12 × 12 element matrices

DOF order: [u_Ax, u_Ay, u_Az, θ_Ax, θ_Ay, θ_Az, u_Bx, u_By, u_Bz, θ_Bx, θ_By, θ_Bz]

Compute the 12 × 12 stiffness and consistent mass matrices of open three-dimensional Timoshenko beams with analytic or point-defined centerlines. Point data can be reconstructed using Chebyshev or cubic-spline interpolation and inspected in 3D; stiffness validation uses the analytical straight-beam solution or a refined straight-element model statically condensed to the two beam endpoints.

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Compute K and M.

Compute K and M.

Compute K and M.

Validation compares K against an independent reference.

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