feat(result-contract-completion): step 0 — beam-element-end-recovery

src/fesa/elements/beam/beam3d2.cpp

@@ -4,8 +4,10 @@
 #include <cmath>
 #include <cstddef>
 #include <optional>
+#include <stdexcept>
 #include <string>
 #include <utility>
+#include <vector>
 
 #include <fesa/fem/gauss_rule.hpp>
 #include <fesa/fem/line2_shape.hpp>
@@ -32,6 +34,20 @@ bool is_positive_finite(const double value) {
     return std::isfinite(value) && value > 0.0;
 }
 
+std::array<double, 6> constitutive_values(
+    const Beam3D2Input& input) {
+    const double shear_modulus =
+        input.material.young / (2.0 * (1.0 + input.material.poisson));
+    return {
+        input.material.young * input.section.area,
+        shear_modulus * input.section.shear_area_y,
+        shear_modulus * input.section.shear_area_z,
+        shear_modulus * input.section.torsion_j,
+        input.material.young * input.section.iy,
+        input.material.young * input.section.iz,
+    };
+}
+
 std::optional<BeamKernelResult> validate_properties(
     const Beam3D2Input& input) {
     if (!std::isfinite(input.material.young) ||
@@ -149,6 +165,34 @@ Matrix12 transform_stiffness(
     return global;
 }
 
+std::array<double, 12> transform_displacement(
+    const Matrix12& transformation,
+    const std::span<const double, 12> global_displacement) {
+    std::array<double, 12> local_displacement{};
+    for (std::size_t row = 0; row < transformation.size(); ++row) {
+        for (std::size_t column = 0;
+             column < transformation[row].size();
+             ++column) {
+            local_displacement[row] +=
+                transformation[row][column] * global_displacement[column];
+        }
+    }
+    return local_displacement;
+}
+
+std::array<double, 6> evaluate_strain(
+    const StrainMatrix& strain_matrix,
+    const std::array<double, 12>& local_displacement) {
+    std::array<double, 6> strain{};
+    for (std::size_t component = 0; component < strain.size(); ++component) {
+        for (std::size_t dof = 0; dof < local_displacement.size(); ++dof) {
+            strain[component] +=
+                strain_matrix[component][dof] * local_displacement[dof];
+        }
+    }
+    return strain;
+}
+
 bool is_finite(const Matrix12& matrix) {
     for (const auto& row : matrix) {
         for (const double value : row) {
@@ -189,16 +233,8 @@ BeamKernelResult compute_beam3d2(const Beam3D2Input& input) {
             "Beam kernel requires a representable positive Jacobian.");
     }
 
-    const double shear_modulus =
-        input.material.young / (2.0 * (1.0 + input.material.poisson));
-    const std::array<double, 6> constitutive{
-        input.material.young * input.section.area,
-        shear_modulus * input.section.shear_area_y,
-        shear_modulus * input.section.shear_area_z,
-        shear_modulus * input.section.torsion_j,
-        input.material.young * input.section.iy,
-        input.material.young * input.section.iz,
-    };
+    const std::array<double, 6> constitutive =
+        constitutive_values(input);
     for (const double value : constitutive) {
         if (!is_positive_finite(value)) {
             return error_result(
@@ -241,4 +277,73 @@ BeamKernelResult compute_beam3d2(const Beam3D2Input& input) {
     };
 }
 
+std::vector<BeamSectionResult> recover_beam3d2(
+    const Beam3D2Input& input,
+    const std::span<const double, 12> element_displacement,
+    const std::span<const std::array<double, 2>> recovery_points) {
+    const BeamKernelResult kernel = compute_beam3d2(input);
+    if (!kernel.contribution.has_value()) {
+        const std::string message = kernel.diagnostics.empty()
+            ? "Beam recovery requires a valid Beam3D2 input."
+            : kernel.diagnostics.front().message;
+        throw std::invalid_argument{message};
+    }
+
+    const Vec3 axis{
+        input.coordinates[1].x - input.coordinates[0].x,
+        input.coordinates[1].y - input.coordinates[0].y,
+        input.coordinates[1].z - input.coordinates[0].z,
+    };
+    const double jacobian = std::hypot(axis.x, axis.y, axis.z) / 2.0;
+    const Matrix12 transformation =
+        beam_transformation(kernel.contribution->frame);
+    const std::array<double, 12> local_displacement =
+        transform_displacement(transformation, element_displacement);
+    const std::array<double, 6> center_strain = evaluate_strain(
+        strain_matrix(0.0, jacobian),
+        local_displacement);
+    const std::array<double, 6> constitutive =
+        constitutive_values(input);
+
+    std::vector<BeamSectionResult> results;
+    results.reserve(input.node_ids.size());
+    for (std::size_t end = 0; end < input.node_ids.size(); ++end) {
+        const double xi = end == 0 ? -1.0 : 1.0;
+        std::array<double, 6> section_strain = evaluate_strain(
+            strain_matrix(xi, jacobian),
+            local_displacement);
+        section_strain[1] = center_strain[1];
+        section_strain[2] = center_strain[2];
+
+        std::array<double, 6> section_force{};
+        for (std::size_t component = 0;
+             component < section_force.size();
+             ++component) {
+            section_force[component] =
+                constitutive[component] * section_strain[component];
+        }
+
+        std::vector<double> sigma_xx;
+        sigma_xx.reserve(recovery_points.size());
+        for (const auto& point : recovery_points) {
+            const double y = point[0];
+            const double z = point[1];
+            sigma_xx.push_back(
+                input.material.young *
+                (section_strain[0] + z * section_strain[4] -
+                 y * section_strain[5]));
+        }
+
+        results.push_back({
+            xi,
+            input.node_ids[end],
+            section_strain,
+            section_force,
+            section_force[0] / input.section.area,
+            std::move(sigma_xx),
+        });
+    }
+    return results;
+}
+
 }  // namespace fesa