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Exact solution of 3D Timoshenko beam problem: Problem-dependent formulation

Problem-dependent interpolation functions for displacements and rotations are obtained from the exact analytical solution of the 3D Timoshenko beam problem by introducing a full set of boundary conditions. The stiffness matrix obtained using these interpolation functions matches the one obtained using engineering beam theory leading to the same end-node results. In addition, the proposed interpolation enables exact strain recovery at any point within the problem domain.

linear analysis; 3D Timoshenko beam; problem-dependent formulation; boundary conditions

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