[docs]def z_faces(n1: NDArray3float, n2: NDArray3float, xform: NDArray33float, dim1: Tuple[float, float, float, float], dim2: Tuple[float, float, float, float]): """builds the Z faces""" faces, points1, points2 = z_setup(dim1, dim2) points_array = _transform_points(n1, n2, points1, points2, xform) return faces, points_array
[docs]def hexa_setup(dim1: Tuple[float, float, float], dim2: Tuple[float, float, float]) -> Tuple[Faces, NDArrayN3float, NDArrayN3float]: """ ^ y | 0-----5 ^ hall / | \ | / | \ | 1 +-----4---z | \ / | \ / | 2_______3 v <-> wtri <-----------> wall """ faces = [ # front face [0, 1, 2, 5], [5, 2, 3, 4], # back face [6, 7, 8, 11], [11, 8, 9, 10], # around the C (counter-clockwise) [0, 6, 7, 1], [1, 7, 8, 2], [2, 8, 9, 3], [3, 9, 10, 4], [4, 10, 11, 5], [5, 11, 6, 0], ] points = [] for dim in (dim1, dim2): wtri, wall, hall = dim pointsi = np.array([ [0., hall/2, -wall/2 + wtri], # 0 [0., 0., -wall/2], # 1 [0., -hall/2, -wall/2 + wtri], # 2 [0., -hall/2, wall/2 - wtri], # 3 [0., 0., wall/2], # 4 [0., hall/2, wall/2 - wtri], # 5 ]) # 12 x 3 points.append(pointsi) return faces, points[0], points[1]
[docs]def hexa_faces(n1: NDArray3float, n2: NDArray3float, xform: NDArray33float, dim1: Tuple[float, float, float], dim2: Tuple[float, float, float]): """builds the HEXA faces""" faces, points1, points2 = hexa_setup(dim1, dim2) points_array = _transform_points(n1, n2, points1, points2, xform) return faces, points_array
[docs]def l_setup(dim1: Tuple[float, float, float], dim2: Tuple[float, float, float]) -> Tuple[Faces, NDArrayN3float, NDArrayN3float]: """ ^y | 0-----5 ^ hall | | | | | | | | | | | | | | 4---3 | ^ tflange | +------|-------> z | | 1---------2 v v <----> tweb <---------> bflange """ faces = [ # front face [0, 1, 4, 5], [1, 2, 3, 4], # back face [6, 7, 10, 11], [7, 8, 9, 10], # around the C (counter-clockwise) [0, 6, 7, 1], [1, 7, 8, 2], [2, 8, 9, 3], [3, 9, 10, 4], [4, 10, 11, 5], [5, 11, 6, 0], ] points = [] for dim in (dim1, dim2): bflange, hall, tflange, tweb = dim pointsi = np.array([ [0., hall - tflange/2, -tweb/2], # 0 [0., -tflange/2, -tweb/2], # 1 [0., -tflange/2, bflange - tweb/2], # 2 [0., tflange/2, bflange - tweb/2], # 3 [0., tflange/2, tweb/2], # 4 [0., hall - tflange/2, tweb/2], # 5 ]) # 12 x 3 points.append(pointsi) return faces, points[0], points[1]
[docs]def l_faces(n1: NDArray3float, n2: NDArray3float, xform: NDArray33float, dim1: Tuple[float, float, float, float], dim2: Tuple[float, float, float, float]): faces, points1, points2 = l_setup(dim1, dim2) points_array = _transform_points(n1, n2, points1, points2, xform) return faces, points_array
[docs]def t_setup(dim1: Tuple[float, float, float, float], dim2: Tuple[float, float, float, float]) -> Tuple[Faces, NDArrayN3float, NDArrayN3float]: """ ^ y | 0----------7 | + |----> z 1---2 5---6 | | | | 3--4 bflange <----------> 8----------15 | + | 9---10 13--14 | | | | 11-12 """ faces = [ # around the T (counter-clockwise) [0, 8, 9, 1], [1, 9, 10, 2], [2, 10, 11, 3], [3, 11, 12, 4], [4, 12, 13, 5], [5, 13, 14, 6], [6, 14, 15, 7], [7, 15, 8, 0], # front face [0, 1, 2, 5, 6, 7], [2, 3, 4, 5], # back face [8, 9, 10, 13, 14, 15], [10, 11, 12, 13], # front/back face #[0, 1, 2, 3, 4, 5, 6, 7], #[8, 9, 10, 11, 12, 13, 14, 15], ] points = [] for dim in (dim1, dim2): bflange, htotal, tflange, tweb = dim #htotal = tflange + hweb pointsi = np.array([ [0., tflange/2, -bflange/2], # 0 [0., -tflange/2, -bflange/2], # 1 [0., -tflange/2, -tweb/2], # 2 [0., -htotal+tflange/2,-tweb/2], # 3 [0., -htotal+tflange/2, tweb/2], # 4 [0., -tflange/2, tweb/2], # 5 [0., -tflange/2, bflange/2], # 6 [0., tflange/2, bflange/2], # 7 ]) # 16 x 3 points.append(pointsi) return faces, points[0], points[1]
[docs]def t_faces(n1: NDArray3float, n2: NDArray3float, xform: NDArray33float, dim1: Tuple[float, float, float, float], dim2: Tuple[float, float, float, float]): """builds the T faces""" faces, points1, points2 = t_setup(dim1, dim2) points_array = _transform_points(n1, n2, points1, points2, xform) return faces, points_array
[docs]def t1_setup(dim1: Tuple[float, float, float, float], dim2: Tuple[float, float, float, float]) -> Tuple[Faces, NDArrayN3float, NDArrayN3float]: """ ^ y | 6---5 ^ hall | | | | | | | | 0----------7 | | | ^ | +-|---> z | | tflange 1----------2 | | v | | | | | | 3---4 v <---------><---> bfoot tweb bflange <----------> """ faces = [ # front face [0, 1, 2, 7], [2, 3, 4, 5, 6, 7], # back face [8, 9, 10, 15], [10, 11, 12, 13, 14, 15], # around the T (counter-clockwise) [0, 8, 9, 1], [1, 9, 10, 2], [2, 10, 11, 3], [3, 11, 12, 4], [4, 12, 13, 5], [5, 13, 14, 6], [6, 14, 15, 7], [7, 15, 8, 0], ] points = [] for dim in (dim1, dim2): hall, bfoot, tweb, tflange = dim #htotal = tflange + hweb pointsi = np.array([ [0., tflange/2, -bfoot - tweb/2], # 0 [0., -tflange/2, -bfoot - tweb/2], # 1 [0., -tflange/2, -tweb/2], # 2 [0., -hall/2, -tweb/2], # 3 [0., -hall/2, tweb/2], # 4 [0., hall/2, tweb/2], # 5 [0., hall/2, -tweb/2], # 6 [0., tflange/2, -tweb/2], # 7 ]) # 16 x 3 points.append(pointsi) return faces, points[0], points[1]
[docs]def t1_faces(n1: NDArray3float, n2: NDArray3float, xform: NDArray33float, dim1: Tuple[float, float, float, float], dim2: Tuple[float, float, float, float]): # validated """builds the T1 faces""" faces, points1, points2 = t1_setup(dim1, dim2) points_list = [] for nid, points in [(n1, points1), (n2, points2)]: pointsi = points @ xform + nid points_list.append(pointsi) return faces, np.vstack(points_list)
[docs]def t2_setup(dim1: Tuple[float, float, float, float], dim2: Tuple[float, float, float, float]) -> Tuple[Faces, NDArrayN3float, NDArrayN3float]: """ <--> tweb ^y | 0--7 ^ | | | hweb | | V 2--1 6--5 ^ hflange | |-|-->z 3--------4 v bflange <--------> """ faces = [ # front face [0, 1, 6, 7], [1, 2, 3, 4, 5, 6], # back face [8, 9, 14, 15], [9, 10, 11, 12, 13, 14], # around the T (counter-clockwise) [0, 8, 9, 1], [1, 9, 10, 2], [2, 10, 11, 3], [3, 11, 12, 4], [4, 12, 13, 5], [5, 13, 14, 6], [6, 14, 15, 7], [7, 15, 8, 0], ] points = [] for dim in (dim1, dim2): bflange, htotal, tflange, tweb = dim hweb = htotal - tflange pointsi = np.array([ # x, y, z [0., hweb + tflange/2, -tweb/2], # 0 [0., tflange/2, -tweb/2], # 1 [0., tflange/2, -bflange/2], # 2 [0., -tflange/2, -bflange/2], # 3 [0., -tflange/2, bflange/2], # 4 [0., tflange/2, bflange/2], # 5 [0., tflange/2, tweb/2], # 6 [0., hweb + tflange/2, tweb/2], # 7 ]) # 16 x 3 points.append(pointsi) return faces, points[0], points[1]
[docs]def t2_faces(n1: NDArray3float, n2: NDArray3float, xform: NDArray33float, dim1: Tuple[float, float, float, float], dim2: Tuple[float, float, float, float]): # validated """builds the T2 faces""" faces, points1, points2 = t2_setup(dim1, dim2) points_array = _transform_points(n1, n2, points1, points2, xform) return faces, points_array
[docs]def hat_setup(dim1: Tuple[float, float, float, float], dim2: Tuple[float, float, float, float]) -> Tuple[Faces, NDArrayN3float, NDArrayN3float]: """ <--------d3-------> 0----------------11 ^ --y3 d4 | A | d4 | <----> +-d2-5-------6-d2-+ <----> | --y2 | B | | B | | d1 2------1----+ +----10-----9 | --y1 | C | | C | t=d2 | 3-----------4 7-----------8 v --y0 | -z0 |-z1 |-z2 |z2 |z1 |z0 """ faces = [ # front face [1, 2, 3, 4], [0, 1, 4, 5], [0, 5, 6, 11], [6, 7, 10, 11], [7, 8, 9, 10], # back face [13, 14, 15, 16], [12, 13, 16, 17], [12, 17, 18, 23], [18, 19, 22, 23], [19, 20, 21, 22], # around the T (counter-clockwise) [0, 12, 13, 1], [1, 13, 14, 2], [2, 14, 15, 3], [3, 15, 16, 4], [4, 16, 17, 5], [5, 17, 18, 6], [6, 18, 19, 7], [7, 19, 20, 8], [8, 20, 21, 9], [9, 21, 22, 10,], [10, 22, 23, 11,], [11, 23, 12, 0], ] points = [] for dim in (dim1, dim2): d1, d2, d3, d4 = dim #hall, that, wmid, bfoot z0 = d3/2 + d4 z1 = d3/2. z2 = d3/2 - d2 y0 = 0. y1 = y0 + d2 y2 = d1 - d2 y3 = d1 pointsi = np.array([ # x, y, z [0., y3, -z1], # 0 [0., y1, -z1], # 1 [0., y1, -z0], # 2 [0., y0, -z0], # 3 [0., y0, -z2], # 4 [0., y2, -z2], # 5 [0., y2, z2], # 6 [0., y0, z2], # 7 [0., y0, z0], # 3 [0., y1, z0], # 2 [0., y1, z1], # 1 [0., y3, z1], # 0 ]) # 24 x 3 points.append(pointsi) return faces, points[0], points[1]
[docs]def hat_faces(n1: NDArray3float, n2: NDArray3float, xform: NDArray33float, dim1: Tuple[float, float, float, float], dim2: Tuple[float, float, float, float]): """builds the HAT faces""" faces, points1, points2 = hat_setup(dim1, dim2) points_array = _transform_points(n1, n2, points1, points2, xform) return faces, points_array