Using Plate Finite Elements for Modeling Fillets in Design, Optimization, and Dynamic Analysis

Fillets are one of the most common design features in structures. Proper finite element modeling of these fillets can frequently be problematic though. If the ratio of the fillet radius to the wall thickness is relatively large, the fillet cannot be ignored because it contributes significantly to structural stiffness, and although the most appropriate element for modeling the structure in general may be the plate element, geometric representation of the fillets requires the use of solid elements. This problem is the motivation for the development of a method that uses “bridge” plate elements connecting the tangent points of the fillet to accurately represent its stiffness and mass. The methodology equates the rotational deflection at the tangent point, derived from the proposed bridge system, with an analytical solution of the fillet itself to generate a pseudo Young’s Modulus and thickness for use in the bridge plates. The method was tested on a typical filleted structure, with the bridge method yielding modal analysis results as accurate as a high-fidelity solid model when compared to modal test but with a 90-percent reduction in number of degrees of freedom. This capability could prove extremely useful in design, dynamic, deflection, and preliminary stress analysis, and optimization.