Finite element analysis of quasi‐prismatic bodies using Chebyshev polynomials

A new kind of finite element is presented in this paper which is designed to work efficiently for bodies that are either prismatic or ‘quasi‐prismatic’ in shape. Quasi‐prismatic shapes are those which can be obtained from prismatic shapes by mere distortion. The element which is formulated in this paper may be coupled with other types of three‐dimensional elements to allow the modelling of structures which are only partially prismatic or which have prismatic shapes within them. The element allows for a variety of boundary conditions, yet yields meshes which are easy to generate. The performance of this element is evaluated by numerical experiments that compare its results with analytical solutions for a thick cylinder problem and a curved beam problem. The element has also been demonstrated on a turbine blade model.