def setUp(self):
self.steel = Steel()
self.elastic_modulus = self.steel.elastic_modulus
self.ixx = np.random.uniform(10e6, 200e6)
self.length = np.random.uniform(2e3, 10e3)
self.q = -np.random.uniform(1, 10)
self.pl = -np.random.uniform(5e3, 50e3)
def setUp(self):
# create materials
steel = Steel()
# create 2d frame analysis object
self.analysis = FrameAnalysis2D()
section1 = Section(area=6e3, ixx=200e6)
section2 = Section(area=4e3, ixx=50e6)
# create nodes
self.node_a = self.analysis.create_node(coords=[0])
self.node_b = self.analysis.create_node(coords=[8000])
self.node_c = self.analysis.create_node(coords=[13000])
# create beam elements
self.element_ab = self.analysis.create_element(
el_type='EB2-2D',
nodes=[self.node_a, self.node_b],
material=steel,
section=section1)
self.element_bc = self.analysis.create_element(
el_type='EB2-2D',
nodes=[self.node_b, self.node_c],
material=steel,
section=section2)
def test_example2_1(self):
nodes = [] # list holding the node objects
elements = [] # list holding the element objects
# create 2d frame analysis object
analysis = FrameAnalysis2D()
# create sections
steel = Steel()
section1 = Section(area=6000)
section2 = Section(area=8000)
# create nodes
nodes.append(analysis.create_node(coords=[0, 0]))
nodes.append(analysis.create_node(coords=[6000, 4000]))
nodes.append(analysis.create_node(coords=[9000, 0]))
# create truss elements
elements.append(analysis.create_element(
el_type='Bar2-2D', nodes=[nodes[0], nodes[1]], material=steel, section=section1
))
elements.append(analysis.create_element(
el_type='Bar2-2D', nodes=[nodes[1], nodes[2]], material=steel, section=section2
))
# add supports
freedom_case = cases.FreedomCase()
freedom_case.add_nodal_support(node=nodes[0], val=0, dof=0)
freedom_case.add_nodal_support(node=nodes[0], val=0, dof=1)
freedom_case.add_nodal_support(node=nodes[2], val=0, dof=0)
freedom_case.add_nodal_support(node=nodes[2], val=0, dof=1)
# add loads
load_case = cases.LoadCase()
load_case.add_nodal_load(node=nodes[1], val=500e3, dof=0)
# add analysis case
analysis_case = cases.AnalysisCase(freedom_case=freedom_case, load_case=load_case)
# linear static solver
LinearStatic(analysis=analysis, analysis_cases=[analysis_case]).solve()
# check node displacement
n1_disp = nodes[1].get_displacements(analysis_case)
u = n1_disp[0]
v = n1_disp[1]
self.assertEqual(np.around(u, 2), 2.41)
self.assertEqual(np.around(v, 2), 0.72)
# check axial forces
(_, n1) = elements[0].get_afd(n=1, analysis_case=analysis_case)
(_, n2) = elements[1].get_afd(n=1, analysis_case=analysis_case)
self.assertEqual(np.around(n1/1e3, 1), 400.6)
self.assertEqual(np.around(n2/1e3, 1), -277.8)
def test_example2_3(self):
# create 2d frame analysis object
analysis = FrameAnalysis2D()
# create sections
steel = Steel()
section1 = Section(area=4000)
section2 = Section(area=1000)
# create nodes
a = analysis.create_node(coords=[0, 0])
b = analysis.create_node(coords=[2000, 2000])
c = analysis.create_node(coords=[-4000, 2000])
# create truss elements
el1 = analysis.create_element(el_type='Bar2-2D',
nodes=[c, a],
material=steel,
section=section1)
el2 = analysis.create_element(el_type='Bar2-2D',
nodes=[a, b],
material=steel,
section=section2)
# add supports
freedom_case = cases.FreedomCase()
freedom_case.add_nodal_support(node=b, val=0, dof=0)
freedom_case.add_nodal_support(node=b, val=0, dof=1)
freedom_case.add_nodal_support(node=c, val=0, dof=0)
freedom_case.add_nodal_support(node=c, val=0, dof=1)
sup1 = freedom_case.add_nodal_support(node=a, val=0, dof=0)
sup2 = freedom_case.add_nodal_support(node=a, val=-5, dof=1)
# add loads
load_case = cases.LoadCase()
# add analysis case
analysis_case = cases.AnalysisCase(freedom_case=freedom_case,
load_case=load_case)
# linear static solver
LinearStatic(analysis=analysis, analysis_cases=[analysis_case]).solve()
# check reactions
self.assertEqual(np.around(sup1.get_reaction(analysis_case) / 1e3, 1),
181.0)
self.assertEqual(np.around(sup2.get_reaction(analysis_case) / 1e3, 1),
-355.7)
def setUp(self):
steel = Steel()
# create a rectangular element
self.width = 5
self.height = 3
self.node1 = Node([0, 0])
self.node2 = Node([self.width, 0])
self.node3 = Node([self.width, self.height])
self.node4 = Node([0, self.height])
self.element = FiniteElement(
nodes=[self.node1, self.node2, self.node3, self.node4],
material=steel,
efs=[True, True, False, False, False, False])
def setUp(self):
steel = Steel()
section = Section()
# create an FrameElement2D elemnetn
self.x = 4
self.y = 3
self.node1 = Node([0, 0])
self.node2 = Node([self.x, self.y])
self.element_frame = FrameElement(
nodes=[self.node1, self.node2], material=steel, section=section,
efs=[True, True, False, False, False, True]
)
self.element_frame2D = FrameElement2D(
nodes=[self.node1, self.node2], material=steel, section=section,
efs=[True, True, False, False, False, False]
)
# ------------
# preprocessor
# ------------
# lists
nodes = [] # list holding the node objects
elements = [] # list holding the element objects
freedom_cases = [] # list holding the freedom cases
load_cases = [] # list holding the load cases
analysis_cases = [] # list holding the analysis cases
# create 2d frame analysis object
analysis = FrameAnalysis2D()
# create materials and sections
steel = Steel()
section = Section(area=3230, ixx=23.6e6)
# create nodes
nodes.append(analysis.create_node(coords=[0, 0]))
nodes.append(analysis.create_node(coords=[1500, 0]))
nodes.append(analysis.create_node(coords=[3000, 1500]))
# create beam elements
for i in range(2):
elements.append(
analysis.create_element(el_type='EB2-2D',
nodes=[nodes[i], nodes[i + 1]],
material=steel,
section=section))
def test_example2_2(self):
# create 2d frame analysis object
analysis = FrameAnalysis2D()
# create sections
steel = Steel()
section1 = Section(area=5000)
section2 = Section(area=3000)
# create nodes
a = analysis.create_node(coords=[0, 0])
b = analysis.create_node(coords=[3000, 3000])
c = analysis.create_node(coords=[3000, -3000])
d = analysis.create_node(coords=[-3000 / np.tan(np.pi / 6), 3000])
e = analysis.create_node(coords=[-3000 / np.tan(np.pi / 6), -3000])
# create truss elements
el1 = analysis.create_element(el_type='Bar2-2D',
nodes=[e, a],
material=steel,
section=section1)
el2 = analysis.create_element(el_type='Bar2-2D',
nodes=[d, a],
material=steel,
section=section1)
el3 = analysis.create_element(el_type='Bar2-2D',
nodes=[b, a],
material=steel,
section=section2)
el4 = analysis.create_element(el_type='Bar2-2D',
nodes=[c, a],
material=steel,
section=section2)
# add supports
freedom_case = cases.FreedomCase()
freedom_case.add_nodal_support(node=b, val=0, dof=0)
freedom_case.add_nodal_support(node=b, val=0, dof=1)
freedom_case.add_nodal_support(node=c, val=0, dof=0)
freedom_case.add_nodal_support(node=c, val=0, dof=1)
freedom_case.add_nodal_support(node=d, val=0, dof=0)
freedom_case.add_nodal_support(node=d, val=0, dof=1)
freedom_case.add_nodal_support(node=e, val=0, dof=0)
freedom_case.add_nodal_support(node=e, val=0, dof=1)
# add loads
load_case = cases.LoadCase()
load_case.add_nodal_load(node=a, val=1000e3, dof=0)
# add analysis case
analysis_case = cases.AnalysisCase(freedom_case=freedom_case,
load_case=load_case)
# linear static solver
LinearStatic(analysis=analysis, analysis_cases=[analysis_case]).solve()
# check node displacement
dofs = a.get_dofs(a.nfs)
u = dofs[0].get_displacement(analysis_case)
v = dofs[1].get_displacement(analysis_case)
self.assertEqual(np.around(u, 2), 2.55)
self.assertEqual(np.around(v, 2), 0)
# check axial forces
n1 = el1.get_afd(n=1, analysis_case=analysis_case)
n2 = el2.get_afd(n=1, analysis_case=analysis_case)
n3 = el3.get_afd(n=1, analysis_case=analysis_case)
n4 = el4.get_afd(n=1, analysis_case=analysis_case)
self.assertEqual(np.around(n1 / 1e3, 1), 368.8)
self.assertEqual(np.around(n2 / 1e3, 1), 368.8)
self.assertEqual(np.around(n3 / 1e3, 1), -255.5)
self.assertEqual(np.around(n4 / 1e3, 1), -255.5)
def setUp(self):
# create materials
self.steel = Steel()
def preprocessor(length, depth, panels, freq):
w = 10 # load per unit length [N/mm]
dx = length / panels # length of a truss panel
# create 2d frame analysis object
analysis = FrameAnalysis2D()
# create materials and sections
steel = Steel()
section_deck = Section(area=3230, ixx=23.6e6) # 200UB25
section_vertical = Section(area=3000, ixx=3.91e6) # 100x9 SHS
section_diagonal = Section(area=314) # 20 dia rod
section_tie = Section(area=1018) # 36 dia rod
# create deck nodes
nodes_deck = []
for i in range(panels + 1):
nodes_deck.append(analysis.create_node(coords=[i * dx]))
# create tie nodes - first node coincides with first deck node
nodes_tie = [nodes_deck[0]]
for i in range(panels - 1):
# fit parabola
x = (i + 1) * dx
y = 4 * depth / length / length * x * x - 4 * depth / length * x
nodes_tie.append(analysis.create_node(coords=[x, y]))
# last node coincides with last deck node
nodes_tie.append(nodes_deck[-1])
# create deck (beam) elements
elements_deck = []
for i in range(panels):
elements_deck.append(
analysis.create_element(el_type='EB2-2D',
nodes=[nodes_deck[i], nodes_deck[i + 1]],
material=steel,
section=section_deck))
# create tie (bar) elements
elements_tie = []
for i in range(panels):
elements_tie.append(
analysis.create_element(el_type='Bar2-2D',
nodes=[nodes_tie[i], nodes_tie[i + 1]],
material=steel,
section=section_tie))
# create vertical (beam) elements
elements_vertical = []
for i in range(panels - 1):
elements_vertical.append(
analysis.create_element(
el_type='EB2-2D',
nodes=[nodes_deck[i + 1], nodes_tie[i + 1]],
material=steel,
section=section_vertical))
# create diagonal (bar) elements
elements_diaongal = []
for i in range(panels - 2):
elements_diaongal.append(
analysis.create_element(
el_type='Bar2-2D',
nodes=[nodes_deck[i + 1], nodes_tie[i + 2]],
material=steel,
section=section_diagonal))
elements_diaongal.append(
analysis.create_element(
el_type='Bar2-2D',
nodes=[nodes_deck[i + 2], nodes_tie[i + 1]],
material=steel,
section=section_diagonal))
# add supports
freedom_case = cases.FreedomCase()
freedom_case.add_nodal_support(node=nodes_deck[0], val=0, dof=0)
freedom_case.add_nodal_support(node=nodes_deck[0], val=0, dof=1)
freedom_case.add_nodal_support(node=nodes_deck[-1], val=0, dof=1)
# add loads
load_case = cases.LoadCase()
# if frequency analysis, don't bother adding load
if not freq:
for el in elements_deck:
load_case.add_element_load(el.generate_udl(q=-w))
# add analysis case
analysis_case = cases.AnalysisCase(freedom_case=freedom_case,
load_case=load_case)
return (analysis, analysis_case)
def test_example5_7(self):
l_a = np.sqrt(8000 * 8000 - 3000 * 3000)
# create materials
steel = Steel()
# create 2d frame analysis object
analysis = FrameAnalysis2D()
section = Section(area=6e3, ixx=200e6)
# create nodes
node_a = analysis.create_node(coords=[0])
node_b = analysis.create_node(coords=[l_a, 3000])
node_c = analysis.create_node(coords=[l_a + 8000, 3000])
# create beam elements
element_ab = analysis.create_element(
el_type='EB2-2D', nodes=[node_a, node_b], material=steel, section=section
)
element_bc = analysis.create_element(
el_type='EB2-2D', nodes=[node_b, node_c], material=steel, section=section
)
# add supports
freedom_case = cases.FreedomCase()
sup_a = [0, 0, 0]
sup_a[0] = freedom_case.add_nodal_support(node=node_a, val=0, dof=0)
sup_a[1] = freedom_case.add_nodal_support(node=node_a, val=0, dof=1)
sup_a[2] = freedom_case.add_nodal_support(node=node_a, val=0, dof=5)
sup_c = [0, 0, 0]
sup_c[0] = freedom_case.add_nodal_support(node=node_c, val=0, dof=0)
sup_c[1] = freedom_case.add_nodal_support(node=node_c, val=0, dof=1)
sup_c[2] = freedom_case.add_nodal_support(node=node_c, val=0, dof=5)
# add loads
load_case = cases.LoadCase()
load_case.add_nodal_load(node=node_b, val=50e3 * 3000 / 8000, dof=0)
load_case.add_nodal_load(node=node_b, val=-50e3 * l_a / 8000, dof=1)
load_case.add_element_load(element_bc.generate_udl(q=-4))
# add analysis case
analysis_case = cases.AnalysisCase(freedom_case=freedom_case, load_case=load_case)
# linear static solver
LinearStatic(analysis=analysis, analysis_cases=[analysis_case]).solve()
# check node displacement
disp_b = node_b.get_displacements(analysis_case)
u_b = disp_b[0]
v_b = disp_b[1]
r_b = disp_b[5]
self.assertEqual(np.around(u_b, 4), 0.9950)
self.assertEqual(np.around(v_b, 3), -4.982)
self.assertEqual(np.around(r_b, 6), -0.000534)
# check reactions
ra_x = sup_a[0].get_reaction(analysis_case=analysis_case)
ra_y = sup_a[1].get_reaction(analysis_case=analysis_case)
ra_m = sup_a[2].get_reaction(analysis_case=analysis_case)
rc_x = sup_c[0].get_reaction(analysis_case=analysis_case)
rc_y = sup_c[1].get_reaction(analysis_case=analysis_case)
rc_m = sup_c[2].get_reaction(analysis_case=analysis_case)
self.assertEqual(np.around(ra_x/1e3, 1), 130.5)
self.assertEqual(np.around(ra_y/1e3, 1), 55.7)
self.assertEqual(np.around(ra_m/1e6, 2), 13.37)
self.assertEqual(np.around(rc_x/1e3, 1), -149.3)
self.assertEqual(np.around(rc_y/1e3, 1), 22.7)
self.assertEqual(np.around(rc_m/1e6, 2), -45.36)
def test_example5_4(self):
# create materials
steel = Steel()
# create 3d frame analysis object
analysis = FrameAnalysis3D()
section_ab = Section(area=20e3)
section_ac = Section(area=30e3)
section_ad = Section(area=40e3)
section_ae = Section(area=30e3)
# create nodes
node_a = analysis.create_node(coords=[2000, 4000, 8000])
node_b = analysis.create_node(coords=[0, 0, 0])
node_c = analysis.create_node(coords=[8000, 0, 0])
node_d = analysis.create_node(coords=[8000, 6000, 0])
node_e = analysis.create_node(coords=[0, 6000, 0])
# create truss elements
element_ab = analysis.create_element(
el_type='Bar2-3D', nodes=[node_a, node_b], material=steel, section=section_ab
)
element_ac = analysis.create_element(
el_type='Bar2-3D', nodes=[node_a, node_c], material=steel, section=section_ac
)
element_ad = analysis.create_element(
el_type='Bar2-3D', nodes=[node_a, node_d], material=steel, section=section_ad
)
element_ae = analysis.create_element(
el_type='Bar2-3D', nodes=[node_a, node_e], material=steel, section=section_ae
)
# add supports
freedom_case = cases.FreedomCase()
sup_b = [0, 0, 0]
sup_c = [0, 0, 0]
sup_d = [0, 0, 0]
sup_e = [0, 0, 0]
sup_b[0] = freedom_case.add_nodal_support(node=node_b, val=0, dof=0)
sup_b[1] = freedom_case.add_nodal_support(node=node_b, val=0, dof=1)
sup_b[2] = freedom_case.add_nodal_support(node=node_b, val=0, dof=2)
sup_c[0] = freedom_case.add_nodal_support(node=node_c, val=0, dof=0)
sup_c[1] = freedom_case.add_nodal_support(node=node_c, val=0, dof=1)
sup_c[2] = freedom_case.add_nodal_support(node=node_c, val=0, dof=2)
sup_d[0] = freedom_case.add_nodal_support(node=node_d, val=0, dof=0)
sup_d[1] = freedom_case.add_nodal_support(node=node_d, val=0, dof=1)
sup_d[2] = freedom_case.add_nodal_support(node=node_d, val=0, dof=2)
sup_e[0] = freedom_case.add_nodal_support(node=node_e, val=0, dof=0)
sup_e[1] = freedom_case.add_nodal_support(node=node_e, val=0, dof=1)
sup_e[2] = freedom_case.add_nodal_support(node=node_e, val=0, dof=2)
# add loads
load_case = cases.LoadCase()
load_case.add_nodal_load(node=node_a, val=200e3, dof=0)
load_case.add_nodal_load(node=node_a, val=600e3, dof=1)
load_case.add_nodal_load(node=node_a, val=-800e3, dof=2)
# add analysis case
analysis_case = cases.AnalysisCase(freedom_case=freedom_case, load_case=load_case)
# linear static solver
LinearStatic(analysis=analysis, analysis_cases=[analysis_case]).solve()
# check node displacement
disp_a = node_a.get_displacements(analysis_case)
u_a = disp_a[0]
v_a = disp_a[1]
w_a = disp_a[2]
self.assertEqual(np.around(u_a, 3), 0.178)
self.assertEqual(np.around(v_a, 3), 2.722)
self.assertEqual(np.around(w_a, 3), -0.487)
# check reactions
rb_x = sup_b[0].get_reaction(analysis_case=analysis_case)
rb_y = sup_b[1].get_reaction(analysis_case=analysis_case)
rb_z = sup_b[2].get_reaction(analysis_case=analysis_case)
rc_x = sup_c[0].get_reaction(analysis_case=analysis_case)
rc_y = sup_c[1].get_reaction(analysis_case=analysis_case)
rc_z = sup_c[2].get_reaction(analysis_case=analysis_case)
rd_x = sup_d[0].get_reaction(analysis_case=analysis_case)
rd_y = sup_d[1].get_reaction(analysis_case=analysis_case)
rd_z = sup_d[2].get_reaction(analysis_case=analysis_case)
re_x = sup_e[0].get_reaction(analysis_case=analysis_case)
re_y = sup_e[1].get_reaction(analysis_case=analysis_case)
re_z = sup_e[2].get_reaction(analysis_case=analysis_case)
self.assertEqual(np.around(rb_x/1e3, 1), -76.4)
self.assertEqual(np.around(rb_y/1e3, 1), -152.8)
self.assertEqual(np.around(rb_z/1e3, 1), -305.6)
self.assertEqual(np.around(rc_x/1e3, 1), 170.8)
self.assertEqual(np.around(rc_y/1e3, 1), -113.9)
self.assertEqual(np.around(rc_z/1e3, 1), -227.8)
self.assertEqual(np.around(rd_x/1e3, 1), -470.8)
self.assertEqual(np.around(rd_y/1e3, 1), -156.9)
self.assertEqual(np.around(rd_z/1e3, 1), 627.8)
self.assertEqual(np.around(re_x/1e3, 1), 176.4)
self.assertEqual(np.around(re_y/1e3, 1), -176.4)
self.assertEqual(np.around(re_z/1e3, 1), 705.6)
def test_example5_6(self):
# create materials
steel = Steel()
# create 2d frame analysis object
analysis = FrameAnalysis2D()
section_ab = Section(area=6e3, ixx=200e6)
section_bc = Section(area=4e3, ixx=50e6)
# create nodes
node_a = analysis.create_node(coords=[0])
node_b = analysis.create_node(coords=[8000])
node_p = analysis.create_node(coords=[10000])
node_c = analysis.create_node(coords=[13000])
# create beam elements
element_ab = analysis.create_element(
el_type='EB2-2D', nodes=[node_a, node_b], material=steel, section=section_ab
)
element_bp = analysis.create_element(
el_type='EB2-2D', nodes=[node_b, node_p], material=steel, section=section_bc
)
element_pc = analysis.create_element(
el_type='EB2-2D', nodes=[node_p, node_c], material=steel, section=section_bc
)
# add supports
freedom_case = cases.FreedomCase()
sup_a = freedom_case.add_nodal_support(node=node_a, val=0, dof=1)
sup_b = freedom_case.add_nodal_support(node=node_b, val=0, dof=1)
sup_c = [0, 0, 0]
sup_c[0] = freedom_case.add_nodal_support(node=node_c, val=0, dof=0)
sup_c[1] = freedom_case.add_nodal_support(node=node_c, val=0, dof=1)
sup_c[2] = freedom_case.add_nodal_support(node=node_c, val=0, dof=5)
# add loads
load_case = cases.LoadCase()
load_case.add_element_load(element_ab.generate_udl(q=-2))
load_case.add_nodal_load(node=node_p, val=-20e3, dof=1)
# add analysis case
analysis_case = cases.AnalysisCase(freedom_case=freedom_case, load_case=load_case)
# linear static solver
LinearStatic(analysis=analysis, analysis_cases=[analysis_case]).solve()
# check node displacement
disp_a = node_a.get_displacements(analysis_case)
disp_b = node_b.get_displacements(analysis_case)
r_a = disp_a[5]
r_b = disp_b[5]
self.assertEqual(np.around(r_a, 7), -5.681e-4)
self.assertEqual(np.around(r_b, 7), 0.696e-4)
# check reactions
ra_y = sup_a.get_reaction(analysis_case=analysis_case)
rb_y = sup_b.get_reaction(analysis_case=analysis_case)
rc_y = sup_c[1].get_reaction(analysis_case=analysis_case)
rc_m = sup_c[2].get_reaction(analysis_case=analysis_case)
self.assertEqual(np.around(ra_y/1e3, 2), 6.13)
self.assertEqual(np.around(rb_y/1e3, 2), 23.00)
self.assertEqual(np.around(rc_y/1e3, 2), 6.87)
self.assertEqual(np.around(rc_m/1e6, 2), -9.32)
def test_example3_3(self):
nodes = [] # list holding the node objects
elements = [] # list holding the element objects
# create 2d frame analysis object
analysis = FrameAnalysis2D()
# create sections
steel = Steel()
section1 = Section(area=15e3)
section2 = Section(area=18e3)
section3 = Section(area=20e3)
# create nodes
nodes.append(analysis.create_node(coords=[0, 0]))
nodes.append(analysis.create_node(coords=[4000/np.tan(np.pi/6), 4000]))
nodes.append(analysis.create_node(coords=[4000/np.tan(np.pi/6) + 4000, 0]))
nodes.append(analysis.create_node(coords=[0, 4000]))
# create truss elements
elements.append(analysis.create_element(
el_type='Bar2-2D', nodes=[nodes[0], nodes[1]], material=steel, section=section1
))
elements.append(analysis.create_element(
el_type='Bar2-2D', nodes=[nodes[1], nodes[2]], material=steel, section=section3
))
elements.append(analysis.create_element(
el_type='Bar2-2D', nodes=[nodes[0], nodes[2]], material=steel, section=section2
))
elements.append(analysis.create_element(
el_type='Bar2-2D', nodes=[nodes[3], nodes[1]], material=steel, section=section3
))
# add supports
freedom_case = cases.FreedomCase()
sup1 = freedom_case.add_nodal_support(node=nodes[0], val=0, dof=0)
sup2 = freedom_case.add_nodal_support(node=nodes[0], val=0, dof=1)
sup3 = freedom_case.add_nodal_support(node=nodes[2], val=0, dof=1)
sup4 = freedom_case.add_nodal_support(node=nodes[3], val=0, dof=0)
sup5 = freedom_case.add_nodal_support(node=nodes[3], val=0, dof=1)
# add loads
load_case = cases.LoadCase()
load_case.add_nodal_load(node=nodes[1], val=500e3*np.cos(2*np.pi/9), dof=0)
load_case.add_nodal_load(node=nodes[1], val=500e3*np.sin(2*np.pi/9), dof=1)
# add analysis case
analysis_case = cases.AnalysisCase(freedom_case=freedom_case, load_case=load_case)
# linear static solver
LinearStatic(analysis=analysis, analysis_cases=[analysis_case]).solve()
# check node displacement
disp_a = nodes[1].get_displacements(analysis_case)
disp_b = nodes[2].get_displacements(analysis_case)
u_a = disp_a[0]
v_a = disp_a[1]
u_b = disp_b[0]
self.assertEqual(np.around(u_a, 2), 0.38)
self.assertEqual(np.around(v_a, 2), 1.23)
self.assertEqual(np.around(u_b, 2), -0.44)
# check reactions
rc_x = sup1.get_reaction(analysis_case=analysis_case)
rc_y = sup2.get_reaction(analysis_case=analysis_case)
rb_y = sup3.get_reaction(analysis_case=analysis_case)
rd_x = sup4.get_reaction(analysis_case=analysis_case)
rd_y = sup5.get_reaction(analysis_case=analysis_case)
self.assertEqual(np.around(rc_x/1e3, 1), -162.5)
self.assertEqual(np.around(rc_y/1e3, 1), -177.1)
self.assertEqual(np.around(rb_y/1e3, 1), -144.3)
self.assertEqual(np.around(rd_x/1e3, 1), -220.5)
self.assertEqual(np.around(rd_y/1e3, 1), 0)
def test_example3_2(self):
nodes = [] # list holding the node objects
elements = [] # list holding the element objects
# create 2d frame analysis object
analysis = FrameAnalysis2D()
# create sections
steel = Steel()
section1 = Section(area=15e3)
section2 = Section(area=18e3)
section3 = Section(area=20e3)
# create nodes
nodes.append(analysis.create_node(coords=[0, 0]))
nodes.append(
analysis.create_node(coords=[4000 / np.tan(np.pi / 6), 4000]))
nodes.append(
analysis.create_node(coords=[4000 / np.tan(np.pi / 6) + 4000, 0]))
# create truss elements
elements.append(
analysis.create_element(el_type='Bar2-2D',
nodes=[nodes[0], nodes[1]],
material=steel,
section=section1))
elements.append(
analysis.create_element(el_type='Bar2-2D',
nodes=[nodes[1], nodes[2]],
material=steel,
section=section3))
elements.append(
analysis.create_element(el_type='Bar2-2D',
nodes=[nodes[0], nodes[2]],
material=steel,
section=section2))
# add supports
freedom_case = cases.FreedomCase()
sup1 = freedom_case.add_nodal_support(node=nodes[0], val=0, dof=0)
sup2 = freedom_case.add_nodal_support(node=nodes[0], val=0, dof=1)
sup3 = freedom_case.add_nodal_support(node=nodes[2], val=0, dof=1)
# add loads
load_case = cases.LoadCase()
load_case.add_nodal_load(node=nodes[1],
val=500e3 * np.cos(2 * np.pi / 9),
dof=0)
load_case.add_nodal_load(node=nodes[1],
val=500e3 * np.sin(2 * np.pi / 9),
dof=1)
# add analysis case
analysis_case = cases.AnalysisCase(freedom_case=freedom_case,
load_case=load_case)
# linear static solver
LinearStatic(analysis=analysis, analysis_cases=[analysis_case]).solve()
# check node displacement
node_a = nodes[1]
node_b = nodes[2]
dofs_a = node_a.get_dofs(node_a.nfs)
dofs_b = node_b.get_dofs(node_b.nfs)
u_a = dofs_a[0].get_displacement(analysis_case)
v_a = dofs_a[1].get_displacement(analysis_case)
u_b = dofs_b[0].get_displacement(analysis_case)
self.assertEqual(np.around(u_a, 2), 0.87)
self.assertEqual(np.around(v_a, 2), 1.24)
self.assertEqual(np.around(u_b, 2), -0.19)
# check axial forces
n1 = elements[0].get_afd(n=1, analysis_case=analysis_case)
n2 = elements[1].get_afd(n=1, analysis_case=analysis_case)
n3 = elements[2].get_afd(n=1, analysis_case=analysis_case)
self.assertEqual(np.around(n1 / 1e3, 1), 515.7)
self.assertEqual(np.around(n2 / 1e3, 1), 89.9)
self.assertEqual(np.around(n3 / 1e3, 1), -63.6)
# check reactions
rc_x = sup1.get_reaction(analysis_case=analysis_case)
rc_y = sup2.get_reaction(analysis_case=analysis_case)
rb_y = sup3.get_reaction(analysis_case=analysis_case)
self.assertEqual(np.around(rc_x / 1e3, 1), -383.0)
self.assertEqual(np.around(rc_y / 1e3, 1), -257.8)
self.assertEqual(np.around(rb_y / 1e3, 1), -63.6)