Online FEA Solver

// CST plane-stress triangle
function cstStiffness(x1,y1,x2,y2,x3,y3, E, nu, t){
  const A = 0.5*Math.abs((x2-x1)*(y3-y1) - (x3-x1)*(y2-y1)) + 1e-12;
  const b1=y2-y3, b2=y3-y1, b3=y1-y2;
  const c1=x3-x2, c2=x1-x3, c3=x2-x1;
  const inv2A = 1/(2*A);
  const B = [
    [b1*inv2A, 0,        b2*inv2A, 0,        b3*inv2A, 0       ],
    [0,        c1*inv2A, 0,        c2*inv2A, 0,        c3*inv2A],
    [c1*inv2A, b1*inv2A, c2*inv2A, b2*inv2A, c3*inv2A, b3*inv2A]
  ];
  const eFac = E/(1-nu*nu);
  const D = [ [eFac, eFac*nu, 0],
              [eFac*nu, eFac, 0],
              [0,0, eFac*(1-nu)/2] ];
  const Bt = transpose(B); // 6x3
  const DB = mul(D,B);     // 3x6
  const Ke = mulScalar( mul(Bt, DB), t*A ); // 6x6
  return {Ke, B, D, A};
}
// Bar element K_e = EA/L * [c^2 cs -c^2 -cs; ...]
function barStiffness(x1,y1,x2,y2, E, Asec){
  const dx=x2-x1, dy=y2-y1; const L=Math.hypot(dx,dy)||1e-9;
  const cx=dx/L, cy=dy/L; const k=E*Asec/L;
  const Ke=[
    [ k*cx*cx,  k*cx*cy, -k*cx*cx, -k*cx*cy],
    [ k*cx*cy,  k*cy*cy, -k*cx*cy, -k*cy*cy],
    [-k*cx*cx, -k*cx*cy,  k*cx*cx,  k*cx*cy],
    [-k*cx*cy, -k*cy*cy,  k*cx*cy,  k*cy*cy]
  ];
  return {Ke, L, cx, cy};
}
// Gaussian elimination with partial pivoting
function solveLinear(K, F){
  const n=F.length; const A=K.map(r=>r.slice()); const b=F.slice();
  for(let i=0;i<n;i++){
    let maxRow=i, maxV=Math.abs(A[i][i]);
    for(let r=i+1;r<n;r++) if(Math.abs(A[r][i])>maxV){maxV=Math.abs(A[r][i]); maxRow=r;}
    if(maxV<1e-12) continue;
    if(maxRow!==i){ [A[i],A[maxRow]]=[A[maxRow],A[i]]; [b[i],b[maxRow]]=[b[maxRow],b[i]]; }
    const piv=A[i][i];
    for(let r=i+1;r<n;r++){
      const f=A[r][i]/piv; if(Math.abs(f)<1e-14) continue;
      for(let c=i;c<n;c++) A[r][c]-=f*A[i][c];
      b[r]-=f*b[i];
    }
  }
  const x=new Array(n).fill(0);
  for(let i=n-1;i>=0;i--){
    let s=b[i];
    for(let j=i+1;j<n;j++) s-=A[i][j]*x[j];
    x[i]=Math.abs(A[i][i])<1e-12?0:s/A[i][i];
  }
  return x;
}
// Von Mises plane stress
function vonMises(sx, sy, txy){ return Math.sqrt(sx*sx - sx*sy + sy*sy + 3*txy*txy); }