A FEM Free Vibration Analysis of Variable Stiffness Composite Plates through Hierarchical Modeling

Abstract

Variable Angle Tow (VAT) laminates offer a promising alternative to classical straight-fiber composites in terms of design and performance. However, analyzing these structures can be more complex due to the introduction of new design variables. Carrera’s unified formulation (CUF) has been successful in previous works for buckling, vibrational, and stress analysis of VAT plates. Typically, one-dimensional (1D) and two-dimensional (2D) CUF models are used, with a linear law describing the fiber orientation variation in the main plane of the structure. The objective of this article is to expand the CUF 2D plate finite elements family to perform free vibration analysis of composite laminated plate structures with curvilinear fibers. The primary contribution is the application of Reissner’s mixed variational theorem (RMVT) to a CUF finite element model. The principle of virtual displacements (PVD) and RMVT are both used as variational statements for the study of monolayer and multilayer VAT plate dynamic behavior. The proposed approach is compared to Abaqus three-dimensional (3D) reference solutions, classical theories and literature results to investigate the effectiveness of the developed models. The results demonstrate that mixed theories provide the best approximation of the reference solution in all cases.

Computational Linear and Nonlinear Free Vibration Analyses of Micro/Nanoscale Composite Plate-Type Structures With/Without Considering Size Dependency Effect: A Comprehensive Review

“…However, the spline finite point method (SFPM) has been employed by Zhou and Li [289] to analyze the FV of various plates with a sandwich structure made of core and laminated faces. Giunta et al [290] employed FEM to investigate the FV of CPs with a variable stiffness by using the Hierarchical modeling where the CUF has been expanded and utilized. Besides, the outcomes show that applying the Reissner mixed variational theorem (RMVT) through the CUF guaranty a remarkable potential in enhancing the accuracy as well as the efficiency of modeling the VAT plates in the FV analyses.…”

Special Issue: “Computational Mechanics of Structures and Materials”

“…They expanded Carrera’s unified formulation (CUF) plate finite elements to composite laminates reinforced by curvilinear fibers. The effectiveness of the solution was proven through a comparison with results available in the literature or obtained through other commercial codes [ 19 ].…”