Differential Quadrature Finite Element Method (DQFEM) for Second-Order Analysis of Non-Prismatic Frame Structures

Most engineering activities place significant reliance on structure weight. Engineers consistently endeavor to utilize material economically. Less structure weight directly correlates with a lower implementation price. The utilization of non-prismatic elements is one procedure for reducing building weight, particularly prominent in industrial structures. Buckling and the behavior of beam-columns under axial loads represent major factors in these structures. Consequently, accurately estimating the post-buckling behavior in beam-columns and understanding the impact of axial load are crucial. Given that the number of factors and graphs is typically extensive for columns with constant cross-sections, and they fail to cover structures with variable cross-sections, a simplified method for calculating moments and displacements must be applied. The method employed in this thesis is the Differential Quadrature Finite Element Method (DQFEM). DQFEM is a numerical technique to solve the problem where analytical solutions are difficult for beam-columns with variable cross-sections. This paper develops DQFEM for the second-order analysis of frames incorporating non-prismatic beam-columns. DQFEM represents a combination of the Differential Quadrature Method (DQM) and the Finite Element Method (FEM). Algebraic operations compute DQFE materials greatly simplifying the construction of higher-order finite elements. Comparing the obtained results with literature available demonstrates the high accuracy of the present method, achieved using a small number of finite elements and DQM sample points. The method's efficiency and practical application are worked out via numerical examples of significant practical interest.