What is it about?

The approximate solution of the boundary value problem by finite element method (FEM) is the basis of many engineering designs. Many researchers are constantly working to improve the accuracy of FEM. An example is an increasing trend of using NURBS and T-spline basis functions in FEM. On the other hand, researchers are trying to reduce the computation cost through dimensionally reduced modelling. Each effort requires some basic changes in the standard FEM framework. The authors here present a novel method of geometric approximation to improve the accuracy and directional enrichment to reduce the computational cost without any compromise in accuracy and effort.

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Why is it important?

The proposed method lies entirely in the standard FEM framework. It uses the same basis functions in the geometric as well as solution approximations without any extra effort and computational cost in contrast to other such methods. The directional enrichment eliminates any specific modelling strategy and extra effort, and numerical examples show better results than the dimensionally reduced models. It also eliminates CAD modelling and a meshing strategy for analysing extruded slender members.


Complex curved, twisted blades such as turbine blades and rotor blades are extremely difficult to analyse due to their complex shapes, high carrying loads, and sometimes hostile environment. The proposed method accurately approximates the geometry of these stiffened slender structures (or any arbitrarily shaped slender structures). Actual three-dimensional stresses in a coupled bending-twisting problem are computed using higher-order directionally enriched elements. We are confident that this research will benefit the entire finite element community.

Aalok Jha
Indian Institute of Technology Kanpur

Read the Original

This page is a summary of: Geometrically conforming and directionally enriched FEM for three dimensional slender members, International Journal for Numerical Methods in Engineering, May 2022, Wiley, DOI: 10.1002/nme.7003.
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