(untitled) (Advances in Applied Mathematics and Mechanics, 2021)
This paper presents a new concept called Unified and Integrated Method for a shear deformable beam element. In this method, Timoshenko beam theory is unified and integrated in such a way that takes into account the effect of transverse shear and maintains the shear locking free condition at the same time to generate proper behavior in the analysis of thin to thick beams. The unified and integrated method is applied to finite element analysis (FEA) and isogeometric analysis (IGA) on two-node beam element. This method will be used to analyze uniformly loaded beams with various boundary conditions. A shear influence factor of φ, which is a function of beam thickness ratio (L/h), is expressed explicitly as control of the transverse shear strain effect. The analysis gives interesting results showing that applying the unified and integrated method in FEA and IGA will yield exact values of DOF's and displacement function even when using only a single element. Numerical examples demonstrate the validity and efficiency of the unified and integrated methods.