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

include/fesa/elements/beam/beam3d2.hpp

@@ -2,22 +2,34 @@
 
 #include <array>
 #include <optional>
+#include <span>
 #include <vector>
 
 #include <fesa/core/diagnostic.hpp>
 #include <fesa/core/vec3.hpp>
 #include <fesa/fem/beam_frame.hpp>
 #include <fesa/model/beam_section.hpp>
+#include <fesa/model/ids.hpp>
 #include <fesa/model/material.hpp>
 
 namespace fesa {
 
 struct Beam3D2Input final {
     std::array<Vec3, 2> coordinates;
+    std::array<NodeId, 2> node_ids;
     IsotropicElastic material;
     BeamSection section;
 };
 
+struct BeamSectionResult final {
+    double xi;
+    NodeId end_node;
+    std::array<double, 6> section_strain;
+    std::array<double, 6> section_force;
+    double centroid_sigma_xx;
+    std::vector<double> sigma_xx;
+};
+
 struct Beam3D2Contribution final {
     Matrix12 local_stiffness;
     Matrix12 global_stiffness;
@@ -32,4 +44,9 @@ struct BeamKernelResult final {
 [[nodiscard]] BeamKernelResult compute_beam3d2(
     const Beam3D2Input& input);
 
+[[nodiscard]] std::vector<BeamSectionResult> recover_beam3d2(
+    const Beam3D2Input& input,
+    std::span<const double, 12> element_displacement,
+    std::span<const std::array<double, 2>> recovery_points);
+
 }  // namespace fesa

phases/index.json

@@ -48,4 +48,4 @@
       "status": "pending"
     }
   ]
-}
+}

src/fesa/assembly/parallel_assembler.cpp

@@ -81,6 +81,7 @@ ElementEvaluation evaluate_element(
             domain.node(element.nodes[0]).position,
             domain.node(element.nodes[1]).position,
         },
+        element.nodes,
         domain.material(element.material),
         domain.section(element.section),
     });

src/fesa/assembly/serial_assembler.cpp

@@ -128,6 +128,7 @@ std::vector<NumericContribution> collect_numeric_contributions(
                 domain.node(element.nodes[0]).position,
                 domain.node(element.nodes[1]).position,
             },
+            element.nodes,
             domain.material(element.material),
             domain.section(element.section),
         });

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

tests/CMakeLists.txt

@@ -360,6 +360,24 @@ add_test(
         --gtest_filter=RigidBody.*
 )
 
+add_test(
+    NAME BeamRecovery
+    COMMAND "$<TARGET_FILE:fesa_beam3d2_tests>"
+        --gtest_filter=BeamRecovery.*
+)
+
+add_test(
+    NAME SectionForce
+    COMMAND "$<TARGET_FILE:fesa_beam3d2_tests>"
+        --gtest_filter=SectionForce.*
+)
+
+add_test(
+    NAME CentroidStress
+    COMMAND "$<TARGET_FILE:fesa_beam3d2_tests>"
+        --gtest_filter=CentroidStress.*
+)
+
 add_executable(fesa_serial_assembly_tests
     unit/assembly/serial_assembler_test.cpp
 )

tests/unit/elements/beam3d2_test.cpp

@@ -22,6 +22,7 @@ constexpr double kShearAreaZ = 0.2;
 fesa::Beam3D2Input make_x_axis_input(const double length) {
     return {
         {{{0.0, 0.0, 0.0}, {length, 0.0, 0.0}}},
+        {fesa::NodeId{1}, fesa::NodeId{2}},
         {fesa::MaterialId{1}, "elastic", kYoung, kPoisson},
         {
             fesa::SectionId{1},
@@ -369,4 +370,191 @@ TEST(Beam3D2, PreservesGlobalEnergyUnderRigidCoordinateRotation) {
         4096.0 * std::numeric_limits<double>::epsilon());
 }
 
+TEST(BeamRecovery, RecoversPureAxialStrainAndForceAtBothEnds) {
+    fesa::Beam3D2Input input = make_x_axis_input(2.0);
+    input.node_ids = {fesa::NodeId{101}, fesa::NodeId{202}};
+    std::array<double, 12> displacement{};
+    displacement[6] = 0.4;
+
+    const auto results = fesa::recover_beam3d2(input, displacement, {});
+
+    ASSERT_EQ(results.size(), 2U);
+    EXPECT_DOUBLE_EQ(results[0].xi, -1.0);
+    EXPECT_EQ(results[0].end_node, fesa::NodeId{101});
+    EXPECT_DOUBLE_EQ(results[1].xi, 1.0);
+    EXPECT_EQ(results[1].end_node, fesa::NodeId{202});
+    for (const auto& result : results) {
+        expect_relative_near(result.section_strain[0], 0.2);
+        expect_relative_near(result.section_force[0], 16.8);
+        expect_relative_near(result.centroid_sigma_xx, 42.0);
+        for (std::size_t component = 1; component < 6; ++component) {
+            expect_relative_near(result.section_strain[component], 0.0);
+            expect_relative_near(result.section_force[component], 0.0);
+        }
+        EXPECT_TRUE(result.sigma_xx.empty());
+    }
+}
+
+TEST(BeamRecovery, RecoversPureTorsionAtBothEnds) {
+    fesa::Beam3D2Input input = make_x_axis_input(2.0);
+    input.node_ids = {fesa::NodeId{101}, fesa::NodeId{202}};
+    std::array<double, 12> displacement{};
+    displacement[9] = 0.6;
+    const double shear_modulus = kYoung / (2.0 * (1.0 + kPoisson));
+
+    const auto results = fesa::recover_beam3d2(input, displacement, {});
+
+    ASSERT_EQ(results.size(), 2U);
+    for (const auto& result : results) {
+        expect_relative_near(result.section_strain[3], 0.3);
+        expect_relative_near(
+            result.section_force[3],
+            shear_modulus * kTorsionJ * 0.3);
+        for (const std::size_t component :
+             std::array<std::size_t, 5>{0, 1, 2, 4, 5}) {
+            expect_relative_near(result.section_strain[component], 0.0);
+            expect_relative_near(result.section_force[component], 0.0);
+        }
+    }
+}
+
+TEST(BeamRecovery, UsesReducedIntegrationPointForShearAtBothEnds) {
+    fesa::Beam3D2Input input = make_x_axis_input(2.0);
+    std::array<double, 12> displacement{};
+    displacement[7] = 1.2;
+    displacement[5] = 0.2;
+    displacement[11] = 0.6;
+    displacement[8] = -0.4;
+    displacement[4] = 0.1;
+    displacement[10] = 0.5;
+    const double shear_modulus = kYoung / (2.0 * (1.0 + kPoisson));
+
+    const auto results = fesa::recover_beam3d2(input, displacement, {});
+
+    ASSERT_EQ(results.size(), 2U);
+    for (const auto& result : results) {
+        expect_relative_near(result.section_strain[1], 0.2);
+        expect_relative_near(result.section_strain[2], 0.1);
+        expect_relative_near(
+            result.section_force[1],
+            shear_modulus * kShearAreaY * 0.2);
+        expect_relative_near(
+            result.section_force[2],
+            shear_modulus * kShearAreaZ * 0.1);
+    }
+}
+
+TEST(BeamRecovery, UsesBeamFrameForGlobalDisplacements) {
+    fesa::Beam3D2Input input = make_x_axis_input(2.0);
+    input.coordinates = {{{0.0, 0.0, 0.0}, {0.0, 2.0, 0.0}}};
+    input.section.orientation = {0.0, 0.0, 1.0};
+    input.node_ids = {fesa::NodeId{101}, fesa::NodeId{202}};
+    std::array<double, 12> displacement{};
+    displacement[7] = 0.4;
+    displacement[10] = 0.6;
+    const double shear_modulus = kYoung / (2.0 * (1.0 + kPoisson));
+
+    const auto results = fesa::recover_beam3d2(input, displacement, {});
+
+    ASSERT_EQ(results.size(), 2U);
+    for (const auto& result : results) {
+        expect_relative_near(result.section_strain[0], 0.2);
+        expect_relative_near(result.section_force[0], 16.8);
+        expect_relative_near(result.section_strain[3], 0.3);
+        expect_relative_near(
+            result.section_force[3],
+            shear_modulus * kTorsionJ * 0.3);
+    }
+}
+
+TEST(SectionForce, RecoversPureBendingAboutLocalYAtBothEnds) {
+    fesa::Beam3D2Input input = make_x_axis_input(2.0);
+    input.node_ids = {fesa::NodeId{101}, fesa::NodeId{202}};
+    std::array<double, 12> displacement{};
+    displacement[4] = -0.4;
+    displacement[10] = 0.4;
+
+    const auto results = fesa::recover_beam3d2(input, displacement, {});
+
+    ASSERT_EQ(results.size(), 2U);
+    for (const auto& result : results) {
+        expect_relative_near(result.section_strain[4], 0.4);
+        expect_relative_near(result.section_force[4], 2.52);
+        for (const std::size_t component :
+             std::array<std::size_t, 5>{0, 1, 2, 3, 5}) {
+            expect_relative_near(result.section_strain[component], 0.0);
+            expect_relative_near(result.section_force[component], 0.0);
+        }
+    }
+}
+
+TEST(SectionForce, RecoversPureBendingAboutLocalZAtBothEnds) {
+    fesa::Beam3D2Input input = make_x_axis_input(2.0);
+    input.node_ids = {fesa::NodeId{101}, fesa::NodeId{202}};
+    std::array<double, 12> displacement{};
+    displacement[5] = 0.25;
+    displacement[11] = -0.25;
+
+    const auto results = fesa::recover_beam3d2(input, displacement, {});
+
+    ASSERT_EQ(results.size(), 2U);
+    for (const auto& result : results) {
+        expect_relative_near(result.section_strain[5], -0.25);
+        expect_relative_near(result.section_force[5], -2.625);
+        for (const std::size_t component :
+             std::array<std::size_t, 5>{0, 1, 2, 3, 4}) {
+            expect_relative_near(result.section_strain[component], 0.0);
+            expect_relative_near(result.section_force[component], 0.0);
+        }
+    }
+}
+
+TEST(SectionForce, PreservesBiaxialBendingSignsAtBothEnds) {
+    fesa::Beam3D2Input input = make_x_axis_input(2.0);
+    input.node_ids = {fesa::NodeId{101}, fesa::NodeId{202}};
+    std::array<double, 12> displacement{};
+    displacement[4] = -0.4;
+    displacement[10] = 0.4;
+    displacement[5] = 0.25;
+    displacement[11] = -0.25;
+
+    const auto results = fesa::recover_beam3d2(input, displacement, {});
+
+    ASSERT_EQ(results.size(), 2U);
+    for (const auto& result : results) {
+        expect_relative_near(result.section_force[4], 2.52);
+        expect_relative_near(result.section_force[5], -2.625);
+    }
+}
+
+TEST(CentroidStress, UsesAxialStressAndPreservesRecoveryPointOrder) {
+    fesa::Beam3D2Input input = make_x_axis_input(2.0);
+    input.node_ids = {fesa::NodeId{101}, fesa::NodeId{202}};
+    std::array<double, 12> displacement{};
+    displacement[6] = 0.2;
+    displacement[4] = -0.2;
+    displacement[10] = 0.2;
+    displacement[5] = 0.3;
+    displacement[11] = -0.3;
+    const std::array<std::array<double, 2>, 3> recovery_points{{
+        {2.0, 3.0},
+        {-1.0, 4.0},
+        {5.0, -2.0},
+    }};
+
+    const auto results = fesa::recover_beam3d2(
+        input,
+        displacement,
+        recovery_points);
+
+    ASSERT_EQ(results.size(), 2U);
+    for (const auto& result : results) {
+        expect_relative_near(result.centroid_sigma_xx, 21.0);
+        ASSERT_EQ(result.sigma_xx.size(), recovery_points.size());
+        expect_relative_near(result.sigma_xx[0], 273.0);
+        expect_relative_near(result.sigma_xx[1], 126.0);
+        expect_relative_near(result.sigma_xx[2], 252.0);
+    }
+}
+
 }  // namespace