AN EFFICIENT CURVED BEAM FINITE ELEMENT

The plane two-node curved beam Þnite element with six degrees of freedom is considered. Knowing the set of 18 exact shape functions their approximation is derived using the expansion of the trigonometric functions in the power series. Unlike the ones commonly used in the FEM analysis the functions suggested by the authors have the coe¦cients dependent on the geometrical and physical properties of the element. From the strain energy formula the sti¤ness matrix of the element is determined. It is very simple and can be split into components responsible for bending, shear and axial forces inßuences on the displacements. The proposed element is totally free of the shear and membrane locking e¤ects. It can be referred to the shear-ßexible (parameter d) and compressible (parameter e) systems. Neglecting d or e yields the Þnite elements in all necessary combinations, i.e. curved EulerÐBernoulli beam or curved Timoshenko beam with or without the membrane e¤ect. Applying the elaborated element in the calculations a very good convergence to the analytical results can be obtained even with a very coarse mesh without the commonly adopted corrections as reduced or selective integration or introduction of the stabilization matrices, additional constraints, etc., for the small depthÐlength ratio