基于Matlab构建压力容器外半径矩阵：压力与L/R比耦合分析

Here's a fixed and integrated MATLAB code that addresses your requirements, along with key fixes and explanations:

Fixed & Integrated Code #

clear all; clc;

% Fixed vessel parameter
L_in = 1; % Total length of the pressure vessel (m)
SF = 2; % Safety factor

% Material properties (as provided)
Sy = 2513; % Yield strength (bar)
Su = 5521; % Ultimate tensile strength (bar)
Density = 0.008027; % kg/m^3
Cost = 18.94; % $/kg

% Define analysis ranges
p_tank = 1:300; % Pressure range: 1 to 300 bar
L_R_ratio = 1:1000; % L/R ratio range: 1 to 1000

% Precompute internal radius for each L/R ratio
num_p = length(p_tank);
num_LR = length(L_R_ratio);
R_in = L_in ./ L_R_ratio; % R_in(j) = total length / L/R ratio

% Precompute internal volume (fixed syntax errors from original code)
V_in = (4/3)*pi*R_in.^3 + (L_in - 2*R_in).*pi.*R_in.^2;

% Initialize result matrices
s_Sy = zeros(num_p, num_LR); % Yield-based thickness
s_Su = zeros(num_p, num_LR); % Ultimate strength-based thickness
s_lim = zeros(num_p, num_LR); % Limiting thickness (governing criterion)
R_ext = zeros(num_p, num_LR); % External radius matrix

% Nested loop to calculate values for all pressure-L/R pairs
for i = 1:num_p
    current_p = p_tank(i);
    for j = 1:num_LR
        current_R_in = R_in(j);
        
        % Calculate thickness based on yield strength (original formula)
        s_Sy(i,j) = current_p * current_R_in / Sy * 1.5;
        
        % Calculate thickness based on ultimate strength (fixed to use Su instead of Sy)
        s_Su(i,j) = current_p * current_R_in / Su * SF;
        
        % Determine limiting thickness (use the larger value to satisfy both criteria)
        if s_Su(i,j) > s_Sy(i,j)
            s_lim(i,j) = s_Su(i,j);
            % Uncomment below to see governing criterion
            % disp(['Pressure: ', num2str(current_p), ' bar, L/R: ', num2str(L_R_ratio(j)), ' - Burst criterion governs']);
        else
            s_lim(i,j) = s_Sy(i,j);
            % Uncomment below to see governing criterion
            % disp(['Pressure: ', num2str(current_p), ' bar, L/R: ', num2str(L_R_ratio(j)), ' - Yield criterion governs']);
        end
        
        % Compute external radius
        R_ext(i,j) = current_R_in + s_lim(i,j);
    end
end

% Optional: Visualization of results
% Plot external radius vs pressure for selected L/R ratios
figure;
selected_LR = [1, 100, 500, 1000];
for lr = selected_LR
    idx = find(L_R_ratio == lr);
    plot(p_tank, R_ext(:,idx), 'DisplayName', ['L/R = ', num2str(lr)]);
    hold on;
end
xlabel('Pressure (bar)');
ylabel('External Radius (m)');
title('External Radius vs Pressure for Different L/R Ratios');
legend;
grid on;

% Plot external radius vs L/R ratio for selected pressures
figure;
selected_p = [1, 100, 200, 300];
for p = selected_p
    idx = find(p_tank == p);
    plot(L_R_ratio, R_ext(idx,:), 'DisplayName', ['Pressure = ', num2str(p), ' bar']);
    hold on;
end
xlabel('L/R Ratio');
ylabel('External Radius (m)');
title('External Radius vs L/R Ratio for Different Pressures');
legend;
grid on;

Key Fixes & Improvements #

• Corrected Ultimate Strength Calculation: The original code incorrectly used yield strength (Sy) instead of ultimate strength (Su) for the burst criterion thickness. This is fixed to use Su in s_Su calculations.
• Valid Criterion Comparison: The original code compared an uninitialized vector s_Su to s_Sy(i), which was invalid. Now we compare the specific values for each pressure-L/R pair.
• Matrix-Based Results: s_lim and R_ext are now matrices where each row corresponds to a pressure (1-300 bar) and each column corresponds to an L/R ratio (1-1000), matching your requirement.
• Fixed Syntax Errors: Corrected invalid operators in the volume calculation (e.g., pi. → pi.*).
• Optional Visualization: Added plots to help analyze how external radius changes with pressure and L/R ratio.

How It Works #

1. Precompute Internal Parameters: Calculate R_in and V_in for all L/R ratios first.
2. Nested Loop Iteration: For each pressure and each L/R ratio:
   • Compute yield and ultimate strength-based thicknesses.
   • Select the limiting thickness (the larger value, as it must satisfy both safety criteria).
   • Calculate the external radius as R_in + s_lim.
3. Visualization: Generate plots to visualize the relationships between external radius, pressure, and L/R ratio.

内容的提问来源于stack exchange，提问作者edo