Finite Element Analysis of Curved Beam Elements Employing Trigonometric Displacement Distribution Patterns

A finite element analysis (FEA) model was developed for Euler and Timoshenko curved beam elements by incorporating trigonometric displacement distribution patterns. Local polar coordinate stiffness matrices were derived based on force-displacement relations static equilibrium conditions. By employing the kinetic energy theorem triangular functions, an expression consistent mass matrix of a obtained. transformation established relating local system to global system. Calculation programs implemented in Fortran language evaluate static–dynamic performance natural frequency characteristics bridges. The obtained results then compared with those using ANSYS solid models “replace curve straight” models. comparison demonstrated strong agreement between However, discrepancies observed when comparing model, particularly terms lateral displacement. This discrepancy suggests that characteristic this study accurately represents beam, making it suitable mechanical It should be noted method overlooks initial curvature bending–torsion coupling effects resulting calculation deviations. On other hand, use numerical provides simple practical approach, which facilitates further research areas such as vehicle–bridge vibrations seismic