>> addpath /clear/www/htdocs/mech517/Akin_FEA_Lib >> Variable_Coeff_GQ_lib (Echo of msh_remarks.txt) ============== Begin Application Remarks ===================== -[K(x) u']' + A(x) u' + C(x) u + Q(x) = 0 with u(0), u(L) given as three layer chimney wall in Ex. 8.2-1 using quadratic L3 els show_e = 3 to show all element matrices show_s = 1 to show assembled matrices, before EBC u(0)=1500 F, u(L)= 150 F, k1=0.72 BTU/(hr ft F), k2=0.08, k3=0.5 x 0.0 0.375 0.75 1.167 1.79 ft 0 4.5 9 11.5 14 17.75 21.5 in node 1 2 3 4 5 6 7 *-----*-----*---*---*----*----* --> x elem (1) (2) (3) Firebrick, insuation, redbrick properties are input at element nodes to test variable properties for the three types of materials (and/or elements) =============== End Application Remarks ======================== User logic flags: turn on(1)/off(0) echo_p listing of properties = 1 el_react listing of element reactions = 0 integral list integral of the solution = 1 load_pt point source (can be zero) = 0 post post-processing option = 1 show_bc debug list S & c, after EBC = 0 show_e list some S_e, M_e and c_e = 3 show_qp list qp post-process results = 1 show_s list assembled S and c = 1 User control variables n_g number of DOF per node = 1 n_n number of nodes per element = 2 n_p dimension of parametric space = 1 n_q number of quadrature points = 2 n_r number of rows in B_e = 1 n_s dimension of physical space = 1 Begin Phase 2, input mesh, properties, sources and EBC Read 7 nodes. (Echo node, file msh_bc_xyz.txt) node, bc_flags, 1 coordinates 1, 1 0 2, 0 0.375 3, 0 0.75 4, 0 0.9583 5, 0 1.1667 6, 0 1.4792 7, 1 1.7917 Read 3 elements with its type & 3 nodes each. Note: maximum element type is 3 Element number, type, connection list 1, 1 1 2 3 2, 2 3 4 5 3, 3 5 6 7 WARNING Read 3 nodes/element; expected 2 Read 3 materials with 12 properties 12 homogeneous material values per elem type (Echoing text file msh_properties.txt) Columns 1 through 6 7.2000e-01 7.2000e-01 7.2000e-01 0 0 0 8.0000e-02 8.0000e-02 8.0000e-02 0 0 0 5.0000e-01 5.0000e-01 5.0000e-01 0 0 0 Columns 7 through 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 K(x) values, and 3 A(x) values 3 C(x) values, and 3 Q(x) values Note: expecting 2 essential BC values. Read 2 EBC data sets (Echo of file text file msh_ebc.txt) Node, DOF, Value. 1 1 1500 7 1 150 Created file plot_input_curve_mesh.png Begin Phase 3, assemble (scatter) element arrays Displaying the first 3 element matrices Element matrix S_e = 2.2400 -2.5600 0.3200 -2.5600 5.1200 -2.5600 0.3200 -2.5600 2.2400 Element matrix A_e = 0 0 0 0 0 0 0 0 0 Element matrix M_e = 0 0 0 0 0 0 0 0 0 Element matrix c_e = 0 0 0 Element matrix S_e = 0.4481 -0.5121 0.0640 -0.5121 1.0239 -0.5118 0.0640 -0.5118 0.4478 Element matrix S_e = 1.8667 -2.1333 0.2667 -2.1333 4.2667 -2.1333 0.2667 -2.1333 1.8667 System matrix S = 2.2400 -2.5600 0.3200 0 0 0 0 -2.5600 5.1200 -2.5600 0 0 0 0 0.3200 -2.5600 2.6881 -0.5121 0.0640 0 0 0 0 -0.5121 1.0239 -0.5118 0 0 0 0 0.0640 -0.5118 2.3145 -2.1333 0.2667 0 0 0 0 -2.1333 4.2667 -2.1333 0 0 0 0 0.2667 -2.1333 1.8667 System matrix c = 0 0 0 0 0 0 0 Total input source terms = 0 Begin Phase 4, modify matrices for EBC Begin Phase 5, solve modified system Computed Solution: Node, 1 results per node 1, 1.500e+03 2, 1.406e+03 3, 1.313e+03 4, 8.439e+02 5, 3.750e+02 6, 2.625e+02 7, 1.500e+02 Created file graph_1d_result.png Reactions at essential BCs Node, DOF, Reaction Value 1 1 1.7999e+02 7 1 -1.7999e+02 Totals = -9.6634e-13 Begin Phase 6, use the answers Element Post-processing: Point location, approximate flux El, Pt, Coordinates . 1, 1, 0.158494 El, Pt, Gradient .... 1, 1, -249.986 El, Pt, Flux ........ 1, 1, -179.99 El, Pt, Coordinates . 1, 2, 0.591506 El, Pt, Gradient .... 1, 2, -249.986 El, Pt, Flux ........ 1, 2, -179.99 El, Pt, Coordinates . 2, 1, 0.838026 El, Pt, Gradient .... 2, 1, -2249.88 El, Pt, Flux ........ 2, 1, -179.99 El, Pt, Coordinates . 2, 2, 1.07861 El, Pt, Gradient .... 2, 2, -2249.88 El, Pt, Flux ........ 2, 2, -179.99 El, Pt, Coordinates . 3, 1, 1.29878 El, Pt, Gradient .... 3, 1, -359.98 El, Pt, Flux ........ 3, 1, -179.99 El, Pt, Coordinates . 3, 2, 1.65962 El, Pt, Gradient .... 3, 2, -359.98 El, Pt, Flux ........ 3, 2, -179.99 Total solution integral = 1570.34