3-node basic displacement functions in analysis of non-prismatic beams

Purpose– analysis of nonprismatic beams has been focused of attention due to wide use in complex structures such as aircraft, turbine blades and space vehicles. apart from aesthetic aspect, optimization of strength and weight is achieved in use of this type of structures. the purpose of this paper is to present new shape functions, namely 3node basic displacement functions (bdfs) for derivation of structural matrices for general nonprismatic eulerbernoulli beam elements. design/methodology/approach– static analysis and free transverse vibration of nonprismatic beams are extracted studied from a mechanical point of view. following structural/mechanical principles, new static shape functions are in terms of bdfs, which are obtained using unitdummyload method. all types of crosssections and crosssectional dimensions of the beam element could be considered in this method. findings– according to the outcome of static analysis, it is verified that exact results are obtained by applying one or a few elements. furthermore, it is observed that results from both static and free transverse vibration analysis are in good agreement with the previous published once in the literature. research limitations/implications– the method can be extended to structural analysis of curved and timoshenko beams as well as plates and shells. furthermore, exact dynamic shape functions can be derived using bdfs by solving the governing equation for transverse vibration of beams. originality/value– the present investigation introduces new shape functions, namely 3node basic displacement functions (bdfs) extended from 2node functions, and then compares its performance with previous element.