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1781 lines (1651 loc) · 59.3 KB
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// SPDX-License-Identifier: AGPL-3.0-or-later
import { BdfDialect } from "./dialects/bdf.js";
import { InpDialect } from "./dialects/inp.js";
import type {
BoundaryActionPayload,
CaeDiagnostic,
FeaModelData,
MaterializeOptions,
ParameterLookup,
} from "./types.js";
/**
* Safe mathematical function and constant environment available inside FEA template `{{ ... }}` expressions.
*/
const MATH_ENV: Record<string, any> = {
sin: Math.sin,
cos: Math.cos,
tan: Math.tan,
asin: Math.asin,
acos: Math.acos,
atan: Math.atan,
atan2: Math.atan2,
sind: (deg: number) => Math.sin((deg * Math.PI) / 180),
cosd: (deg: number) => Math.cos((deg * Math.PI) / 180),
tand: (deg: number) => Math.tan((deg * Math.PI) / 180),
rad: (deg: number) => (deg * Math.PI) / 180,
deg: (rad: number) => (rad * 180) / Math.PI,
sqrt: Math.sqrt,
cbrt: Math.cbrt,
abs: Math.abs,
exp: Math.exp,
log: Math.log,
log10: Math.log10,
log2: Math.log2,
pow: Math.pow,
min: Math.min,
max: Math.max,
floor: Math.floor,
ceil: Math.ceil,
round: Math.round,
pi: Math.PI,
PI: Math.PI,
e: Math.E,
E: Math.E,
};
/**
* Set of permitted built-in function and constant identifiers in `MATH_ENV`.
*/
const ALLOWED_IDENTIFIERS = new Set(Object.keys(MATH_ENV));
/**
* Lexical token produced by `tokenizeArithmeticExpression`.
*/
type ExprToken =
| { kind: "number"; value: number }
| { kind: "string"; value: string }
| { kind: "ident"; value: string }
| { kind: "op"; value: string }
| { kind: "lparen" }
| { kind: "rparen" }
| { kind: "comma" };
/**
* Tokenizes an FEA template arithmetic or string expression into a sequence of `ExprToken` items.
*/
function tokenizeArithmeticExpression(input: string): ExprToken[] {
const tokens: ExprToken[] = [];
let i = 0;
while (i < input.length) {
const ch = input[i]!;
if (/\s/.test(ch)) {
i++;
continue;
}
if (ch === '"' || ch === "'") {
const quote = ch;
let j = i + 1;
let str = "";
while (j < input.length && input[j] !== quote) {
if (input[j] === "\\" && j + 1 < input.length) {
str += input[j + 1];
j += 2;
} else {
str += input[j];
j++;
}
}
if (j >= input.length) {
throw new Error(`Unterminated string literal in expression: ${input}`);
}
tokens.push({ kind: "string", value: str });
i = j + 1;
continue;
}
const numMatch = input.slice(i).match(/^(?:\d+(?:\.\d*)?|\.\d+)(?:[eE][+-]?\d+)?/);
if (numMatch) {
tokens.push({ kind: "number", value: Number(numMatch[0]) });
i += numMatch[0].length;
continue;
}
const identMatch = input.slice(i).match(/^[A-Za-z_][A-Za-z0-9_.]*/);
if (identMatch) {
tokens.push({ kind: "ident", value: identMatch[0] });
i += identMatch[0].length;
continue;
}
if (input.startsWith("**", i)) {
tokens.push({ kind: "op", value: "^" });
i += 2;
continue;
}
if (ch === "+" || ch === "-" || ch === "*" || ch === "/" || ch === "%" || ch === "^") {
tokens.push({ kind: "op", value: ch });
i++;
continue;
}
if (ch === "(") {
tokens.push({ kind: "lparen" });
i++;
continue;
}
if (ch === ")") {
tokens.push({ kind: "rparen" });
i++;
continue;
}
if (ch === ",") {
tokens.push({ kind: "comma" });
i++;
continue;
}
throw new Error(`Expression contains illegal characters: ${input}`);
}
return tokens;
}
/**
* Evaluates an arithmetic expression string with parameter lookup and safe math functions.
*/
export function evaluateFeaExpression(
exprStr: string,
lookup?: ParameterLookup | Record<string, number | string>,
diagnostics?: CaeDiagnostic[],
): number | string {
const trimmed = exprStr.trim();
if (!trimmed) return "";
if ((trimmed.startsWith('"') && trimmed.endsWith('"')) || (trimmed.startsWith("'") && trimmed.endsWith("'"))) {
return trimmed.slice(1, -1);
}
const resolveVal = (token: string): number | string | undefined => {
if (!isNaN(Number(token))) return Number(token);
if (typeof lookup === "function") {
const val = lookup(token);
if (val !== undefined) return val;
} else if (lookup && typeof lookup === "object") {
if (token in lookup) return lookup[token];
}
return undefined;
};
if (/^[A-Za-z_][A-Za-z0-9_.]*$/.test(trimmed)) {
if (trimmed in MATH_ENV) {
const val = MATH_ENV[trimmed];
if (typeof val === "number") return val;
}
const val = resolveVal(trimmed);
if (val !== undefined) return val;
}
try {
const tokens = tokenizeArithmeticExpression(trimmed);
let pos = 0;
const peek = (): ExprToken | undefined => tokens[pos];
const consume = (): ExprToken => {
const tok = tokens[pos];
if (!tok) throw new Error(`Unexpected end of expression: '${trimmed}'`);
pos++;
return tok;
};
const toNum = (v: number | string): number => {
if (typeof v === "number") return v;
const n = Number(v);
if (isNaN(n)) throw new Error(`Expected numeric operand, got '${v}'`);
return n;
};
const parseAddSub = (): number | string => {
let left = parseMulDiv();
while (true) {
const next = peek();
if (next?.kind === "op" && (next.value === "+" || next.value === "-")) {
consume();
const right = parseMulDiv();
if (next.value === "+") {
if (typeof left === "string" || typeof right === "string") {
left = `${left}${right}`;
} else {
left = left + right;
}
} else {
left = toNum(left) - toNum(right);
}
} else {
break;
}
}
return left;
};
const parseMulDiv = (): number | string => {
let left = parseUnary();
while (true) {
const next = peek();
if (next?.kind === "op" && (next.value === "*" || next.value === "/" || next.value === "%")) {
consume();
const right = parseUnary();
const lNum = toNum(left);
const rNum = toNum(right);
if (next.value === "*") left = lNum * rNum;
else if (next.value === "/") left = lNum / rNum;
else left = lNum % rNum;
} else {
break;
}
}
return left;
};
const parseUnary = (): number | string => {
const next = peek();
if (next?.kind === "op" && (next.value === "+" || next.value === "-")) {
consume();
const operand = toNum(parseUnary());
return next.value === "-" ? -operand : operand;
}
return parsePower();
};
const parsePower = (): number | string => {
const base = parsePrimary();
const next = peek();
if (next?.kind === "op" && next.value === "^") {
consume();
const exponent = parseUnary();
return Math.pow(toNum(base), toNum(exponent));
}
return base;
};
const parsePrimary = (): number | string => {
const tok = consume();
if (tok.kind === "number") return tok.value;
if (tok.kind === "string") return tok.value;
if (tok.kind === "lparen") {
const inner = parseAddSub();
const close = consume();
if (close.kind !== "rparen") {
throw new Error(`Expected closing parenthesis in '${trimmed}'`);
}
return inner;
}
if (tok.kind === "ident") {
const ident = tok.value;
if (peek()?.kind === "lparen") {
if (!ALLOWED_IDENTIFIERS.has(ident) || typeof MATH_ENV[ident] !== "function") {
throw new Error(`Expression contains illegal identifier: '${ident}'`);
}
consume(); // '('
const args: number[] = [];
if (peek()?.kind !== "rparen") {
args.push(toNum(parseAddSub()));
while (peek()?.kind === "comma") {
consume();
args.push(toNum(parseAddSub()));
}
}
const close = consume();
if (close.kind !== "rparen") {
throw new Error(`Expected closing parenthesis for call to '${ident}'`);
}
return Number(MATH_ENV[ident](...args));
}
if (ident in MATH_ENV && typeof MATH_ENV[ident] === "number") {
return MATH_ENV[ident] as number;
}
const resolved = resolveVal(ident);
if (resolved === undefined) {
throw new Error(`Unresolved parameter: '${ident}'`);
}
if (typeof resolved === "number") return resolved;
if (typeof resolved === "string" && resolved.trim() !== "" && !isNaN(Number(resolved))) {
return Number(resolved);
}
return resolved;
}
throw new Error(`Unexpected token in expression: '${trimmed}'`);
};
const result = parseAddSub();
if (pos < tokens.length) {
const trailing = tokens[pos]!;
if (trailing.kind === "ident") {
throw new Error(`Expression contains illegal identifier: '${trailing.value}'`);
}
throw new Error(`Unexpected trailing tokens in expression: '${trimmed}'`);
}
if (typeof result === "number" && !isNaN(result)) {
return result;
}
if (typeof result === "string") {
return result;
}
} catch (err: any) {
if (diagnostics) {
diagnostics.push({
severity: "error",
message: err.message || String(err),
expression: trimmed,
});
} else {
console.warn(`[fea:materializer] Failed to evaluate expression '${trimmed}':`, err.message || err);
}
}
return trimmed;
}
/**
* Materializes an FEA deck template by replacing all {{ expression }} blocks
* with their evaluated numeric or string values.
*/
export function materializeFeaDeck(templateText: string, options: MaterializeOptions = {}): string {
const { evaluator, formatNumber, diagnostics } = options;
const defaultFormat = (val: number): string => {
if (Number.isInteger(val)) return val.toString();
if (Math.abs(val) >= 1e9 || (Math.abs(val) < 1e-4 && Math.abs(val) > 0)) {
return val.toExponential(6);
}
return parseFloat(val.toFixed(6)).toString();
};
const formatter = formatNumber || defaultFormat;
return templateText.replace(/\{\{([^{}]+)\}\}/g, (_match, expr, offset: number) => {
const prevDiagLen = diagnostics ? diagnostics.length : 0;
const evaluated = evaluateFeaExpression(expr.trim(), evaluator, diagnostics);
if (diagnostics && diagnostics.length > prevDiagLen) {
let targetOffset = offset + 2 + expr.indexOf(expr.trim());
const diag = diagnostics[diagnostics.length - 1]!;
const paramMatch = diag.message.match(/Unresolved parameter: '([^']+)'|illegal identifier: '([^']+)'/);
const offendingToken = paramMatch?.[1] ?? paramMatch?.[2];
if (offendingToken) {
const tokenIdx = expr.indexOf(offendingToken);
if (tokenIdx >= 0) {
targetOffset = offset + 2 + tokenIdx;
}
}
const prefix = templateText.slice(0, targetOffset);
const lastNewline = prefix.lastIndexOf("\n");
diag.line = (prefix.match(/\n/g)?.length ?? 0) + 1;
diag.column = lastNewline === -1 ? targetOffset + 1 : targetOffset - lastNewline;
}
if (typeof evaluated === "number") {
return formatter(evaluated);
}
return String(evaluated);
});
}
/**
* Groups an array of 1-based DOF indices into sorted, deduplicated contiguous `[start, end]` intervals.
*/
function groupContiguousDofs(dofs: number[]): [number, number][] {
const sorted = Array.from(new Set(dofs.filter((d) => Number.isInteger(d) && d >= 1 && d <= 6))).sort((a, b) => a - b);
if (sorted.length === 0) return [];
const ranges: [number, number][] = [];
let start = sorted[0]!;
let prev = start;
for (let i = 1; i < sorted.length; i++) {
const cur = sorted[i]!;
if (cur === prev + 1) {
prev = cur;
} else {
ranges.push([start, prev]);
start = cur;
prev = cur;
}
}
ranges.push([start, prev]);
return ranges;
}
/**
* Synthesizes a syntactic boundary or load directive for FEA decks (CalculiX / .inp / NASTRAN BDF).
*/
export function synthesizeFeaBoundary(
action: BoundaryActionPayload,
dialect: "calculix" | "abaqus" | "bdf" | string = "calculix",
): string {
const targetId = action.targetId;
const normDialect = dialect.toLowerCase();
if (normDialect === "calculix" || normDialect === "abaqus" || normDialect === ".inp" || normDialect === "inp") {
switch (action.kind) {
case "fix": {
const ranges =
action.dofs && action.dofs.length > 0 ? groupContiguousDofs(action.dofs) : [[1, 3] as [number, number]];
const lines = ["*BOUNDARY"];
for (const [dofStart, dofEnd] of ranges) {
lines.push(`${targetId}, ${dofStart}, ${dofEnd}, 0.0`);
}
return lines.join("\n");
}
case "displacement": {
const mag = action.magnitude ?? 0.0;
const ranges =
action.dofs && action.dofs.length > 0 ? groupContiguousDofs(action.dofs) : [[1, 1] as [number, number]];
const lines = ["*BOUNDARY"];
for (const [dofStart, dofEnd] of ranges) {
lines.push(`${targetId}, ${dofStart}, ${dofEnd}, ${mag}`);
}
return lines.join("\n");
}
case "force": {
if (action.vector) {
const lines: string[] = ["*CLOAD"];
if (action.vector[0] !== 0) lines.push(`${targetId}, 1, ${action.vector[0]}`);
if (action.vector[1] !== 0) lines.push(`${targetId}, 2, ${action.vector[1]}`);
if (action.vector[2] !== 0) lines.push(`${targetId}, 3, ${action.vector[2]}`);
if (lines.length === 1) lines.push(`${targetId}, 3, ${action.magnitude ?? -1000.0}`);
return lines.join("\n");
}
const dof = action.dofs && action.dofs.length > 0 ? action.dofs[0] : 3;
const mag = action.magnitude ?? -1000.0;
return `*CLOAD\n${targetId}, ${dof}, ${mag}`;
}
case "moment": {
const dof = action.dofs && action.dofs.length > 0 ? action.dofs[0] : 4;
const mag = action.magnitude ?? 100.0;
return `*CLOAD\n${targetId}, ${dof}, ${mag}`;
}
case "pressure": {
const mag = action.magnitude ?? 1e5;
return `*DLOAD\n${targetId}, P, ${mag}`;
}
default:
return `** Boundary ${targetId}: ${action.kind}`;
}
} else if (normDialect === "bdf" || normDialect === "dat" || normDialect === "nastran" || normDialect === ".bdf") {
switch (action.kind) {
case "fix": {
const dofs = action.dofs && action.dofs.length > 0 ? action.dofs.join("") : "123456";
return `SPC1, 1, ${dofs}, ${targetId}`;
}
case "force": {
const vec = action.vector ?? [0, 0, action.magnitude ?? -1000.0];
const mag = Math.hypot(...vec) || 1.0;
return `FORCE, 1, ${targetId}, 0, ${mag.toFixed(2)}, ${(vec[0] / mag).toFixed(4)}, ${(vec[1] / mag).toFixed(4)}, ${(vec[2] / mag).toFixed(4)}`;
}
case "moment": {
let vec: [number, number, number];
if (action.vector) {
vec = action.vector;
} else {
const dof = action.dofs && action.dofs.length > 0 ? action.dofs[0] : 6;
const m = action.magnitude ?? 100.0;
vec = dof === 4 ? [m, 0, 0] : dof === 5 ? [0, m, 0] : [0, 0, m];
}
const vecMag = Math.hypot(...vec);
const mag = action.magnitude !== undefined ? action.magnitude : vecMag || 100.0;
const norm = vecMag > 0 ? vecMag : 1.0;
return `MOMENT, 1, ${targetId}, 0, ${mag.toFixed(2)}, ${(vec[0] / norm).toFixed(4)}, ${(vec[1] / norm).toFixed(4)}, ${(vec[2] / norm).toFixed(4)}`;
}
default:
return `$ Boundary ${targetId}: ${action.kind}`;
}
}
return `** Boundary ${targetId}: ${action.kind}`;
}
/**
* Injects or updates a boundary constraint or load in an FEA deck template.
*/
export function applyBoundaryActionToDeck(
deckText: string,
action: BoundaryActionPayload,
dialect: string = "calculix",
): string {
const snippet = synthesizeFeaBoundary(action, dialect);
if (!snippet) return deckText;
const normDialect = dialect.toLowerCase();
if (normDialect === "bdf" || normDialect === "dat" || normDialect === "nastran" || normDialect === ".bdf") {
const endDataMatch = deckText.match(/\bENDDATA\b/i);
if (endDataMatch && endDataMatch.index !== undefined) {
return `${deckText.slice(0, endDataMatch.index).trimEnd()}\n${snippet}\n${deckText.slice(endDataMatch.index)}`;
}
return `${deckText.trimEnd()}\n${snippet}\n`;
}
// Case-insensitive search for *END STEP
const endStepMatch = deckText.match(/\*END\s+STEP/i);
if (endStepMatch && endStepMatch.index !== undefined) {
// Find the last occurrence of *END STEP
const matches = [...deckText.matchAll(/\*END\s+STEP/gi)];
const lastMatch = matches[matches.length - 1];
if (lastMatch && lastMatch.index !== undefined) {
return `${deckText.slice(0, lastMatch.index).trimEnd()}\n${snippet}\n${deckText.slice(lastMatch.index)}`;
}
}
// If no step block exists, append snippet
return `${deckText.trimEnd()}\n${snippet}\n`;
}
/**
* Structural mass, Von Mises stress, nodal displacement, and yield safety metrics computed from an FEA deck.
*/
export interface FeaSlicingProperties {
mass: number;
totalMass: number;
maxVonMisesPa: number;
maxVonMisesStress: number;
yieldStrengthPa: number;
safetyFactor: number;
isSafe: boolean;
totalVolumeM3?: number | undefined;
maxDisplacementM?: number | undefined;
nodeCount?: number | undefined;
elementCount?: number | undefined;
nodalDisplacements?: Record<number, [number, number, number]> | undefined;
elementVonMisesPa?: Record<number, number> | undefined;
}
/**
* Computes the signed 6x volume (`det6`), positive volume, and linear shape-function spatial gradients
* $(\nabla N_0, \nabla N_1, \nabla N_2, \nabla N_3)$ for a 4-node constant-strain tetrahedron (C3D4 / CTETRA).
*/
function computeTetrahedronVolumeAndGradients(
p0: { x: number; y: number; z: number },
p1: { x: number; y: number; z: number },
p2: { x: number; y: number; z: number },
p3: { x: number; y: number; z: number },
): {
det6: number;
volume: number;
grads:
| [[number, number, number], [number, number, number], [number, number, number], [number, number, number]]
| null;
} {
const j00 = p1.x - p0.x,
j01 = p1.y - p0.y,
j02 = p1.z - p0.z;
const j10 = p2.x - p0.x,
j11 = p2.y - p0.y,
j12 = p2.z - p0.z;
const j20 = p3.x - p0.x,
j21 = p3.y - p0.y,
j22 = p3.z - p0.z;
const det6 = j00 * (j11 * j22 - j12 * j21) - j01 * (j10 * j22 - j12 * j20) + j02 * (j10 * j21 - j11 * j20);
const volume = Math.abs(det6) / 6.0;
if (Math.abs(det6) < 1e-18) {
return { det6: 0, volume: 0, grads: null };
}
const invDet = 1.0 / det6;
// Columns of J^{-1} are grad(N1), grad(N2), grad(N3) for nodes 1, 2, 3
const g1x = (j11 * j22 - j12 * j21) * invDet;
const g1y = (j12 * j20 - j10 * j22) * invDet;
const g1z = (j10 * j21 - j11 * j20) * invDet;
const g2x = (j02 * j21 - j01 * j22) * invDet;
const g2y = (j00 * j22 - j02 * j20) * invDet;
const g2z = (j01 * j20 - j00 * j21) * invDet;
const g3x = (j01 * j12 - j02 * j11) * invDet;
const g3y = (j02 * j10 - j00 * j12) * invDet;
const g3z = (j00 * j11 - j01 * j10) * invDet;
const g0x = -(g1x + g2x + g3x);
const g0y = -(g1y + g2y + g3y);
const g0z = -(g1z + g2z + g3z);
return {
det6,
volume,
grads: [
[g0x, g0y, g0z],
[g1x, g1y, g1z],
[g2x, g2y, g2z],
[g3x, g3y, g3z],
],
};
}
/**
* Constructs the $6 \times 6$ 3D isotropic linear-elasticity constitutive matrix $D(E, \nu)$ in Voigt notation.
*/
function buildIsotropicConstitutiveMatrix(E: number, nu: number): Float64Array {
const safeNu = Math.min(Math.max(nu, 0.0), 0.495);
const lambda = (E * safeNu) / ((1.0 + safeNu) * (1.0 - 2.0 * safeNu));
const G = E / (2.0 * (1.0 + safeNu));
const diag = lambda + 2.0 * G;
const D = new Float64Array(36);
D[0 * 6 + 0] = diag;
D[0 * 6 + 1] = lambda;
D[0 * 6 + 2] = lambda;
D[1 * 6 + 0] = lambda;
D[1 * 6 + 1] = diag;
D[1 * 6 + 2] = lambda;
D[2 * 6 + 0] = lambda;
D[2 * 6 + 1] = lambda;
D[2 * 6 + 2] = diag;
D[3 * 6 + 3] = G;
D[4 * 6 + 4] = G;
D[5 * 6 + 5] = G;
return D;
}
/**
* Constructs the $6 \times 12$ strain-displacement matrix $B$ for a 4-node tetrahedral element from its shape-function gradients.
*/
function buildTetStrainDisplacementMatrix(
grads: [[number, number, number], [number, number, number], [number, number, number], [number, number, number]],
): Float64Array {
const B = new Float64Array(6 * 12);
for (let i = 0; i < 4; i++) {
const [bx, cy, dz] = grads[i]!;
const c0 = 3 * i;
const c1 = 3 * i + 1;
const c2 = 3 * i + 2;
// eps_xx
B[0 * 12 + c0] = bx;
// eps_yy
B[1 * 12 + c1] = cy;
// eps_zz
B[2 * 12 + c2] = dz;
// gamma_xy
B[3 * 12 + c0] = cy;
B[3 * 12 + c1] = bx;
// gamma_yz
B[4 * 12 + c1] = dz;
B[4 * 12 + c2] = cy;
// gamma_zx
B[5 * 12 + c0] = dz;
B[5 * 12 + c2] = bx;
}
return B;
}
/**
* Solves the dense $n \times n$ linear system $A x = b$ via Gaussian elimination with partial pivoting.
*/
function solveDenseLinearSystem(A: Float64Array, b: Float64Array, n: number): Float64Array {
const M = new Float64Array(A);
const x = new Float64Array(b);
for (let k = 0; k < n; k++) {
let maxRow = k;
let maxVal = Math.abs(M[k * n + k]!);
for (let i = k + 1; i < n; i++) {
const val = Math.abs(M[i * n + k]!);
if (val > maxVal) {
maxVal = val;
maxRow = i;
}
}
if (maxVal < 1e-18) {
continue;
}
if (maxRow !== k) {
for (let j = k; j < n; j++) {
const tmp = M[k * n + j]!;
M[k * n + j] = M[maxRow * n + j]!;
M[maxRow * n + j] = tmp;
}
const tmpB = x[k]!;
x[k] = x[maxRow]!;
x[maxRow] = tmpB;
}
const pivot = M[k * n + k]!;
for (let i = k + 1; i < n; i++) {
const factor = M[i * n + k]! / pivot;
if (factor === 0) continue;
for (let j = k + 1; j < n; j++) {
M[i * n + j] = M[i * n + j]! - factor * M[k * n + j]!;
}
x[i] = x[i]! - factor * x[k]!;
}
}
const sol = new Float64Array(n);
for (let i = n - 1; i >= 0; i--) {
let sum = x[i]!;
for (let j = i + 1; j < n; j++) {
sum -= M[i * n + j]! * sol[j]!;
}
const diag = M[i * n + i]!;
sol[i] = Math.abs(diag) > 1e-18 ? sum / diag : 0.0;
}
return sol;
}
/**
* Solves a sparse symmetric positive-definite linear system $K u = F$ in Compressed Sparse Row (CSR)
* format using Jacobi-Preconditioned Conjugate Gradient (PCG), with automatic fallback to dense
* Gaussian elimination for small or ill-conditioned systems.
*/
function solveSparseLinearSystem(sparseRows: Map<number, number>[], F: Float64Array, n: number): Float64Array {
const rowPtr = new Int32Array(n + 1);
let nnz = 0;
for (let i = 0; i < n; i++) {
rowPtr[i] = nnz;
nnz += sparseRows[i]!.size;
}
rowPtr[n] = nnz;
const colIdx = new Int32Array(nnz);
const values = new Float64Array(nnz);
const invDiag = new Float64Array(n);
let ptr = 0;
for (let i = 0; i < n; i++) {
let dVal = 0.0;
for (const [col, val] of sparseRows[i]!.entries()) {
colIdx[ptr] = col;
values[ptr] = val;
if (col === i) dVal = val;
ptr++;
}
invDiag[i] = Math.abs(dVal) > 1e-18 ? 1.0 / dVal : 1.0;
}
const x = new Float64Array(n);
const r = new Float64Array(F);
const z = new Float64Array(n);
const p = new Float64Array(n);
const Ap = new Float64Array(n);
let bNormSq = 0.0;
let rz = 0.0;
for (let i = 0; i < n; i++) {
const ri = r[i]!;
bNormSq += ri * ri;
const zi = invDiag[i]! * ri;
z[i] = zi;
p[i] = zi;
rz += ri * zi;
}
if (bNormSq <= 1e-30) {
return x;
}
const tolSq = 1e-20 * bNormSq;
const maxIter = Math.min(Math.max(n * 3, 500), 15000);
let converged = false;
for (let iter = 0; iter < maxIter; iter++) {
let pAp = 0.0;
for (let i = 0; i < n; i++) {
let sum = 0.0;
const start = rowPtr[i]!;
const end = rowPtr[i + 1]!;
for (let k = start; k < end; k++) {
sum += values[k]! * p[colIdx[k]!]!;
}
Ap[i] = sum;
pAp += p[i]! * sum;
}
if (pAp <= 1e-30) break;
const alpha = rz / pAp;
let rNormSq = 0.0;
for (let i = 0; i < n; i++) {
x[i] = x[i]! + alpha * p[i]!;
const ri = r[i]! - alpha * Ap[i]!;
r[i] = ri;
rNormSq += ri * ri;
}
if (rNormSq <= tolSq) {
converged = true;
break;
}
let rzNew = 0.0;
for (let i = 0; i < n; i++) {
const zi = invDiag[i]! * r[i]!;
z[i] = zi;
rzNew += r[i]! * zi;
}
if (rzNew <= 1e-30) break;
const beta = rzNew / rz;
for (let i = 0; i < n; i++) {
p[i] = z[i]! + beta * p[i]!;
}
rz = rzNew;
}
if (!converged && n <= 1500) {
const denseK = new Float64Array(n * n);
for (let i = 0; i < n; i++) {
const start = rowPtr[i]!;
const end = rowPtr[i + 1]!;
for (let k = start; k < end; k++) {
denseK[i * n + colIdx[k]!] = values[k]!;
}
}
return solveDenseLinearSystem(denseK, F, n);
}
return x;
}
/**
* Auto-detects whether `deckText` uses NASTRAN Bulk Data (`.bdf`) or Abaqus/CalculiX (`.inp`) syntax and parses it.
*/
function parseDeckModel(deckText: string): FeaModelData {
const isBdf =
!/\*(?:NODE|ELEMENT|MATERIAL|BOUNDARY|CLOAD|STEP)\b/i.test(deckText) &&
/\b(?:GRID|CTETRA|CHEXA|CPENTA|CQUAD4|CTRIA3|CBAR|CROD|MAT1|SPC1|SPC|FORCE|BEGIN\s+BULK)\b/i.test(deckText);
const dialect = isBdf ? new BdfDialect() : new InpDialect();
return dialect.parse(deckText);
}
function extractCardLines(deckText: string, cardPrefix: string): string[] {
const lines = deckText.split(/\r?\n/);
const result: string[] = [];
let inCard = false;
const pfx = "*" + cardPrefix.toUpperCase();
for (const rawLine of lines) {
const trimmed = rawLine.trim();
if (trimmed.startsWith("*")) {
if (inCard) break;
if (trimmed.toUpperCase().startsWith(pfx)) inCard = true;
} else if (inCard && trimmed.length > 0 && !trimmed.startsWith("**")) {
result.push(trimmed);
}
}
return result;
}
function extractAllCardBlocks(deckText: string, cardPrefix: string): string[][] {
const lines = deckText.split(/\r?\n/);
const blocks: string[][] = [];
let currentBlock: string[] | null = null;
const pfx = "*" + cardPrefix.toUpperCase();
for (const rawLine of lines) {
const trimmed = rawLine.trim();
if (trimmed.startsWith("*")) {
if (currentBlock) {
blocks.push(currentBlock);
currentBlock = null;
}
if (trimmed.toUpperCase().startsWith(pfx)) {
currentBlock = [];
}
} else if (currentBlock && trimmed.length > 0 && !trimmed.startsWith("**")) {
currentBlock.push(trimmed);
}
}
if (currentBlock) blocks.push(currentBlock);
return blocks;
}
/**
* Evaluates an FEA input deck by parsing nodes, elements, materials, boundary conditions,
* and loads, assembling the 3D linear elasticity stiffness matrix K * u = F, solving for
* nodal displacements, and computing element Von Mises stresses and structural mass.
*/
export function extractFeaSlicingProperties(deckText: string): FeaSlicingProperties {
const modelData = parseDeckModel(deckText);
const massMatch = deckText.match(/\bmass\s*=\s*([\d.e+-]+)\s*kg/i);
const misesMatch = deckText.match(/\bmax_von_mises\s*=\s*([\d.e+-]+)\s*MPa/i);
const yieldMatch = deckText.match(/\byield_strength\s*=\s*([\d.e+-]+)\s*MPa/i);
// Extract default material properties from parsed materials or deck cards
let defaultE = 70.0e9;
let defaultNu = 0.33;
let defaultDensity = 2700.0;
let yieldStrengthPa = 180.0e6;
for (const mat of modelData.materials.values()) {
if (mat.E !== undefined && Number.isFinite(mat.E) && mat.E > 0) {
defaultE = mat.E;
}
if (mat.nu !== undefined && Number.isFinite(mat.nu) && mat.nu > 0) {
defaultNu = mat.nu;
}
if (mat.rho !== undefined && Number.isFinite(mat.rho) && mat.rho > 0) {
defaultDensity = mat.rho;
}
if (mat.yieldStrength !== undefined && Number.isFinite(mat.yieldStrength) && mat.yieldStrength > 0) {
yieldStrengthPa = mat.yieldStrength < 1e4 ? mat.yieldStrength * 1e6 : mat.yieldStrength;
}
}
const densityLines = extractCardLines(deckText, "DENSITY");
if (densityLines.length > 0 && modelData.materials.size <= 1) {
const parsedRho = parseFloat(densityLines[0]!);
if (Number.isFinite(parsedRho) && parsedRho > 0) defaultDensity = parsedRho;
}
const plasticLines = extractCardLines(deckText, "PLASTIC");
if (plasticLines.length > 0) {
const parsedYield = parseFloat(plasticLines[0]!);
if (Number.isFinite(parsedYield) && parsedYield > 0) {
yieldStrengthPa = parsedYield < 1e4 ? parsedYield * 1e6 : parsedYield;
}
}
if (yieldMatch && yieldMatch[1]) {
yieldStrengthPa = parseFloat(yieldMatch[1]) * 1e6;
}
// Extract optional shell thickness or beam cross-sectional area
const shellLines = extractCardLines(deckText, "SHELL SECTION");
const defaultThickness = shellLines.length > 0 ? parseFloat(shellLines[0]!) || 0.005 : 0.005;
const defaultCrossArea = defaultThickness * defaultThickness;
// Map nodes to indices 0 .. N-1
const nodeIds = Array.from(modelData.nodes.keys()).sort((a, b) => a - b);
const nodeIndex = new Map<number, number>();
nodeIds.forEach((id, idx) => nodeIndex.set(id, idx));
const numNodes = nodeIds.length;
const numDofs = numNodes * 3;
const numElements = modelData.elements.size;
const sparseRows: Map<number, number>[] | null =
numDofs > 0 ? Array.from({ length: numDofs }, () => new Map<number, number>()) : null;
const F = numDofs > 0 ? new Float64Array(numDofs) : null;
const addK = (r: number, c: number, val: number) => {
if (!sparseRows || val === 0.0) return;
const row = sparseRows[r]!;
row.set(c, (row.get(c) ?? 0.0) + val);
};
interface SubTet {
elemId: number;
nodeIndices: [number, number, number, number];
volume: number;
B: Float64Array;
D: Float64Array;
weight: number;
}
interface SubTri {
elemId: number;
nodeIndices: [number, number, number];
area: number;
thickness: number;
Bm: Float64Array;
Dps: Float64Array;
e3: [number, number, number];
gradX: [number, number, number];
gradY: [number, number, number];
G: number;
weight: number;
}
interface BarEdge {
elemId: number;
idxA: number;
idxB: number;
length: number;
dir: [number, number, number];
area: number;
E: number;
}
const subTets: SubTet[] = [];
const subTris: SubTri[] = [];
const barEdges: BarEdge[] = [];
let totalVolumeM3 = 0.0;
let totalMassKg = 0.0;
const resolveElementMaterial = (elset?: string): { E: number; nu: number; rho: number } => {
if (elset && modelData.elsetMaterials) {
const matName = modelData.elsetMaterials.get(elset.toUpperCase());
if (matName) {
const mat = modelData.materials.get(matName);
if (mat) {
return {
E: mat.E !== undefined && mat.E > 0 ? mat.E : defaultE,
nu: mat.nu !== undefined && mat.nu > 0 ? mat.nu : defaultNu,
rho: mat.rho !== undefined && mat.rho > 0 ? mat.rho : defaultDensity,
};
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