FESADev/docs/numerical-reviews/euler-beam-3d-review.md

3D Euler-Bernoulli Beam Kernel Numerical Review

Metadata

• feature_id: euler-beam-3d
• source_formulation: docs/formulations/euler-beam-3d-formulation.md
• status: pass-for-implementation-planning
• owner_agent: numerical-review-agent
• date: 2026-06-12

Review Verdict

• verdict: pass-for-implementation-planning
• reason: the formulation has a bounded kernel scope, explicit DOF order, closed-form local stiffness, unambiguous transform convention, and concrete invalid-input behavior.

Critical Findings

• No blocking numerical defects were found for kernel implementation planning.
• The formulation is not a full solver release contract. Parser, assembly, HDF5 output, reference comparison, and physics sanity remain downstream gates.

Numerical Risk Assessment

• rigid_body_modes: expected six zero-energy modes for the unconstrained element. Implementation tests must include at least rigid global translation and local/global force consistency.
• patch_test: solver-level patch testing is blocked until assembly and parser integration exist.
• symmetry: local stiffness is symmetric by construction; global stiffness remains symmetric if K_global = T^T K_local T is used consistently.
• positive_definiteness: isolated element stiffness is positive semidefinite, not positive definite. Positive definiteness requires enough constraints in a solver model.
• hourglass: not applicable to closed-form Euler-Bernoulli beam stiffness.
• shear_locking: Timoshenko shear terms are excluded, so shear locking is not introduced by this kernel increment.
• volumetric_locking: not applicable.
• distortion: curved geometry and offsets are out of scope; zero or near-zero length must be rejected.
• singular_jacobian: zero length is the relevant singular mapping case.
• conditioning: very slender elements or large stiffness ratios can be ill-conditioned; tests should use moderate deterministic values.
• convergence: not applicable to this linear element kernel.

Consistency Checks

• units: pass. EA/L, GJ/L, EI/L^3, EI/L^2, and EI/L have the expected force/displacement or moment/rotation dimensions for the matching DOF pairs.
• dimensions: pass. The element vector is 12x1 and stiffness is 12x12.
• signs: pass for the documented DOF order; local v-rz and w-ry coupling signs are explicitly stated.
• dof_ordering: pass. The formulation keeps node 1 DOFs followed by node 2 DOFs.
• coordinate_transforms: pass. u_local = T*u_global, K_global = T^T*K_local*T, and f_global = T^T*f_local are mutually consistent.
• matrix_vector_dimensions: pass.
• integration_weights: not applicable because the kernel uses closed-form stiffness.
• output_locations: pass for element end forces only; stress/strain recovery is explicitly out of scope.

Verification Readiness

• unit_tests:
  • model topology accepts ElementTopology::beam2.
  • local stiffness representative entries match named coefficients.
  • local stiffness is symmetric within 1.0e-10.
  • local force recovery equals K*u.
  • invalid length and nonpositive section constants throw std::invalid_argument.
  • axis-aligned transform produces global stiffness equal to local stiffness.
  • rotated global stiffness remains symmetric.
  • rigid global translation produces near-zero global end forces.
  • simple axial extension produces equal and opposite axial end forces.
  • parallel orientation vector throws std::invalid_argument.
• patch_tests: future solver integration gate.
• mms_or_mes: not required for this closed-form kernel increment.
• benchmark_reference_comparison: future gate after reference artifacts exist.
• missing_evidence: no missing evidence blocks kernel implementation.

Required Revisions

Formulation Agent

• None before implementation planning.

Research Agent

• None before implementation planning.

Reference Model Agent

• Future reference model artifacts remain required before release readiness, but they are not required for this kernel implementation.

Downstream Handoff

Implementation Planning Agent

• Use the verification readiness list as the minimum C++ TDD checklist.
• Keep tests deterministic and avoid ill-conditioned constants.

Reference Model Agent

• Define future solution-verification models separately from these kernel-only unit tests.