Merge remote-tracking branch 'origin/release' into release

pymoto/common/domain.py

@@ -184,10 +184,10 @@ def eval_shape_fun(self, pos: np.ndarray):
         """
         v = np.prod(self.element_size[:self.dim])
         assert v > 0.0, 'Element volume needs to be positive'
-        ret = np.ones(self.nnodes)/v
+        shapefn = np.ones(self.elemnodes)/v
         for i in range(self.dim):
-            ret *= np.array([self.element_size[i] + n[i]*pos[i] for n in self.node_numbering])
-        return ret
+            shapefn *= np.array([self.element_size[i]/2 + n[i]*pos[i] for n in self.node_numbering])
+        return shapefn
 
     def eval_shape_fun_der(self, pos: np.ndarray):
         """ Evaluates the shape function derivatives in x, y, and optionally z-direction.

tests/test_assembly.py

@@ -0,0 +1,91 @@
+import unittest
+import numpy as np
+import pymoto as pym
+import numpy.testing as npt
+
+
+class TestAssembleStiffness(unittest.TestCase):
+    def test_FEA_pure_tensile_2d_one_element(self):
+        Lx, Ly, Lz = 0.1, 0.2, 0.3
+        domain = pym.DomainDefinition(1, 1, unitx=Lx, unity=Ly, unitz=Lz)
+        nodidx_left = domain.get_nodenumber(0, np.arange(domain.nely + 1))
+        # Fixed at bottom, roller at the top in y-direction
+        nodidx_right = domain.get_nodenumber(domain.nelx, np.arange(domain.nely + 1))
+        dofidx_left = np.concatenate([nodidx_left*2, np.array([nodidx_left[0]*2 + 1])])
+
+        E, nu = 210e+9, 0.3
+
+        s_x = pym.Signal('x', state=np.ones(domain.nel))
+
+        # Assemble stiffness matrix
+        m_K = pym.AssembleStiffness(s_x, domain=domain, bc=dofidx_left, e_modulus=E, poisson_ratio=nu, plane='stress')
+        s_K = m_K.sig_out[0]
+
+        m_K.response()
+        F = 1.5
+        f = np.zeros(domain.nnodes*2)
+        f[nodidx_right * 2] = F/nodidx_right.size
+        x = np.linalg.solve(s_K.state.toarray(), f)
+
+        # Bottom y displacement should be zero
+        npt.assert_allclose(x[nodidx_right[0]*2+1], 0, atol=1e-10)
+
+        # Analytical axial displacement using stiffness k = EA/L
+        ux_chk = F * Lx / (E * Ly * Lz)
+        npt.assert_allclose(x[nodidx_right*2], ux_chk, rtol=1e-10)
+
+        # Transverse displacement using Poisson's effect
+        e_xx = ux_chk / Lx  # Strain in x-direction
+        e_yy = - nu * e_xx
+        uy_chk = e_yy * Ly
+        npt.assert_allclose(x[nodidx_right[1]*2+1], uy_chk, rtol=1e-10)
+
+    def test_FEA_pure_tensile_3d_one_element(self):
+        Lx, Ly, Lz = 0.1, 0.2, 0.3
+        domain = pym.DomainDefinition(1, 1, 1, unitx=Lx, unity=Ly, unitz=Lz)
+        nodidx_left = domain.get_nodenumber(*np.meshgrid(0, range(domain.nely + 1), range(domain.nelz + 1))).flatten()
+        # Fixed at (0,0,0), roller in z-direction at (0, 1, 0), roller in y-direction at (0, 0, 1)
+        nod_00 = domain.get_nodenumber(0, 0, 0)
+        nod_10 = domain.get_nodenumber(0, 1, 0)
+        nod_01 = domain.get_nodenumber(0, 0, 1)
+        dofidx_left = np.concatenate([nodidx_left * 3, np.array([nod_00, nod_01]) * 3 + 1, np.array([nod_00, nod_10]) * 3 + 2])
+        nodidx_right = domain.get_nodenumber(*np.meshgrid(1, range(domain.nely + 1), range(domain.nelz + 1))).flatten()
+
+        E, nu = 210e+9, 0.3
+
+        s_x = pym.Signal('x', state=np.ones(domain.nel))
+
+        # Assemble stiffness matrix
+        m_K = pym.AssembleStiffness(s_x, domain=domain, bc=dofidx_left, e_modulus=E, poisson_ratio=nu)
+        s_K = m_K.sig_out[0]
+
+        m_K.response()
+        F = 1.5e+3
+        f = np.zeros(domain.nnodes * 3)
+        f[nodidx_right * 3] = F / nodidx_right.size
+        x = np.linalg.solve(s_K.state.toarray(), f)
+
+        # y and z displacements at (1, 0, 0) should be zero
+        npt.assert_allclose(x[domain.get_nodenumber(1, 0, 0) * 3 + 1], 0, atol=1e-10)
+        npt.assert_allclose(x[domain.get_nodenumber(1, 0, 0) * 3 + 2], 0, atol=1e-10)
+
+        # Z displacement at (1, 1, 0) should be zero
+        npt.assert_allclose(x[domain.get_nodenumber(1, 1, 0) * 3 + 2], 0, atol=1e-10)
+
+        # Y displacement at (1, 0, 1) should be zero
+        npt.assert_allclose(x[domain.get_nodenumber(1, 0, 1) * 3 + 1], 0, atol=1e-10)
+
+        # Analytical axial displacement using stiffness k = EA/L
+        ux_chk = F * Lx / (E * Ly * Lz)
+        npt.assert_allclose(x[nodidx_right * 3], ux_chk, rtol=1e-10)
+
+        # Transverse displacement using Poisson's effect
+        e_xx = ux_chk / Lx  # Strain in x-direction
+        e_trans = - nu * e_xx
+        uy_chk = e_trans * Ly
+        npt.assert_allclose(x[domain.get_nodenumber(1, 1, 0) * 3 + 1], uy_chk, rtol=1e-10)
+        npt.assert_allclose(x[domain.get_nodenumber(1, 1, 1) * 3 + 1], uy_chk, rtol=1e-10)
+
+        uz_chk = e_trans * Lz
+        npt.assert_allclose(x[domain.get_nodenumber(1, 0, 1) * 3 + 2], uz_chk, rtol=1e-10)
+        npt.assert_allclose(x[domain.get_nodenumber(1, 1, 1) * 3 + 2], uz_chk, rtol=1e-10)