An innovative co-rotational pointwise equilibrating polynomial element based on Timoshenko beam theory for second-order analysis

摘要

The pointwise equilibrating polynomial (PEP) beam-column element has been widely used in engineering applications since 1994 as it can accurately and efficiently account for second-order P-delta effect. However, the PEP element was derived from Euler-Bernoulli beam theory and therefore the transverse shear deformation cannot be considered. In this paper, the original PEP element is rederived based on Timoshenko beam theory. The shape function for lateral displacement field adopts a fifth-order polynomial and therefore the shear strain field along the element length could be theoretically assumed as a consistent, first or second-order polynomial. This paper comprehensively studies the influence of shear strain field in different forms. It is found that the new PEP element with quadric order shear strain field can provide the most accurate results for practical use. To enhance numerical efficiency, an innovative co-rotational algorithm for three-dimensional spatial frames allowing for large load step is also proposed for second-order analysis. Several examples demonstrate the high accuracy and efficiency of the proposed element allowing for shear deformation.