FEA (CalculiX, Abaqus & NASTRAN)

@modelscript/fea (languages/fea) provides native parsing, parametric template materialization, 3D CAD boundary condition synthesis, structural theory slicing, and cross-domain TGG synchronization for Finite Element Analysis input decks.

Supported Dialects & Extensions

Extension	Dialect	Key Directives
`.inp`	CalculiX / Abaqus input deck	`HEADING`, `NODE`, `ELEMENT`, `NSET`, `ELSET`, `MATERIAL`, `ELASTIC`, `DENSITY`, `SOLID SECTION`, `STEP`, `STATIC`, `FREQUENCY`, `BOUNDARY`, `CLOAD`, `*DLOAD`
`.inpt`	Parametric CalculiX / Abaqus template	Supports `{{ expression }}` mustache substitutions over workspace parameters
`.bdf`	NASTRAN Bulk Data Deck	`SOL`, `CEND`, `BEGIN BULK`, `GRID`, `CTETRA`, `CHEXA`, `PSOLID`, `MAT1`, `SPC1`, `FORCE`, `MOMENT`, `LOAD`, `ENDDATA`
`.fea`	ModelScript native FEA configuration	Structured material, mesh, boundary, and load study definitions

Parametric Template Materialization (`{{ expr }}`)

Input decks (.inpt, .inp, .bdf, .fea) can embed parametric expressions enclosed in {{ ... }} placeholders:

ini

*MATERIAL, NAME=AL7075
*ELASTIC
{{ E_modulus }}, {{ poisson_ratio }}
*DENSITY
{{ rho_al }}
*CLOAD
LOAD_SET, 3, {{ -tip_mass * 9.81 }}

materializeFeaDeck(templateText, parameters) (languages/fea/src/materializer.ts) evaluates arithmetic expressions (+, -, *, /, ^), functions (sin, cos, tan, sqrt, abs, min, max, log, exp), and built-in constants (PI, E) via evaluateFeaExpression, formatting values in engineering notation and recording any unresolved symbols or syntax errors.

3D CAD Face Boundary Condition & Load Synthesis

When a user selects a topological face in the 3D CAD viewer, synthesizeFeaBoundary and applyBoundaryActionToDeck (languages/fea/src/boundary-synthesizer.ts) automatically generate solver-native boundary and load cards for the target dialect:

Boundary Kind	CalculiX / Abaqus (`.inp`)	NASTRAN Bulk Data (`.bdf`)
Fixed Support (`fixed`)	`*BOUNDARY` constraining DOFs `1, 6` (or `1, 3`) on `NSET_<FACE>`	`SPC1` card locking DOFs `123456` (or `123`) on `SET_<FACE>`
Point / Concentrated Force (`force`)	`*CLOAD` directional nodal force components $(F_{x}, F_{y}, F_{z})$ along the face normal	`FORCE` card with magnitude and normal unit vector $(n_{x}, n_{y}, n_{z})$
Distributed Pressure (`pressure`)	`*DLOAD` surface pressure (`P`) applied to `ELSET_<FACE>`	`PLOAD4` / `FORCE` cards distributed across face elements
Torque / Moment (`moment`)	`*CLOAD` rotational DOFs `4, 5, 6`	`MOMENT` card around face normal axis

Structural Theory Slicing & Safety Margin Extraction

extractFeaSlicingProperties(text) (languages/fea/src/language.ts) extracts structural parameters (DENSITY, VOLUME, MAX_VON_MISES_STRESS, YIELD_STRENGTH) directly from the CST and evaluates the structural safety margin:

Safety Factor (SF) = \frac{σ_{yield}}{σ_{von Mises, max}}, isSafe ⟺ σ_{von Mises, max} \leq σ_{yield}

Returning { mass, maxVonMisesPa, yieldStrengthPa, safetyFactor, isSafe } directly to the Multi-Domain Theory Coordinator (CaeContractOracle) and SysML v2 requirement verifiers.

Built-In Solver & IDE Actions

@modelscript/fea registers three interactive actions in feaLanguage.actions:

open_fea_viewer: Opens the 3D FEA mesh, boundary condition, and von Mises stress contour viewer.
materialize_deck: Evaluates all {{ expr }} template placeholders against workspace parameters to produce a concrete .inp or .bdf deck.
run_simulation (fea_run_simulation): Parses *MATERIAL, *ELASTIC, *BOUNDARY, and *CLOAD/*DLOAD sections, solves the 3D tetrahedral finite element stiffness matrix, and returns nodal displacements and element von Mises stress contours.

Polyglot TGG Rules

@modelscript/fea defines 6 bidirectional Triple Graph Grammar (TGG) rules in languages/fea/src/language.ts:

Rule Name	Source (`fea`)	Target Language	Target Construct
`FeaStressMassToModelicaParam`	`FeaDeck` (`mass`, `maxVonMisesPa`)	`modelica`	`ComponentClause` (`parameter Real`)
`FeaStressMassToSysmlAttribute`	`FeaDeck` (`safetyFactor`, `mass`)	`sysml2`	`AttributeUsage`
`FeaMaterialToSysmlAttribute`	`Section` (`*MATERIAL` / `MAT1`)	`sysml2`	`AttributeUsage`
`FeaBoundaryFixToModelicaFixed`	`Section` (`*BOUNDARY` / `SPC1`)	`modelica`	`ComponentClause` (`Modelica.Mechanics.MultiBody.Parts.Fixed`)
`FeaSpringToModelicaSpring`	`Section` (`*SPRING`)	`modelica`	`ComponentClause` (`Modelica.Mechanics.Translational.Components.Spring`)
`FeaLoadCaseToSysmlRequirement`	`Section` (`*STEP` / `SUBCASE`)	`sysml2`	`RequirementUsage`

Command Line Interface (`msx fea`)

bash

msx fea <action> [files...] [options]

Action	Description	Key Options
`lint`	Validates CalculiX, Abaqus, and NASTRAN syntax, element topologies, material cards, and constraints.	—
`summary`	Prints structural summary: element count by kind (C3D4, C3D10, CHEXA), materials, and load steps.	—
`inspect`	Dumps parsed boundary sets, node coordinates, material elastic moduli, and load cases.	—
`to-modelica`	Generates Modelica equivalent structural stiffness models and translational boundary ports.	`--out=<file.mo>`
`to-dae`	Lowers structural mass and stiffness matrices into ModelScript linear-memory DAE arena.	`--out=<file.json>`
`solve`	Solves linear elastostatic stiffness matrix for nodal displacements and von Mises stress contours.	—

Examples

bash

# Validate element connectivity and material properties in an Abaqus deck
msx fea lint BracketAssembly.inp

# Display mesh statistics, node count, and material properties
msx fea summary ChassisStructure.bdf

# Solve linear static displacement and print max von Mises stress
msx fea solve BracketAssembly.inp

Diagnostic Rules

8 rules6 error2 warning Run with msx lint

Code	Rule	Severity	Message
`F1001`	`zero-elastic-modulus`	error	Material '`<mat>`' has non-positive Young's modulus '`<val>`'.
`F1002`	`poisson-ratio-limit`	error	Poisson's ratio '`<val>`' for material '`<mat>`' violates physical stability bounds (-1.0 < nu < 0.5).
`F1003`	`unconstrained-rigid-body`	warning	Structural mesh '`<name>`' has only '`<count>`' constrained boundary nodes; rigid-body motion may be unconstrained.
`F1004`	`empty-mesh`	error	FEA deck '`<name>`' does not contain any defined finite elements.
`F1005`	`missing-material-definition`	error	Element set '`<elset>`' lacks an assigned material specification or section.
`F1006`	`degenerate-element-nodes`	error	Element '`<elemId>`' of type '`<type>`' contains duplicate or degenerate node references.
`F1007`	`negative-yield-stress`	error	Plastic yield strength '`<val>`' for material '`<mat>`' must be strictly positive.
`F1008`	`negative-density`	warning	Mass density '`<val>`' for material '`<mat>`' must be strictly positive for dynamic analysis.

Generated from languages/fea/src/errors.ts. All languages →

FEA (CalculiX, Abaqus & NASTRAN) ​

Supported Dialects & Extensions ​

Parametric Template Materialization ({{ expr }}) ​

3D CAD Face Boundary Condition & Load Synthesis ​

Structural Theory Slicing & Safety Margin Extraction ​

Built-In Solver & IDE Actions ​

Polyglot TGG Rules ​

Command Line Interface (msx fea) ​

Examples ​

Diagnostic Rules ​