FINITE ELEMENT ANALYSIS OF SPATIAL CIRCULAR CURVED BEAM ELEMENTS BASED ON POLYNOMIAL DISPLACEMENT DISTRIBUTION PATTERNS

To meet the needs of finite element analysis for curved beam bridges, displacement shape functions for curved beam elements are constructed using polynomial displacement distribution patterns based on the finite element analysis theory. The stiffness matrix and consistent mass matrix expressions for the curved beam element in the local coordinate system are derived using the principle of virtual work. A coordinate transformation matrix between the local and global coordinate systems is established based on the spatial coordinates of the curved beam element. A corresponding finite element calculation program is developed using Fortran language to analyze and compare the static and dynamic performances and resonance characteristics of three models for validation. The results show that the curved beam element model matches well with the solid model's calculation results, confirming the accuracy of the curved beam element stiffness matrix and mass matrix. This study provides theoretical reference for the mechanical performance analysis of future curved beam bridges, and can provide strong support for the design and evaluation of engineering practice.