Development of a MATLAB/ANSYS code for a large 3D finite element model to an equivalent beam element model for static and free vibration analysis

Abstract

In many real-life engineering problems, the analysis of large structures can be tedious and complicated. This project explores a new finite element model reduction method to covert large 3D finite element models into equivalent beam element models. The proposed method utilises the concept of “shape vectors” to condense a large 3D model into a beam element model. The shape vectors are computed using ANSYS Mechanical APDL. The shape vectors, the stiffness matrix [K] and mass matrix [M] are written into the disk. This forms the input to the MATLAB code. The code first assembles all the shape vectors to obtain the “shape vector matrix” [N]. The stiffness and mass matrices are multiplied appropriately with the shape vector matrix to obtain the reduced stiffness matrix ([N]^T [K][N]) and mass matrix ([N]^T [M][N]), which are then used for the calculation of natural frequencies and mode shapes of typical validation problems. The proposed method is applied to convert a 3D solid element model of rods of square as well as circular cross-section rods. The natural frequencies of the beam element model obtained in MATLAB are compare with the natural frequencies of the original 3D solid element model given by ANSYS. For long rods, the agreement is good. For short rods, there is considerable difference in the frequencies. This is attributed to the fact that the “shape vector” approach used in this FYP does not accurately represent the shear stress distribution across the cross-section of the rod.