C 代码 实施各种二维有限元法（FEM）计算.rar

02 March 2022 06:30:28 PM FEM2D_PACK_TEST: C version Test FEM2D_PACK. TEST03 BASIS_11_T3_TEST - Test the T3 basis functions. BASIS_11_T4_TEST - Test the T4 basis functions. BASIS_11_T6_TEST - Test the T6 basis functions. BASIS_11_T3_TEST: Verify basis functions for element T3. Number of nodes = 3 Physical Nodes: 0 2 0 1 4 3 2 0 4 The basis function values at basis nodes should form the identity matrix. 1 0 0 -0 1 0 0 0 1 The X and Y derivatives should sum to 0. dPhidX sum, dPhidY sum: 0 0 0 0 0 0 BASIS_11_T4_TEST: Verify basis functions for element T4. Number of nodes = 4 Physical Nodes: 0 2 0 1 4 3 2 0 4 3 2 2.33333 The basis function values at basis nodes should form the identity matrix. 1 0 0 0 0 1 0 -0 0 0 1 0 -1.11022e-16 -5.55112e-17 -5.55112e-17 1 The X and Y derivatives should sum to 0. dPhidX sum, dPhidY sum: 0 0 0 0 0 0 2.08167e-17 1.73472e-17 BASIS_11_T6_TEST: Verify basis functions for element T6. Number of nodes = 6 Physical Nodes: 0 2 0 1 4 3 2 0 4 3 3 1.5 4 2 3.5 5 1 2 The basis function values at basis nodes should form the identity matrix. 1 0 0 -0 0 -0 0 1 -0 -0 0 0 0 0 1 0 -0 -0 0 -0 -0 1 -0 0 -0 0 0 0 1 -0 -0 -0 -0 -0 0 1 The X and Y derivatives should sum to 0. dPhidX sum, dPhidY sum: 0 0 0 0 0 0 0 0 -2.77556e-17 0 0 0 TEST04 Test the computation of basis functions by evaluating them at the nodes that define the basis functions. BASIS_MN_Q4_TEST - for the Q4 element. BASIS_MN_T3_TEST - for the T3 element. BASIS_MN_T4_TEST - for the T4 element. BASIS_MN_T6_TEST - for the T6 element. BASIS_MN_Q4_TEST: Verify basis functions for element Q4. Number of nodes = 4 Physical Nodes: 0 3 1 1 5 1 2 5 4 3 3 4 The basis function values at basis nodes should form the identity matrix. 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 The X and Y derivatives should sum to 0. dPhidX sum, dPhidY sum: 0 0 0 0 0 0 0 0 BASIS_MN_T3_TEST: Verify basis functions for element T3. Number of nodes = 3 Physical Nodes: 0 2 0 1 4 3 2 0 4 The basis function values at basis nodes should form the identity matrix. 1 0 0 -0 1 0 0 0 1 The X and Y derivatives should sum to 0. dPhidX sum, dPhidY sum: 0 0 0 0 0 0 BASIS_MN_T4_TEST: Verify basis functions for element T4. Number of nodes = 4 Physical Nodes: 0 2 0 1 4 2 2 0 4 3 2 2 The basis function values at basis nodes should form the identity matrix. 1 0 0 0 0 1 0 -0 0 0 1 0 0 0 0 1 The X and Y derivatives should sum to 0. dPhidX sum, dPhidY sum: 0 0 0 0 0 0 0 0 BASIS_MN_T6_TEST: Verify basis functions for element T6. Number of nodes = 6 Physical Nodes: 0 2 0 1 4 3 2 0 4 3 3 1.5 4 2 3.5 5 1 2 The basis function values at basis nodes should form the identity matrix. 1 0 0 -0 0 -0 -0 1 -0 -0 0 -0 -0 -0 1 -0 -0 -0 -0 0 -0 1 0 -0 -0 -0 0 -0 1 0 0 -0 -0 0 -0 1 The X and Y derivatives should sum to 0. dPhidX sum, dPhidY sum: 0 0 0 0 -1.11022e-16 0 0 0 -2.77556e-17 0 0 0 TEST105 GRID_NODES_01 computes a regular grid in the unit square. NUM_X = 5 NUM_Y = 3 NODE_NUM = 15 0 0 0 1 0.25 0 2 0.5 0 3 0.75 0 4 1 0 5 0 0.5 6 0.25 0.5 7 0.5 0.5 8 0.75 0.5 9 1 0.5 10 0 1 11 0.25 1 12 0.5 1 13 0.75 1 14 1 1 TEST12 INTERP_TEST tests the interpolating power of the element. INTERP_TEST for element "Q4". Number of nodes = 4 Interpolate R^0 * S^0 (R,S,U): 0 0 1 (R,S,U): 1 0 1 (R,S,U): 1 1 1 (R,S,U): 0 1 1 (R,S): 0.218418 0.956318 (U ,U* ,Error): 1 1 0 (Ur,Ur*,Error): 0 0 0 (Us,Us*,Error): 0 0 0 (R,S): 0.829509 0.561695 (U ,U* ,Error): 1 1 0 (Ur,Ur*,Error): 0 0 0 (Us,Us*,Error): 0 0 0 (R,S): 0.415307 0.0661187 (U ,U* ,Error): 1 1 0 (Ur,Ur*,Error): 0 0 0 (Us,Us*,Error): 0 0 0 (R,S): 0.257578 0.109957 (U ,U* ,Error): 1 1 0 (Ur,Ur*,Error): 0 0 0 (Us,Us*,Error): 0 0 0 (R,S): 0.043829 0.633966 (U ,U* ,Error): 1 1 0 (Ur,Ur*,Error): 0 0 0 (Us,Us*,Error): 0 0 0 Interpolate R^0 * S^1 (R,S,U): 0 0 0 (R,S,U): 1 0 0 (R,S,U): 1 1 1 (R,S,U): 0 1 1 (R,S):