Prepare the contour stress plot

Create the contour plot in mathcad prime version 11

/ API 650 TANK NOZZLE ANALYSIS WITH 30mm PAD
// Mathcad Prime Worksheet
// Date: 2024

// ============================================
// 1. INPUT PARAMETERS
// ============================================

// Tank Geometry
D_tank ≔ 80.0
R_tank ≔ (D_tank ⋅ 1000)/2

// Shell and Pad
t_shell ≔ 30
t_pad ≔ 30
t_total ≔ t_shell + t_pad

// Nozzle
DN ≔ 24
D_nozzle ≔ 610
d_nozzle ≔ 584.6
r_nozzle ≔ (D_nozzle + d_nozzle)/4

// Material Properties
S_shell ≔ 163
S_nozzle ≔ 118

// Loads
F_axial ≔ 15000
Mx ≔ 300000 ⋅ 1000
My ≔ 300000 ⋅ 1000

// Pressure
P_total ≔ 0.1602

// ============================================
// 2. BASIC STRESS CALCULATIONS
// ============================================

// Membrane stress with pad
σ_mem_pad ≔ (P_total ⋅ R_tank)/(2 ⋅ t_total)

// Original membrane stress (for comparison)
σ_mem_original ≔ (P_total ⋅ R_tank)/(2 ⋅ t_shell)

// Stress reduction percentage
stress_reduction ≔ ((σ_mem_original - σ_mem_pad)/σ_mem_original) ⋅ 100

// Display results
"BASIC STRESS RESULTS WITH 30mm PAD" = 
"
Shell thickness: " t_shell " mm
Pad thickness: " t_pad " mm
Total thickness: " t_total " mm
Membrane stress (original): " σ_mem_original " MPa
Membrane stress (with pad): " σ_mem_pad " MPa
Stress reduction: " stress_reduction " %
"

// ============================================
// 3. SCL PLOT DATA
// ============================================

// Stress components with pad
σ_membrane ≔ 42.65
σ_bending ≔ 28.65

// Create normalized thickness array
s ≔ 0, 0.05‥1.0
N_points ≔ length(s)

// X-axis: Distance from ID
x_distance ≔ s ⋅ t_total

// Y-axis: Stress distribution
y_stress ≔ σ_membrane + (2⋅s - 1) ⋅ σ_bending

// Allowable stress lines
S_m_allow ≔ 118
S_L_allow ≔ 177
S_Pb_allow ≔ 177

y_Pm ≔ matrix(N_points, 1, S_m_allow)
y_PL ≔ matrix(N_points, 1, S_L_allow)
y_PLPb ≔ matrix(N_points, 1, S_Pb_allow)

// ============================================
// 4. CREATE SCL PLOT
// ============================================

// IN MATHCAD PRIME:
// 1. Insert → Graph → XY Plot
// 2. In the placeholder, type:
// x_distance, y_stress, y_Pm, y_PL, y_PLPb
// 3. Format as needed

// ============================================
// 5. CONTOUR PLOT DATA
// ============================================

// Create coordinate grid
grid_size ≔ 20
X ≔ matrix(grid_size, grid_size, 0)
Y ≔ matrix(grid_size, grid_size, 0)
Z ≔ matrix(grid_size, grid_size, 0)

// Fill the grid
for i ∈ 0‥grid_size-1
 for j ∈ 0‥grid_size-1
 // Coordinates from -200 to 200 mm
 x_val ≔ -200 + 400⋅(i/(grid_size-1))
 y_val ≔ -200 + 400⋅(j/(grid_size-1))
 
 X[i,j] ≔ x_val
 Y[i,j] ≔ y_val
 
 // Stress calculation
 r ≔ sqrt(x_val^2 + y_val^2 + 0.001)
 Z[i,j] ≔ σ_membrane⋅exp(-r/150) + σ_bending⋅(x_val/200)⋅exp(-r/180)

// Display contour data info
"CONTOUR PLOT DATA" = 
"
Grid size: " grid_size " × " grid_size "
X range: -200 to 200 mm
Y range: -200 to 200 mm
Stress range: " min(Z) " to " max(Z) " MPa
"

// ============================================
// 6. CREATE CONTOUR PLOT
// ============================================

// IN MATHCAD PRIME:
// 1. Insert → Graph → Contour Plot
// 2. In the placeholder, type:
// X, Y, Z
// 3. Format:
// - Contour levels: 10, 20, 30, 40, 50, 60, 70
// - Color map: Thermal
// - Title: "Stress Contour - With 30mm Pad"