engleski

A shear locking-free beam finite element based on the modified Timoshenko beam theory

An outline of the Timoshenko beam theory is presented. Two differential equations of motion in terms of deflection and cross-section rotation are comprised in one equation and analytical expressions for displacements and sectional forces are given. Two different displacement fields are recognized, i.e. flexural and axial shear, and a modified beam theory with extension is worked out. Flexural and axial shear locking-free beam finite elements are developed. Reliability of the finite elements is demonstrated with numerical examples for a simply supported, clamped and free beam by comparing the obtained results with analytical solutions.

Timoshenko beam theory; modified beam theory; flexural vibrations; axial shear vibrations; beam finite element; shear locking

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