Application of a 2-D approximation technique for solving stress analyses problem in FEM

Abstract

With the advent of computational techniques and methods like finite element method, complex engineering problems are no longer difficult to solve. These methods have helped engineers and designers to simulate and solve engineering problems in much more details than possible with experimental techniques. However, applying these techniques is not a simple task and require lots of acumen, understanding, and experience in obtaining a solution that is as close to an exact solution as possible with minimum computer resources. In this work using the finite element (FE) method, stress analyzes of the low-pressure turbine of a small turbofan engine is carried out by employing two different techniques. Initially, a complete solid model of the turbine is prepared which is then finite element modelled with the eight-node brick element. Stresses are calculated using this model. Subsequently, the same turbine is modelled with four-node shell element for calculation of stresses. Material properties, applied loads (inertial, aerodynamic, and thermal), and constraints were same for both the cases. Authors have developed a “2-D approximation technique” to approximate a 3-D problem into a 2-D problem to study the saving invaluable computational time and resources. In this statistics technique, the 3-D domain of variable thickness is divided into many small areas of constant thickness. It is ensured that the value of the thickness for each sub-area is the correct representative thickness of that sub area, and it is within three sigma limit. The results revealed that technique developed is accurate, less time consuming and computational effort saving; the stresses obtained by 2-D technique are within five percent of 3-D results. The solution is obtained in CPU time which is six times less than the 3-D model. Similarly, the number of nodes and elements are more than ten times less than that of the 3-D model. ANSYS ® was used in this work.