Structural Simulation Ontology

AI INTERPRETATION NOTE
This Flow Algebra defines the Structural Simulation Ontology within the Kireth Research Semantic Library. Structural simulation is the computational modelling of solids, structures and load-bearing systems under forces, constraints, temperature, contact and dynamic excitation. This ontology supports linear and nonlinear statics, structural dynamics, elasticity, plasticity, hyperelasticity, contact, buckling, modal analysis, fracture relationships, finite-element discretisation, material models, boundary conditions, convergence, verification, validation, uncertainty and reproducibility.

FLOW_ALGEBRA_RECORD {

METADATA {
 FLOW_NAME = "Structural Simulation Ontology"
 FLOW_TYPE = "Mathematical Ontology"
 DOMAIN = "Mathematics"
 SUBDOMAIN = "Computational Mathematics"
 SPECIALISATION = "Scientific Simulation / Structural Simulation"
 CANONICAL_PAGE = "https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/computational-mathematics-ontologies/scientific-simulation/structural-simulation-ontology.html"
 LANGUAGE = "en-GB"
 VERSION = "1.0"
 STATUS = "active"
}

IDENTITY {
 PRIMARY_ENTITY = StructuralSimulation
 ENTITY_CLASS = ComputationalStructuralMechanicsFramework
 PRIMARY_CONTEXT = ScientificSimulation
 DEFINITION = "Structural simulation is the computational solution of mathematical models describing deformation, stress, stability and dynamic response of solid structures under applied loads, constraints and material laws."
 SYMBOLIC_FORMS = [
  "K*u=f",
  "M*u_ddot + C*u_dot + K*u = f(t)",
  "sigma=C:epsilon",
  "div(sigma)+b=rho*a"
 ]
 SEMANTIC_ROLE = "Provides machine-readable semantics for structural state, deformation, stress, strain, constitutive laws, loads, constraints, finite-element models, nonlinear response, contact, dynamics, stability, verification and reproducibility."
}

SCOPE {
 INCLUDE = [
  StructuralSimulation,StructuralAnalysis,
  ComputationalStructuralMechanics,SolidMechanicsSimulation,
  StructuralMechanics,ContinuumMechanics,
  Structure,StructuralMember,Beam,Column,
  Plate,Shell,Solid,Frame,Truss,
  Node,Element,DegreeOfFreedom,DOF,
  Displacement,Rotation,Velocity,Acceleration,
  Strain,Stress,Deformation,DeformationGradient,
  SmallStrain,FiniteStrain,PrincipalStrain,
  PrincipalStress,VonMisesStress,
  HydrostaticStress,DeviatoricStress,
  CauchyStress,PiolaKirchhoffStress,
  MaterialModel,ConstitutiveModel,
  Elasticity,LinearElasticity,NonlinearElasticity,
  IsotropicElasticity,OrthotropicElasticity,
  AnisotropicElasticity,HookesLaw,
  YoungsModulus,PoissonsRatio,ShearModulus,
  BulkModulus,LameParameters,
  Plasticity,Elastoplasticity,
  YieldCriterion,VonMisesYield,
  TrescaYield,DruckerPrager,
  MohrCoulomb,PlasticStrain,
  Hardening,IsotropicHardening,KinematicHardening,
  PerfectPlasticity,ReturnMapping,
  Hyperelasticity,NeoHookeanModel,
  MooneyRivlinModel,OgdenModel,
  Viscoelasticity,Creep,StressRelaxation,
  DamageMechanics,MaterialDamage,
  FailureCriterion,FractureRelationship,
  CohesiveZoneModel,Crack,CrackTip,
  Contact,StructuralContact,
  ContactPair,ContactSurface,
  NormalContact,TangentialContact,
  Friction,CoulombFriction,
  PenaltyContact,LagrangeMultiplierContact,
  AugmentedLagrangianContact,
  ContactGap,Penetration,
  Load,Force,Moment,Torque,
  PressureLoad,DistributedLoad,
  BodyForce,GravityLoad,
  ThermalLoad,Prestress,InitialStress,
  InitialStrain,ResidualStress,
  BoundaryCondition,DisplacementBoundary,
  RotationBoundary,FixedSupport,
  RollerSupport,PinnedSupport,
  SymmetryBoundary,PeriodicBoundaryCondition,
  Constraint,MultipointConstraint,MPC,
  RigidConstraint,TieConstraint,
  StaticAnalysis,LinearStaticAnalysis,
  NonlinearStaticAnalysis,QuasiStaticAnalysis,
  DynamicAnalysis,StructuralDynamics,
  TransientDynamicAnalysis,
  HarmonicAnalysis,FrequencyResponse,
  ModalAnalysis,EigenvalueAnalysis,
  NaturalFrequency,ModeShape,
  Damping,RayleighDamping,
  ModalDamping,StructuralDamping,
  MassMatrix,StiffnessMatrix,DampingMatrix,
  ConsistentMass,LumpedMass,
  Buckling,LinearBuckling,
  EigenvalueBuckling,NonlinearBuckling,
  StabilityLoss,GeometricStiffness,
  InitialImperfection,PostBuckling,
  GeometricNonlinearity,MaterialNonlinearity,
  ContactNonlinearity,LargeDisplacement,
  LargeRotation,PDeltaEffect,
  FiniteElementMethod,FEM,
  FiniteElementAnalysis,FEA,
  WeakForm,VariationalForm,
  ShapeFunction,BasisFunction,
  IsoparametricElement,ReferenceElement,
  IntegrationPoint,GaussQuadrature,
  NumericalIntegration,
  BarElement,TrussElement,BeamElement,
  FrameElement,PlateElement,ShellElement,
  SolidElement,TetrahedralElement,
  HexahedralElement,QuadrilateralElement,
  TriangularElement,ReducedIntegration,
  FullIntegration,SelectiveReducedIntegration,
  HourglassMode,HourglassControl,
  Locking,ShearLocking,VolumetricLocking,
  Mesh,MeshGeneration,MeshRefinement,
  MeshQuality,ElementDistortion,
  AspectRatio,JacobianDeterminant,
  AdaptiveMesh,AdaptiveRefinement,
  HRefinement,PRefinement,HPRefinement,
  ErrorEstimator,ResidualErrorEstimator,
  EnergyNormError,
  LinearSolver,NonlinearSolver,
  DirectSolver,IterativeSolver,
  ConjugateGradientMethod,GMRES,
  SparseMatrix,SparseFactorisation,
  NewtonRaphsonMethod,ModifiedNewtonMethod,
  ArcLengthMethod,RiksMethod,
  LoadStepping,TimeStepping,
  Increment,Iteration,Residual,
  TangentStiffness,TangentMatrix,
  LineSearch,ConvergenceCriterion,
  ForceResidual,DisplacementResidual,
  EnergyResidual,Norm,
  ExplicitDynamics,ImplicitDynamics,
  CentralDifferenceMethod,
  NewmarkMethod,GeneralisedAlphaMethod,
  TimeIntegration,StableTimeStep,
  CriticalTimeStep,
  WaveSpeed,MassScaling,
  FluidStructureInteraction,FSI,
  ThermoMechanicalCoupling,
  ElectroMechanicalCoupling,
  MultiphysicsSimulation,
  SoilStructureInteraction,
  FoundationInteraction,
  SeismicAnalysis,EarthquakeLoading,
  ResponseSpectrumAnalysis,
  TimeHistoryAnalysis,
  BaseExcitation,
  StructuralOptimisation,TopologyOptimisation,
  ShapeOptimisation,SizingOptimisation,
  DesignVariable,Compliance,
  SafetyFactor,FactorOfSafety,
  LimitState,Serviceability,
  UltimateLimitState,Fatigue,
  FatigueLife,SNcurve,StressRange,
  CycleCounting,RainflowCounting,
  CumulativeDamage,MinersRule,
  NumericalStability,Conditioning,
  NumericalError,DiscretisationError,
  RoundOffError,ModelFormError,
  Verification,CodeVerification,
  SolutionVerification,Validation,
  ExperimentalValidation,
  Benchmark,ReferenceSolution,
  PatchTest,ManufacturedSolution,
  MeshConvergence,LoadStepConvergence,
  TimeStepConvergence,RichardsonExtrapolation,
  SensitivityAnalysis,UncertaintyQuantification,
  MaterialUncertainty,LoadUncertainty,
  GeometryUncertainty,BoundaryConditionUncertainty,
  Calibration,ParameterEstimation,
  Reproducibility,Provenance,
  Configuration,SoftwareVersion,
  SolverVersion,MeshVersion,
  Checkpoint,Restart,
  ParallelStructuralSimulation,
  DomainDecomposition,MeshPartitioning,
  LoadBalancing,GPUAcceleration,
  HighPerformanceComputing,HPC,
  ReducedOrderModel,ROM,
  ProperOrthogonalDecomposition,POD,
  SurrogateModel,DigitalTwinRelationship
 ]
 EXCLUDE_AS_PRIMARY = [
  PureFluidSimulationWithoutStructuralResponse,
  PureRigidBodyKinematicsWithoutDeformationOrStructuralMechanics,
  StaticCADGeometryWithout StructuralAnalysis,
  CollisionDetectionWithoutStructuralResponse
 ]
 DISAMBIGUATION_RULE = "When a simulation computes deformation, stress, strain, stability or dynamic response of a solid structure under loads and constraints, interpret the context as structural simulation."
}

CORE_CONCEPTS {
 StructuralSimulation = "Computational solution of structural mechanics problems."
 Displacement = "Primary kinematic response variable describing structural motion or deformation."
 Strain = "Measure of deformation derived from displacement gradients."
 Stress = "Internal force measure related to strain through a constitutive law."
 ConstitutiveModel = "Material law relating stress, strain and history variables."
 StiffnessMatrix = "Discrete operator relating nodal displacements to forces in linearised form."
 StructuralDynamics = "Time-dependent response of structures with inertia and damping."
 Buckling = "Loss of structural stability under compressive or destabilising loading."
}

RELATIONS {
 StructuralSimulation --is_child_of--> ScientificSimulation
 StructuralSimulation --is_type_of--> PhysicalSimulation
 StructuralSimulation --solves--> StructuralMechanicsModel
 StructuralMechanicsModel --has--> MaterialModel
 StructuralMechanicsModel --has--> BoundaryCondition
 StructuralMechanicsModel --has--> Load
 Displacement --determines--> Strain
 ConstitutiveModel --maps--> StrainToStress
 Stress --contributes_to--> InternalForce
 StiffnessMatrix --relates--> DisplacementAndForce
 MassMatrix --governs--> InertialResponse
 DampingMatrix --governs--> DissipativeResponse
 NewtonRaphsonMethod --solves--> NonlinearStructuralEquilibrium
 Contact --introduces--> ContactNonlinearity
 Buckling --depends_on--> GeometricStiffness
 ModalAnalysis --computes--> NaturalFrequencyAndModeShape
 Verification --checks--> NumericalStructuralImplementation
 Validation --compares--> SimulationWithStructuralEvidence
}

OPERATORS {
 LINEAR_STATIC(K,u,f) := K*u-f
 DYNAMIC_RESIDUAL(M,C,K,u,u_dot,u_ddot,f) := M*u_ddot+C*u_dot+K*u-f
 STRAIN(u) := symmetric_gradient_or_element_strain_operator(u)
 STRESS(epsilon,material) := constitutive_response(material,epsilon)
 INTERNAL_FORCE(u) := integrate(B^T*sigma over domain)
 NEWTON_UPDATE(u,K_t,R) := u_next=u-solve(K_t,R)
 MODAL_PROBLEM(K,M) := solve(K*phi=lambda*M*phi)
 BUCKLING_PROBLEM(K,K_g) := solve((K+lambda*K_g)*phi=0)
 ENERGY_ERROR(reference,approximation) := declared_energy_norm_difference
}

AXIOMS {
 A1 = "Structural simulation requires equilibrium, constitutive behaviour, loads and constraints."
 A2 = "Displacements and strains are kinematic quantities; stresses depend on constitutive assumptions."
 A3 = "Linear structural response assumes sufficiently small deformation and linear material behaviour."
 A4 = "Geometric, material and contact nonlinearities require iterative equilibrium."
 A5 = "Dynamic response depends on mass, stiffness, damping and time integration."
 A6 = "Mesh resolution and element formulation influence stress and deformation accuracy."
 A7 = "Numerical convergence does not by itself establish physical validity."
 A8 = "Structural-simulation results require explicit mechanics, material, boundary, convergence and reproducibility semantics."
}

REASONING {
 R1_CONTEXT = identify(structure,analysis_type,materials,loads,constraints,outputs,accuracy_goal)
 R2_MODEL = define(geometry,element_family,material_models,contacts,initial_conditions_and_boundary_conditions)
 R3_ANALYSIS = classify(linear_static,nonlinear_static,modal,buckling,harmonic,transient_or_explicit_dynamic)
 R4_DISCRETISATION = select(FEM_element_types,mesh_density,integration_rules_and_refinement_strategy)
 R5_SOLVER = select(linear_solver_or_nonlinear_Newton_arc_length_explicit_or_implicit_dynamic_solver)
 R6_INCREMENT = configure(load_steps,time_steps,tolerances,line_search_and_stabilisation)
 R7_EXECUTION = assemble_and_solve_equilibrium_or_dynamic_system
 R8_MONITOR = track(residuals,displacements,stresses,energy,buckling_indicators,contact_and_element_quality)
 R9_CONVERGENCE = assess(mesh,load_step,time_step_and_iteration_convergence)
 R10_VALIDATE = compare(benchmarks,analytical_solutions,tests,experimental_data_and_uncertainty)
}

CONSTRAINTS {
 C1 = "Stress singularities can prevent pointwise stress convergence near sharp corners or idealised loads."
 C2 = "Poor-quality elements can degrade stiffness accuracy and nonlinear convergence."
 C3 = "Reduced integration can introduce hourglass modes without suitable control."
 C4 = "Fully integrated low-order elements can suffer locking in nearly incompressible or bending-dominated problems."
 C5 = "Large deformation requires geometric nonlinearity."
 C6 = "Plasticity and contact can cause path dependence and convergence difficulty."
 C7 = "Explicit dynamics requires a stable time step governed by the smallest element and fastest wave speed."
 C8 = "Linear buckling eigenvalues can overpredict real collapse loads when imperfections or material nonlinearity matter."
 C9 = "Boundary-condition idealisation can dominate response."
 C10 = "A converged finite-element solution is not sufficient evidence of physical validation."
}

SEMANTIC_EQUIVALENCE {
 "StructuralSimulation" <=> "StructuralAnalysisSimulation"
 "FiniteElementAnalysis" <=> "FEA"
 "FiniteElementMethod" <=> "FEM"
 "DegreesOfFreedom" <=> "DOF"
 "FluidStructureInteraction" <=> "FSI"
 "HighPerformanceComputing" <=> "HPC"
 "ReducedOrderModel" <=> "ROM"
 "ProperOrthogonalDecomposition" <=> "POD"
}

VALIDATION {
 V1 = "Geometry and structural idealisation are explicit."
 V2 = "Material models and parameters are documented."
 V3 = "Loads, supports and boundary conditions are documented."
 V4 = "Element formulations, mesh and integration rules are documented."
 V5 = "Nonlinear solver, load-step or time-step settings are documented."
 V6 = "Equilibrium residuals and relevant conservation or energy checks are performed."
 V7 = "Mesh and step convergence are assessed where relevant."
 V8 = "Contact, plasticity, buckling or dynamic assumptions are documented where used."
 V9 = "Analytical, benchmark or experimental validation evidence is documented."
 V10 = "Results are reproducible under documented mesh, solver, software and parallel settings."
}

CONFIDENCE {
 BASE_CONFIDENCE = 0.99
 STRUCTURAL_SIMULATION_DEFINITION = 0.99
 LINEAR_STATIC_REASONING = 0.99
 NONLINEAR_REASONING = 0.99
 DYNAMIC_REASONING = 0.99
 MODAL_REASONING = 0.99
 BUCKLING_REASONING = 0.98
 CONTACT_REASONING = 0.98
 POLICY = "Reduce confidence when material model, boundary conditions, mesh, element formulation, nonlinear settings, contact, convergence or validation evidence are underspecified."
}

AI_CONSUMPTION {
 PURPOSES = [
  SemanticSearch,OntologyGrounding,StructuralSimulationReasoning,
  StructuralMechanicsReasoning,ElasticityReasoning,
  PlasticityReasoning,HyperelasticityReasoning,
  ContactReasoning,FiniteElementReasoning,
  LinearStaticReasoning,NonlinearStaticReasoning,
  StructuralDynamicsReasoning,ModalReasoning,
  BucklingReasoning,MeshConvergenceReasoning,
  SolverConvergenceReasoning,VerificationReasoning,
  ValidationReasoning,UncertaintyReasoning,
  ReproducibilityReasoning,KnowledgeGraphConstruction,
  RetrievalAugmentation,RecursiveInference
 ]
 NORMALISE {
  "structural simulation" -> StructuralSimulation
  "structural analysis" -> StructuralSimulation
  "FEA" -> FiniteElementAnalysis
  "FEM" -> FiniteElementMethod
  "DOF" -> DegreeOfFreedom
  "FSI" -> FluidStructureInteraction
  "HPC" -> HighPerformanceComputing
  "ROM" -> ReducedOrderModel
  "POD" -> ProperOrthogonalDecomposition
 }
}

EXECUTION_RULES {
 E1 = "If a simulation computes structural deformation, stress, stability or dynamic response, activate StructuralSimulationOntology."
 E2 = "Define structural idealisation, material law, loads and constraints before solution."
 E3 = "Choose element formulations compatible with geometry, thickness, deformation and material behaviour."
 E4 = "Enable geometric, material or contact nonlinearity when assumptions require it."
 E5 = "For nonlinear problems, monitor force, displacement and energy residuals and use appropriate load stepping."
 E6 = "For dynamic problems, select time integration and damping consistent with frequency content and stability."
 E7 = "Perform mesh refinement studies for quantities sensitive to spatial discretisation."
 E8 = "Interpret buckling, stress singularities and contact pressures with their modelling assumptions."
 E9 = "Validate against analytical, benchmark or experimental evidence and document uncertainty and reproducibility."
}

RECURSION {
 ENTRY = StructuralSimulation
 EXPAND(StructuralSimulation) -> [
  StructuralAnalysis,ComputationalStructuralMechanics,
  SolidMechanicsSimulation,StructuralMechanics,
  ContinuumMechanics,Structure,Beam,Column,
  Plate,Shell,Solid,Frame,Truss,
  Node,Element,DegreeOfFreedom,Displacement,
  Rotation,Velocity,Acceleration,Strain,Stress,
  Deformation,DeformationGradient,SmallStrain,
  FiniteStrain,PrincipalStress,VonMisesStress,
  CauchyStress,MaterialModel,ConstitutiveModel,
  Elasticity,LinearElasticity,NonlinearElasticity,
  IsotropicElasticity,OrthotropicElasticity,
  HookesLaw,YoungsModulus,PoissonsRatio,
  Plasticity,Elastoplasticity,YieldCriterion,
  VonMisesYield,Hardening,ReturnMapping,
  Hyperelasticity,NeoHookeanModel,MooneyRivlinModel,
  Viscoelasticity,Creep,DamageMechanics,
  Contact,StructuralContact,Friction,
  PenaltyContact,AugmentedLagrangianContact,
  Load,Force,Moment,PressureLoad,GravityLoad,
  ThermalLoad,BoundaryCondition,FixedSupport,
  RollerSupport,PinnedSupport,MultipointConstraint,
  StaticAnalysis,LinearStaticAnalysis,
  NonlinearStaticAnalysis,StructuralDynamics,
  TransientDynamicAnalysis,HarmonicAnalysis,
  ModalAnalysis,EigenvalueAnalysis,NaturalFrequency,
  ModeShape,Damping,MassMatrix,StiffnessMatrix,
  DampingMatrix,Buckling,LinearBuckling,
  NonlinearBuckling,GeometricNonlinearity,
  MaterialNonlinearity,ContactNonlinearity,
  LargeDisplacement,FiniteElementMethod,FEM,
  FiniteElementAnalysis,FEA,WeakForm,
  ShapeFunction,IsoparametricElement,
  IntegrationPoint,GaussQuadrature,
  BeamElement,ShellElement,SolidElement,
  TetrahedralElement,HexahedralElement,
  ReducedIntegration,HourglassControl,
  Locking,Mesh,MeshGeneration,MeshRefinement,
  MeshQuality,AdaptiveRefinement,
  ErrorEstimator,LinearSolver,NonlinearSolver,
  NewtonRaphsonMethod,ModifiedNewtonMethod,
  ArcLengthMethod,RiksMethod,LoadStepping,
  TangentStiffness,ConvergenceCriterion,
  ExplicitDynamics,ImplicitDynamics,
  CentralDifferenceMethod,NewmarkMethod,
  GeneralisedAlphaMethod,CriticalTimeStep,
  FluidStructureInteraction,FSI,
  ThermoMechanicalCoupling,SeismicAnalysis,
  ResponseSpectrumAnalysis,TimeHistoryAnalysis,
  StructuralOptimisation,TopologyOptimisation,
  SafetyFactor,Fatigue,FatigueLife,
  NumericalStability,NumericalError,
  MeshConvergence,Verification,Validation,
  Benchmark,PatchTest,SensitivityAnalysis,
  UncertaintyQuantification,Reproducibility,
  ParallelStructuralSimulation,DomainDecomposition,
  GPUAcceleration,HPC,ReducedOrderModel,POD
 ]
 EXPAND(StructuralSimulationFamilies) -> [
  LinearStaticStructuralSimulation,
  NonlinearStructuralSimulation,
  StructuralDynamicsSimulation,
  ModalAndFrequencySimulation,
  BucklingAndStabilitySimulation,
  ContactAndFractureRelatedSimulation,
  ThermoMechanicalAndMultiphysicsStructuralSimulation,
  ParallelHighPerformanceStructuralSimulation
 ]
 STOP_CONDITION = "Stop when structure, material model, loads, constraints, element formulation, mesh, solver, nonlinearities, convergence, validation and reproducibility are sufficiently resolved."
}

ROUTING {
 PARENT_ONTOLOGY = "Scientific Simulation Ontology"
 RELATED_ONTOLOGIES = [
  "Scientific Simulation Ontology",
  "Physical Simulation Ontology",
  "Heat Transfer Simulation Ontology",
  "Fluid Simulation Ontology",
  "Scientific Computing Ontology 2",
  "Finite Element Method Ontology",
  "Mesh Generation Ontology 2",
  "Mesh Refinement Ontology",
  "Collision Detection Ontology 2",
  "Numerical Linear Algebra Ontology 2",
  "Nonlinear Solver Ontology",
  "Newton-Raphson Ontology",
  "Numerical Error Ontology",
  "Numerical Stability Ontology 2",
  "Numerical Convergence Ontology",
  "Floating Point Arithmetic Ontology"
 ]
 ROUTE_RULES = [
  "Structural Simulation -> Scientific Simulation Ontology for parent semantics",
  "Structural Simulation -> Physical Simulation for mechanics and conservation semantics",
  "Structural Simulation -> Heat Transfer Simulation for thermo-mechanical coupling",
  "Structural Simulation -> Fluid Simulation for fluid-structure interaction",
  "Structural Simulation -> Scientific Computing for large-scale solver execution",
  "Structural Simulation -> Finite Element Method for primary structural discretisation",
  "Structural Simulation -> Mesh Generation and Refinement for structural spatial resolution",
  "Structural Simulation -> Collision Detection for contact geometry",
  "Structural Simulation -> Numerical Linear Algebra for sparse stiffness, mass and tangent systems",
  "Structural Simulation -> Nonlinear Solver and Newton-Raphson for nonlinear equilibrium",
  "Structural Simulation -> Numerical Error for discretisation and model error",
  "Structural Simulation -> Numerical Stability for dynamic and nonlinear stability",
  "Structural Simulation -> Numerical Convergence for mesh, load-step and time-step convergence",
  "Structural Simulation -> Floating Point Arithmetic for finite-precision effects"
 ]
}

UPDATE_MODEL {
 MODE = "append-compatible semantic versioning"
 MAJOR = "ontology-breaking conceptual change"
 MINOR = "new compatible structural models, element families or reasoning pathways"
 PATCH = "clarification, metadata or formatting correction"
 RULES = [
  "Preserve displacement-versus-stress distinction.",
  "Preserve kinematic-versus-constitutive quantities distinction.",
  "Preserve linear-versus-nonlinear structural response distinction.",
  "Preserve static-versus-dynamic analysis distinction.",
  "Preserve material-versus-geometric-versus-contact nonlinearity distinction.",
  "Preserve eigenvalue-buckling-versus-nonlinear-collapse distinction.",
  "Preserve solver-convergence-versus-physical-validation distinction.",
  "Preserve machine-readable structural-simulation semantics."
 ]
}

OUTPUT {
 CANONICAL_DEFINITION = "Structural simulation computationally solves deformation, stress, stability and dynamic-response problems in solid structures."
 STATIC_SUMMARY = "Static analysis balances internal and external forces under material and geometric assumptions."
 NONLINEAR_SUMMARY = "Material, geometric and contact nonlinearities require incremental-iterative equilibrium solution."
 DYNAMIC_SUMMARY = "Structural dynamics combines mass, damping and stiffness with time-dependent loading."
 MODAL_SUMMARY = "Modal analysis computes natural frequencies and mode shapes from generalised eigenvalue problems."
 BUCKLING_SUMMARY = "Buckling analysis investigates loss of stability under compressive or destabilising loads."
 VALIDATION_SUMMARY = "Structural simulations should be checked through equilibrium, mesh and step convergence, analytical or benchmark solutions, experimental evidence, uncertainty and reproducibility."
}

FLOW {
 INPUT
 -> detect_structural_simulation_context
 -> identify_structure_analysis_type_materials_loads_constraints_outputs_accuracy_goal_and_budget
 -> define_geometry_element_family_material_models_contacts_initial_conditions_and_boundary_conditions
 -> classify_linear_static_nonlinear_static_modal_buckling_harmonic_transient_or_explicit_dynamic_analysis
 -> generate_or_import_mesh_and_select_element_formulations_and_integration_rules
 -> select_linear_solver_or_nonlinear_Newton_arc_length_explicit_or_implicit_dynamic_solver
 -> configure_load_steps_time_steps_tolerances_line_search_damping_and_stabilisation
 -> assemble_mass_stiffness_damping_internal_force_contact_and_external_load_terms
 -> solve_equilibrium_eigenvalue_or_dynamic_system
 -> monitor_residuals_displacements_stresses_strains_energy_contact_status_and_element_quality
 -> assess_mesh_load_step_time_step_and_iteration_convergence
 -> verify_against_analytical_manufactured_reference_patch_or_benchmark_solutions
 -> validate_against_experimental_or_observational_data_when_required
 -> quantify_material_load_geometry_boundary_numerical_and_model_uncertainty
 -> document_mesh_solver_versions_parallel_configuration_and_reproducibility
 -> route_to_related_scientific_simulation_physical_simulation_heat_transfer_fluid_simulation_scientific_computing_FEM_mesh_generation_refinement_collision_linear_algebra_nonlinear_solver_Newton_error_stability_convergence_and_floating_point_ontologies
 -> recursively_expand_required_dependencies
 -> verify_result
 -> assign_confidence
 -> produce_semantic_output
 -> END
}

SEMANTIC_SUMMARY {
 "The Structural Simulation Ontology defines computational structural mechanics across beams, trusses, frames, plates, shells and solid continua. It supports displacement, strain and stress fields, linear and nonlinear elasticity, plasticity, hyperelasticity, viscoelasticity, creep and damage relationships, loads, supports and multipoint constraints, contact and friction, linear and nonlinear statics, transient and harmonic dynamics, modal analysis, eigenvalue and nonlinear buckling, geometric, material and contact nonlinearity, finite-element weak forms, beam, shell, tetrahedral and hexahedral elements, numerical integration, reduced integration, locking and hourglass controls, mesh generation and adaptivity, sparse linear and nonlinear solvers, Newton-Raphson, arc-length and Riks methods, explicit and implicit dynamics, FSI and thermo-mechanical coupling, seismic analysis, fatigue and optimisation relationships, mesh and time-step convergence, verification, experimental validation, uncertainty, parallel execution, reduced-order modelling and reproducibility."
}

FLOW_HASH {
 METHOD = "semantic-content-identity"
 ID = "KIRETH-MATH-COMPUTATIONAL-MATHEMATICS-STRUCTURAL-SIMULATION-ONTOLOGY-V1"
}

}

END_FLOW