Development of a MATLAB code for 2D finite element free vibration analysis of structures including the effect of 'pendulum-like' oscillations due to gravity

• Main Author: Goh, Ignatius Qian Zheng
• Other Authors: Sellakkutti Rajendran
• Format: Final Year Project
• Language: English
• Published: Nanyang Technological University 2024
• Subjects: Engineering
• Online Access: https://hdl.handle.net/10356/176618
• Institution: Nanyang Technological University

Finite Element Method (FEM) is a powerful numerical tool widely used in mechanical, civil, and aerospace engineering. Typical applications include stress analysis, vibration analysis, buckling analysis, seepage analysis, etc. There are many commercial finite element packages available for finite analysis of the given problem. These are useful for solving common engineering problems. However, it is useful to develop in-house finite element packages for solving research problems in academics. The development of finite element code in MATLAB involves writing functions to calculate the stiffness and mass matrices, assembling them to get the global stiffness and mass matrices, and finally, solving them to get the results. (viz., nodal displacements, natural frequencies, mode shapes etc.) The mesh for all problems considered in this project is generated in ANSYS Mechanical APDL, from which, the NLIST, ELIST, DLIST, and FLIST of the generated model are extracted by the MATLAB code for computation of the stiffness and mass matrices. The development of the finite element code is done in three stages. Firstly, it is developed to carry out static analysis, followed by free vibration analysis. Finally, the code is modified to generate the gravitational stiffness matrix which is used for the computation of the natural frequency of “pendulum-like” oscillation of the structure. At each stage, the code developed is validated using simple test problems that have analytical solutions so as to ensure that the code works well. The code has been applied to several validation problems and the nodal displacements and natural frequencies have been computed using the code developed and also using ANSYS for comparison purposes. The results tally closely.