hollow_circle_properties.hpp

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#pragma once
 
#include <cmath>
#include <numbers>
#include <stdexcept>
 
#include "beam_section.hpp"
#include "generate_sectional_properties.hpp"
 
namespace kynema::beams {
 
struct HollowCircleProperties {
    double area;  
    double Ixx;   
    double Iyy;   
    double J;     
    double kx;    
    double ky;    
};
 
static HollowCircleProperties CalculateHollowCircleProperties(
    double outer_diameter, double wall_thickness, double nu = 0.33
) {
    //--------------------------------------------------------------------------
    // Check input arguments
    //--------------------------------------------------------------------------
    if (wall_thickness >= outer_diameter / 2.) {
        throw std::invalid_argument("Wall thickness must be less than outer radius");
    }
 
    //--------------------------------------------------------------------------
    // Calculate geometric properties
    //--------------------------------------------------------------------------
    const double outer_radius = outer_diameter / 2.;
    const double inner_radius = outer_radius - wall_thickness;
 
    // Calculate geometric properties using difference of circles
    const double area = std::numbers::pi * (std::pow(outer_radius, 2) - std::pow(inner_radius, 2));
    const double Ixx =
        std::numbers::pi * (std::pow(outer_radius, 4) - std::pow(inner_radius, 4)) / 4.;
    const double Iyy = Ixx;  // Circular symmetry
    const double J = std::numbers::pi * (std::pow(outer_radius, 4) - std::pow(inner_radius, 4)) / 2.;
 
    // Shear correction factors for hollow circular sections
    const double kx = (6. * (1. + nu)) / (7. + 6. * nu);  // Timoshenko-Ehrenfest beam theory
    const double ky = kx;                                 // Circular symmetry
 
    return HollowCircleProperties{area, Ixx, Iyy, J, kx, ky};
}
 
static BeamSection GenerateHollowCircleSection(
    double s, double E, double G, double rho, double outer_diameter, double wall_thickness,
    double nu, double x_C = 0., double y_C = 0., double theta_p = 0., double x_S = 0.,
    double y_S = 0., double theta_s = 0., double x_G = 0., double y_G = 0., double theta_i = 0
) {
    auto properties = CalculateHollowCircleProperties(outer_diameter, wall_thickness, nu);
 
    // Calculate mass properties
    const double m = rho * properties.area;   // Mass per unit length
    const double I_x = rho * properties.Ixx;  // Mass moment of inertia about x-axis
    const double I_y = rho * properties.Iyy;  // Mass moment of inertia about y-axis
    const double I_p = I_x + I_y;             // Polar mass moment of inertia
 
    // Calculate stiffness properties
    const double EA = E * properties.area;
    const double EI_x = E * properties.Ixx;
    const double EI_y = E * properties.Iyy;
    const double GKt = G * properties.J;
    const double GA = G * properties.area;
 
    // Generate mass and stiffness matrices and return BeamSection
    const auto mass = GenerateMassMatrix(m, I_x, I_y, I_p, x_G, y_G, theta_i);
    const auto stiffness = GenerateStiffnessMatrix(
        EA, EI_x, EI_y, GKt, GA, properties.kx, properties.ky, x_C, y_C, theta_p, x_S, y_S, theta_s
    );
 
    return {s, mass, stiffness};
}
 
}  // namespace kynema::beams