Developing of Chebyshev Collocation Spectral Method for Analysis of Multiple Structural Mechanics

In this work, the spectral collocation method based on Chebyshev polynomials is developed and utilized for analysis of static, free vibration, and dynamic behavior of one and two-dimensional solid structures. The main objective of the work is to introduce the spectral collocation method with Chebyshev polynomials as a powerful numerical method for solid mechanic analysis. To show the advantage and effortlessness of this method, one and two-dimensional solid structures as case studies were considered and the spectral collocation method was directly applied to the analysis and the governing equation was solved. Moreover, the homogeneous material properties and functionally graded material properties were analyzed to show the capability of the introduced method for solving the more complicated equations of motion. The results obtained for each case were compared with analytical and numerical results presented in the literature and some results were also compared with ANSYS. The results showed that the presented method has very good accuracy and efficiency to solve structural-mechanical properties.