A Timoshenko Beam Element for Large Displacement Analysis of Planar Beams and Frames

A Timoshenko beam element for large displacement analysis of planar beam and frame structures is formulated in the context of the co-rotational method. The shallow arch expression is adopted for the local strain, and cubic and quadratic polynomials obtained from the field consistence approach are respectively employed to interpolate the transversal displacement and rotation. The numerical examples show that the proposed element is capable of furnishing accurate results with a smaller number of elements as compared to the elements previously used in the examples. It has also shown that the nonlinear term in the expression of the local strain plays an important role in the accuracy of the element in the large displacement analysis of beam and frame structures.