Extraction of effective elastic constants of perforated plates with triangular hole pattern using modal analysis

Abstract

To extract the effective modulus of elasticity and effective Poisson's ratio, the natural frequencies of fully perforated circular plates with a triangular hole pattern are analyzed using FEA software. Finite element analysis models with clamped and simply supported boundary conditions are examined to separate the effective material constants from the flexural rigidity, treating the perforated circular plate as a homogeneous structure with these effective material properties. The results show that the effective modulus of elasticity decreases, as the hole size increases. Meanwhile, the behavior of the effective Poisson's ratio turns out to be more complex: it initially decreases to a negative value and then rises to approximately zero with further increases in hole size. A theoretical method for calculating the natural frequencies of a centrally perforated circular plate is also proposed using the Rayleigh-Ritz method and incorporating the effective material properties. The calculated natural frequencies are validated using FEA results, confirming the accuracy of the effective elastic constants and the proposed theory. The derived effective elastic constants, as a function of ligament efficiency, can be applied to the dynamic analysis of perforated plates in reactor internals, enhancing finite element modeling efficiency and achieving effective seismic analyses.