Below is the uncorrected machine-read text of this chapter, intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text of each book. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.
E-1 APPENDIX E Data on numerical simulations COMSOL Model Report 1. Table of Contents ⢠Title - COMSOL Model Report ⢠Table of Contents ⢠Model Properties ⢠Geometry ⢠Geom1 ⢠Materials/Coefficients Library ⢠Solver Settings ⢠Postprocessing ⢠Variables
E-2 2. Model Properties Property Value Model name Author Company Department Reference URL Saved date Aug 3, 2006 7:35:11 PM Creation date Aug 3, 2006 3:11:10 PM COMSOL version COMSOL 3.2.0.222 File name: C:\Documents and Settings\rperez\Mis documentos\PACO\Modelos\paca 6\paca6.mph Application modes and modules used in this model: ⢠Geom1 (2D) o Plane Stress 3. Geometry Number of geometries: 1 3.1. Geom1
E-3 3.1.1. Subdomain mode
E-4 4. Geom1 Space dimensions: 2D Independent variables: x, y, z 4.1. Mesh 4.1.1. Mesh Parameters Parameter Value Maximum element size Maximum element size scaling factor 1 Element growth rate 1.3 Mesh curvature factor 0.3 Mesh curvature cut off 0.001 Resolution of narrow regions 1 Resolution of geometry 10 x-direction scale factor 1.0 y-direction scale factor 1.0 Mesh geometry to level Subdomain Subdomain 1-6 Maximum element size Element growth rate Boundary 1-36 Maximum element size Element growth rate Mesh curvature factor Mesh curvature cut off Point 1-32 Maximum element size Element growth rate 4.1.2. Mesh Statistics Number of degrees of freedom 65454 Number of boundary elements 952 Number of elements 16129 Minimum element quality 0.4382
E-5 4.2. Application Mode: Plane Stress (ps) Application mode type: Plane Stress Application mode name: ps 4.2.1. Application Mode Properties Property Value Default element type Lagrange - Quadratic Analysis type Static linear Specify eigenvalues using Eigenfrequency Frame Reference frame Weak constraints Off 4.2.2. Variables Dependent variables: u, v Shape functions: shlag(2,'u'), shlag(2,'v') Interior boundaries not active
E-6 4.2.3. Point Settings Point 1-32 name '' Point load (force) x-dir. (Fx) N 0 Amp. factor point load x-dir. (FxAmp) 1 1 Phase angle point load x-dir. (FxPh) 1 0 Point load (force) y-dir. (Fy) N 0 Amp. factor point load y-dir. (FyAmp) 1 1 Phase angle point load y-dir. (FyPh) 1 0 loadcoord 'global' constrcoord 'global' constrtype 'standard' H Matrix (H) 1 {0,0;0,0} R Vector (R) m {0;0} Constraint x-dir. (Rx) m 0 Hx 1 0 Constraint y-dir. (Ry) m 0 Hy 1 0 weakconstr 1 Shape functions (wcshape) [] Initial value (wcinit) {0;0} style {0,{0,0,0}}
E-7 4.2.4. Boundary Settings Boundary 1-3, 5, 7, 9, 11-16, 18-22, 25-36 10, 17, 24 name Edge load x-dir. (Fx) 1 0 0 Amp. factor edge load x-dir. (FxAmp) 1 1 1 Phase angle edge load x-dir. (FxPh) 1 0 0 Edge load y-dir. (Fy) 1 0 -45000 Amp. factor edge load y-dir. (FyAmp) 1 1 1 Phase angle edge load y-dir. (FyPh) 1 0 0 loadcoord global global loadtype length length constrcoord global global constrtype standard standard H Matrix (H) 1 {0,0;0,0} {0,0;0,0} R Vector (R) m {0;0} {0;0} Constraint x-dir. (Rx) m 0 0 Hx 1 0 0 Constraint y-dir. (Ry) m 0 0 Hy 1 0 0 weakconstr 1 1 Integration order (wcgporder) 2 2 Initial value (wcinit) {0;0} {0;0}
E-8 4.2.5. Subdomain Settings Subdomain 1, 5-6 2-4 Shape functions (shape) shlag(2,'u') shlag(2,'v') shlag(2,'u') shlag(2,'v') Integration order (gporder) 4 4 4 4 Constraint order (cporder) 2 2 2 2 name Young's modulus (E) Pa 25e9 (Concrete) 200e9 (High-strength alloy steel) Density (rho) kg/m3 2300 (Concrete) 7850 (High-strength alloy steel) Mass damping parameter (alphadM) 1/s 1 1 Stiffness damping parameter (betadK) s 0.001 0.001 Initial value (dinit) {0;0} {0;0} materialcoord global global materialmodel iso iso mixedform 0 0 hypertype neo_hookean neo_hookean Initial shear modulus (mu) Pa 8e5 8e5 Model parameter (C10) Pa 2e5 2e5 Model parameter (C01) Pa 2e5 2e5 Initial bulk modulus (kappa) Pa 1e10 1e10 hardeningmodel iso iso yieldtype mises mises isodata tangent tangent Kinematic tangent modulus (ETkin) Pa 2.0e10 2.0e10 Isotropic tangent modulus (ETiso) Pa 2.0e10 2.0e10 Yield stress level (Sys) Pa 2.0e8 2.0e8 Yield function Pa mises_ps mises_ps
E-9 (Syfunc) Yield function (Syfunc_kin) Pa misesKin_ps misesKin_ps Hardening function (Shard) Pa 2.0e10/(1-2.0e10/2.0e11)*epe_ps 2.0e10/(1-2.0e10/2.0e11)*epe_ps ini_stress 0 0 ini_strain 0 0 Initial shear stress sxy (sxyi) Pa 0 0 Initial shear strain exy (exyi) 1 0 0 Initial normal stress sx (sxi) Pa 0 0 Initial normal strain ex (exi) 1 0 0 Initial normal stress sy (syi) Pa 0 0 Initial normal strain ey (eyi) 1 0 0 Initial normal stress sz (szi) Pa 0 0 Initial normal strain ez (ezi) 1 0 0 Thermal expansion coeff. (alpha) 1/K 1.2e-5 1.2e-5 Poisson's ratio (nu) 1 0.33 (Concrete) 0.33 (High-strength alloy steel) Shear_modulus xy plane (Gxy) Pa 7.52e10 7.52e10 Poisson's ratio xy plane (nuxy) 1 0.33 0.33 Thermal expansion coeff. x-dir. (alphax) 1/K 1.2e-5 1.2e-5 Young's modulus x-dir. (Ex) Pa 2.0e11 2.0e11 Poisson's ratio yz plane (nuyz) 1 0.33 0.33 Thermal expansion coeff. y-dir. (alphay) 1/K 1.2e-5 1.2e-5 Young's modulus y-dir. (Ey) Pa 2.0e11 2.0e11 Poisson's ratio xz plane (nuxz) 1 0.33 0.33
E-10 Thermal expansion coeff. z-dir. (alphaz) 1/K 1.2e-5 1.2e-5 Young's modulus z-dir. (Ez) Pa 2.0e11 2.0e11 Elasticity matrix (D) Pa {'2.0e11/((1+0.33)*(1-2*0.33))*(1- 0.33)','2.0e11/((1+0.33)*(1- 2*0.33))*0.33','2.0e11/((1+0.33)*(1- 2*0.33))*0.33',0;'2.0e11/((1+0.33)*(1- 2*0.33))*0.33','2.0e11/((1+0.33)*(1- 2*0.33))*(1-0.33)','2.0e11/((1+0.33)*(1- 2*0.33))*0.33',0;'2.0e11/((1+0.33)*(1- 2*0.33))*0.33','2.0e11/((1+0.33)*(1- 2*0.33))*0.33','2.0e11/((1+0.33)*(1- 2*0.33))*(1- 0.33)',0;0,0,0,'2.0e11/((1+0.33)*2)'} {'2.0e11/((1+0.33)*(1-2*0.33))*(1- 0.33)','2.0e11/((1+0.33)*(1- 2*0.33))*0.33','2.0e11/((1+0.33)*(1- 2*0.33))*0.33',0;'2.0e11/((1+0.33)*(1- 2*0.33))*0.33','2.0e11/((1+0.33)*(1- 2*0.33))*(1-0.33)','2.0e11/((1+0.33)*(1- 2*0.33))*0.33',0;'2.0e11/((1+0.33)*(1- 2*0.33))*0.33','2.0e11/((1+0.33)*(1- 2*0.33))*0.33','2.0e11/((1+0.33)*(1- 2*0.33))*(1- 0.33)',0;0,0,0,'2.0e11/((1+0.33)*2)'} Thermal expansion vector (alphavector) 1/K {1.2e-5;1.2e-5;1.2e-5;0} {1.2e-5;1.2e-5;1.2e-5;0} Thickness (thickness) m 0.01 0.01 Body load x- dir. (Fx) 1 0 0 Amp. factor body load x-dir. (FxAmp) 1 1 1 Phase angle body load x-dir. (FxPh) 1 0 0 Body load y- dir. (Fy) 1 0 0 Amp. factor body load y-dir. (FyAmp) 1 1 1 Phase angle body load y-dir. (FyPh) 1 0 0 loadcoord global global Tflag 0 0 Strain temperature (Temp) K 0 0 Strain ref. temperature (Tempref) K 0 0 loadtype area area constrcoord global global constrtype standard standard H Matrix (H) 1 {0,0;0,0} {0,0;0,0}
E-11 R Vector (R) m {0;0} {0;0} Constraint x- dir. (Rx) m 0 0 Hx 1 0 0 Constraint y- dir. (Ry) m 0 0 Hy 1 0 0 weakconstr 1 1 Subdomain initial value 1, 5-6 2-4 x-displacement (u) m 0 0 y-displacement (v) m 0 0
E-12 5. Materials/Coefficients Library 5.1. Concrete Parameter Value Young's modulus (E) 25e9 Thermal expansion coeff. (alpha) 10e-6 Thermal conductivity (k) 1.8 Poisson's ratio (nu) 0.33 Density (rho) 2300 5.2. High-strength alloy steel Parameter Value Heat capacity (C) 475 Young's modulus (E) 200e9 Thermal expansion coeff. (alpha) 12.3e-6 Relative permittivity (epsilonr) 1 Thermal conductivity (k) 44.5 Relative permeability (mur) 1 Poisson's ratio (nu) 0.33 Density (rho) 7850 Electrical conductivity (sigma) 4.032e6
E-13 6. Solver Settings Solve using a script: off Analysis type Static_linear Auto select solver On Solver Stationary linear Solution form Automatic Symmetric Off Adaption Off 6.1. Direct (UMFPACK) Solver type: Linear system solver Parameter Value Pivot threshold 0.1 Memory allocation factor 0.7 6.2. Advanced Parameter Value Constraint handling method Elimination Null-space function Automatic Assembly block size 5000 Use Hermitian transpose of constraint matrix Off Use complex functions with real input Off Type of scaling Automatic Manual scaling Row equilibration On Manual control of reassembly Off Load constant On Constraint constant On Mass constant On Damping (mass) constant On Jacobian constant On Constraint Jacobian constant On
E-14 7. Postprocessing
E-15 8. Variables 8.1. Point Name Description Expression Fxg_ps Point load in global x-dir. 0 Fyg_ps Point load in global y-dir. 0 disp_ps Total displacement sqrt(real(u)^2+real(v)^2) 8.2. Boundary Name Description Expression Fxg_ps Edge load in global x-dir. 0 Fyg_ps Edge load in global y-dir. 0 disp_ps Total displacement sqrt(real(u)^2+real(v)^2) Tax_ps Surface traction (force/area) in x-dir. sx_ps * nx_ps+sxy_ps * ny_ps Tay_ps Surface traction (force/area) in y-dir. sxy_ps * nx_ps+sy_ps * ny_ps 8.3. Subdomain Name Description Expression Fxg_ps Body load in global x-dir. 0 Fyg_ps Body load in global y-dir. 0 disp_ps Total displacement sqrt(real(u)^2+real(v)^2) sx_ps sx normal stress global sys. E_ps/((1+nu_ps) * (1-2 * nu_ps)) * (1-nu_ps) * ex_ps+E_ps/((1+nu_ps) * (1-2 * nu_ps)) * nu_ps * ey_ps+E_ps/((1+nu_ps) * (1-2 * nu_ps)) * nu_ps * ez_ps sy_ps sy normal stress global sys. E_ps/((1+nu_ps) * (1-2 * nu_ps)) * nu_ps * ex_ps+E_ps/((1+nu_ps) * (1-2 * nu_ps)) * (1-nu_ps) * ey_ps+E_ps/((1+nu_ps) * (1-2 * nu_ps)) * nu_ps * ez_ps sxy_ps sxy shear stress global sys. E_ps/(1+nu_ps) * exy_ps ex_ps ex normal strain global sys. ux ey_ps ey normal strain global sys. vy ez_ps ez normal strain -(E_ps/((1+nu_ps) * (1-2 * nu_ps)) * nu_ps * ex_ps+E_ps/((1+nu_ps) * (1-2 * nu_ps)) * nu_ps * ey_ps)/(E_ps/((1+nu_ps) * (1-2 * nu_ps)) * (1-nu_ps)) exy_ps exy shear strain global sys. 0.5 * (uy+vx) K_ps Bulk modulus E_ps/(3 * (1-2 * nu_ps)) G_ps Shear modulus E_ps/(2 * (1+nu_ps)) mises_ps von Mises stress sqrt(sx_ps^2+sy_ps^2-sx_ps * sy_ps+3 * sxy_ps^2) Ws_ps Strain energy density 0.5 * thickness_ps * (ex_ps * sx_ps+ey_ps * sy_ps+2 * exy_ps * sxy_ps) evol_ps Volumetric strain ex_ps+ey_ps+ez_ps sz_ps sz normal stress global sys. 0 tresca_ps Tresca stress max(max(abs(s1_ps-s2_ps),abs(s2_ps-s3_ps)),abs(s1_ps-s3_ps))
