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Bending stiffness for curved shells in flex.

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PiperOrigin-RevId: 796361841
Change-Id: I105ea235fe2a8e1bcbde67276d77fa92eed214a1
This commit is contained in:
Alessio Quaglino
2025-08-18 04:12:34 -07:00
committed by Copybara-Service
parent 972ffd7b90
commit b66175eba6
18 changed files with 488 additions and 250 deletions
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src/user/user_mesh.cc
+30 -12
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@@ -3716,7 +3716,7 @@ static void CreateFlapStencil(std::vector<StencilFlap>& flaps,
}
// cotangent between two edges
double inline cot(double* x, int v0, int v1, int v2) {
double inline cot(const double* x, int v0, int v1, int v2) {
double normal[3];
double edge1[3] = {x[3*v1]-x[3*v0], x[3*v1+1]-x[3*v0+1], x[3*v1+2]-x[3*v0+2]};
double edge2[3] = {x[3*v2]-x[3*v0], x[3*v2+1]-x[3*v0+1], x[3*v2+2]-x[3*v0+2]};
@@ -3749,20 +3749,38 @@ void inline ComputeBending(double* bending, double* pos, const int v[4], double
// cotangent operator from Wardetzky at al., "Discrete Quadratic Curvature
// Energies", https://cims.nyu.edu/gcl/papers/wardetzky2007dqb.pdf
mjtNum a01 = cot(pos, v[0], v[1], v[2]);
mjtNum a02 = cot(pos, v[0], v[3], v[1]);
mjtNum a03 = cot(pos, v[1], v[2], v[0]);
mjtNum a04 = cot(pos, v[1], v[0], v[3]);
mjtNum c[4] = {a03 + a04, a01 + a02, -(a01 + a03), -(a02 + a04)};
mjtNum volume = ComputeVolume(pos, v) +
ComputeVolume(pos, vadj);
double a01 = cot(pos, v[0], v[1], v[2]);
double a02 = cot(pos, v[0], v[3], v[1]);
double a03 = cot(pos, v[1], v[2], v[0]);
double a04 = cot(pos, v[1], v[0], v[3]);
double c[4] = {a03 + a04, a01 + a02, -(a01 + a03), -(a02 + a04)};
double volume = ComputeVolume(pos, v) + ComputeVolume(pos, vadj);
double stiffness = 3 * mu * pow(thickness, 3) / (24 * volume);
// Garg et al., "Cubic Shells", https://cims.nyu.edu/gcl/papers/garg2007cs.pdf
const double* v0 = pos + 3*v[0];
const double* v1 = pos + 3*v[1];
const double* v2 = pos + 3*v[2];
const double* v3 = pos + 3*v[3];
double e0[3] = {v1[0] - v0[0], v1[1] - v0[1], v1[2] - v0[2]};
double e1[3] = {v2[0] - v0[0], v2[1] - v0[1], v2[2] - v0[2]};
double e2[3] = {v3[0] - v0[0], v3[1] - v0[1], v3[2] - v0[2]};
double e3[3] = {v2[0] - v1[0], v2[1] - v1[1], v2[2] - v1[2]};
double e4[3] = {v3[0] - v1[0], v3[1] - v1[1], v3[2] - v1[2]};
double t0[3] = {-(a03*e1[0] + a01*e3[0]), -(a03*e1[1] + a01*e3[1]), -(a03*e1[2] + a01*e3[2])};
double t1[3] = {-(a04*e2[0] + a02*e4[0]), -(a04*e2[1] + a02*e4[1]), -(a04*e2[2] + a02*e4[2])};
double sqr = mjuu_dot3(e0, e0);
double cos_theta = -mjuu_dot3(t0, t1) / sqr;
for (int v1 = 0; v1 < T::kNumVerts; v1++) {
for (int v2 = 0; v2 < T::kNumVerts; v2++) {
bending[4 * v1 + v2] +=
1.5 * c[v1] * c[v2] / volume * mu * pow(thickness, 3) / 12;
bending[4 * v1 + v2] += c[v1] * c[v2] * cos_theta * stiffness;
}
}
double n[3];
mjuu_crossvec(n, e0, e1);
bending[16] = mjuu_dot3(n, e2) * (a01 - a03) * (a04 - a02) * stiffness / (sqr * sqrt(sqr));
}
//----------------------------- linear elasticity --------------------------------------------------
@@ -4305,10 +4323,10 @@ void mjCFlex::Compile(const mjVFS* vfs) {
if (thickness < 0) {
throw mjCError(this, "thickness must be positive for bending stiffness");
}
bending.assign(nedge*16, 0);
bending.assign(nedge*17, 0);
for (unsigned int e = 0; e < nedge; e++) {
ComputeBending<StencilFlap>(bending.data() + 16 * e, vertxpos.data(), flaps[e].vertices,
ComputeBending<StencilFlap>(bending.data() + 17 * e, vertxpos.data(), flaps[e].vertices,
young / (2 * (1 + poisson)), thickness);
}
}