A constitutive model based on energy density for power-law variable thickness plates and its application

Variable thickness plates are relatively common structure in large-scale transportation equipment such as aerospace and ships. Due to their high running speed and large structural dimensions, such structures are usually induced high-frequency severe vibrations, which likely lead to structural damage. Therefore, it is crucial to accurately predict the high-frequency dynamic response characteristics during the structural design phase. The energy finite element method (EFEM) is a powerful tool for predicting high-frequency dynamic response. But, in recent EFEM for variable thickness plates, an approximate method (AEFEM) using a large number of constant thickness plate elements to approximate variable thickness plates is used. Due to that AEFEM is based on the constitutive equation for constant thickness plate, it will be imprecise and time-consuming. Aiming at power-law variable thickness plates, the constitutive equation based on energy density is derived and the finite element discrete scheme of the constitutive equation was studied. In this way, the precise new EFEM (NEFEM) for variable thickness plates was established. In addition, the dynamic response of a variable thickness plate was predicted by NEFEM presented and finite element method (FEM) respectively. The results are consistent. It is shown that the constitutive model presented is reliable and time-saving. Comparison of the results from AEFEM, the NEFEM can get more accurate results with fewer elements. The NEFEM based on the constitutive model presented can be used to predict precisely the high-frequency dynamic response for power-law variable thickness plates.