engleski

Linked Interpolation of Arbitrary Order in Static Linear Analysis of 3D Thick Beam Elements

Linked interpolation functions for straight 3D Timoshenko beam elements, which provide exact solution for a general static loading, are derived in this work by solving the differential equation for the problem and expressing the solution in terms of the nodal values for the positions and rotations. If only the boundaries of the beam element are taken as the nodal points, the resulting interpolation becomes dependent on the geometric, material and loading parameters of the problem. On the other hand, for arbitrary polynomial loading and a sufficient number of nodal points N, the exact solution may also be provided by independent interpolation for the rotation field and the position field with the Lagrangian polynomials of order N-1 and N, respectively.

linked interpolation; thick beams; problem-dependent and problem-independent interpolation

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