feat(euler-beam-3d): add global transform recovery

2026-06-12 18:10:35 +09:00
parent 95ca95180a
commit 7845ebec68
4 changed files with 323 additions and 9 deletions
@@ -0,0 +1,151 @@
+#include <fesa/elements/euler_beam_3d.hpp>
+
+#include <cmath>
+#include <cstddef>
+#include <stdexcept>
+
+namespace {
+
+constexpr double tolerance = 1.0e-9;
+
+bool close(double actual, double expected, double tol = tolerance)
+{
+    return std::abs(actual - expected) <= tol;
+}
+
+double entry(const fesa::elements::Matrix12& matrix, int row, int column)
+{
+    return matrix[static_cast<std::size_t>(row * 12 + column)];
+}
+
+fesa::elements::EulerBeam3DSection section()
+{
+    return fesa::elements::EulerBeam3DSection{
+        210.0,
+        80.0,
+        3.0,
+        4.0,
+        5.0,
+        6.0
+    };
+}
+
+bool matrices_close(const fesa::elements::Matrix12& lhs, const fesa::elements::Matrix12& rhs)
+{
+    for (std::size_t index = 0; index < lhs.size(); ++index) {
+        if (!close(lhs[index], rhs[index])) {
+            return false;
+        }
+    }
+    return true;
+}
+
+bool symmetric(const fesa::elements::Matrix12& matrix)
+{
+    for (int row = 0; row < 12; ++row) {
+        for (int column = 0; column < 12; ++column) {
+            if (!close(entry(matrix, row, column), entry(matrix, column, row))) {
+                return false;
+            }
+        }
+    }
+    return true;
+}
+
+bool throws_parallel_orientation()
+{
+    const fesa::elements::EulerBeam3DGeometry geometry{
+        {0.0, 0.0, 0.0},
+        {2.0, 0.0, 0.0},
+        {1.0, 0.0, 0.0}
+    };
+
+    try {
+        (void)fesa::elements::euler_beam_3d_global_stiffness(geometry, section());
+    } catch (const std::invalid_argument&) {
+        return true;
+    }
+    return false;
+}
+
+bool throws_zero_orientation()
+{
+    const fesa::elements::EulerBeam3DGeometry geometry{
+        {0.0, 0.0, 0.0},
+        {2.0, 0.0, 0.0},
+        {0.0, 0.0, 0.0}
+    };
+
+    try {
+        (void)fesa::elements::euler_beam_3d_global_stiffness(geometry, section());
+    } catch (const std::invalid_argument&) {
+        return true;
+    }
+    return false;
+}
+
+} // namespace
+
+int main()
+{
+    const auto beam_section = section();
+    const fesa::elements::EulerBeam3DGeometry axis_aligned{
+        {0.0, 0.0, 0.0},
+        {2.0, 0.0, 0.0},
+        {0.0, 1.0, 0.0}
+    };
+
+    const auto local = fesa::elements::euler_beam_3d_local_stiffness(2.0, beam_section);
+    const auto global_identity =
+        fesa::elements::euler_beam_3d_global_stiffness(axis_aligned, beam_section);
+    if (!matrices_close(global_identity, local)) {
+        return 1;
+    }
+
+    const fesa::elements::EulerBeam3DGeometry rotated{
+        {0.0, 0.0, 0.0},
+        {0.0, 2.0, 0.0},
+        {1.0, 0.0, 0.0}
+    };
+    const auto rotated_stiffness =
+        fesa::elements::euler_beam_3d_global_stiffness(rotated, beam_section);
+    if (!symmetric(rotated_stiffness)) {
+        return 2;
+    }
+
+    fesa::elements::Vector12 rigid_translation{};
+    rigid_translation[0] = 0.2;
+    rigid_translation[1] = -0.1;
+    rigid_translation[2] = 0.3;
+    rigid_translation[6] = 0.2;
+    rigid_translation[7] = -0.1;
+    rigid_translation[8] = 0.3;
+    const auto rigid_forces =
+        fesa::elements::euler_beam_3d_global_end_forces(rotated, beam_section, rigid_translation);
+    for (double force : rigid_forces) {
+        if (!close(force, 0.0)) {
+            return 3;
+        }
+    }
+
+    fesa::elements::Vector12 axial_extension{};
+    axial_extension[6] = 0.1;
+    const auto axial_forces = fesa::elements::euler_beam_3d_global_end_forces(
+        axis_aligned,
+        beam_section,
+        axial_extension);
+    if (!close(axial_forces[0], -31.5) ||
+        !close(axial_forces[6], 31.5) ||
+        !close(axial_forces[0] + axial_forces[6], 0.0)) {
+        return 4;
+    }
+
+    if (!throws_parallel_orientation()) {
+        return 5;
+    }
+    if (!throws_zero_orientation()) {
+        return 6;
+    }
+
+    return 0;
+}