On the Convergence of Laminated Composite Plates of Arbitrary Shape through Finite Element Models

Abstract

Abstract:The present work considers a computational study on laminated composite plates by using a linear theory for moderately thick structures. The present problem is solved numerically because analytical solutions cannot be found for such plates when lamination schemes are general and when all the stiffness constants are activated at the constitutive level. Strong and weak formulations are used to solve the present problem and several comparisons are given. The strong form is dealt with using the so-called Strong Formulation Finite Element Method (SFEM) and the weak form is solved using commercial Finite Element (FE) packages. Both techniques are based on the domain decomposition technique according to geometric discontinuities. The SFEM solves the strong form inside each element and needs the implementation of kinematic and static inter-element conditions, whereas the FE solves the weak form and the continuity conditions among the elements are given in terms of displacements only. The results are reported in graphical form in terms of the first three natural frequencies. The accuracy and stability of SFEM and FE are thoroughly discussed.

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

“…Moreover, Vidal et al [364] employed the variable separation method (VSM) to investigate the FV of LCPs, and the FEM has been used for the in-plane description. Furthermore, Fantuzzi et al [365] performed a simulation analysis on LCPs with various geometries by utilizing the linear approach of moderately thick plates, and the strong form of FEM as well as WFm was used for solving the problem. The results obtained of the first two NFs of circular LCPs with symmetric lamination by utilizing different types of elements revealed that fewer adequate elements were found through Quad 4 element from Straus7.…”

Scale Effects in Orthotropic Composite Assemblies as Micropolar Continua: A Comparison between Weak- and Strong-Form Finite Element Solutions

“…In the present paper, the irregularity is due to a concentrated load which is applied on a linear edge; therefore, Lagrangian mapping with four nodes is sufficient to have an exact geometrical approximation. It was observed that the most common source of errors in the geometrical mapping is due to the presence of curvilinear boundaries [ 53 , 54 ]. In most of the published references, the GDQ method is presented in one-dimensional (1D) form because the numerical structure does not change much when the problem is 2D.…”

“…Finally, for the sake of comparison and to select the most appropriate numerical approach for the solution of the micropolar elastic problem, discussed in detail in Reference [ 48 ] with reference to a heterogeneous elastic panel in tension, two different numerical approaches based on weak and strong formulations are adopted herein. The results provided by the finite element method (FEM) are carried out using an in-house finite element formulation in terms of mixed bi-quadratic displacement and bi-linear micro-rotations implemented in COMSOL Multiphysics®, and the so-called strong-formulation finite element method (SFEM) [ 49 , 50 , 51 , 52 , 53 , 54 ]. The results are presented in terms of contour plots for both displacements and stresses.…”

A meshfree moving least squares-Tchebychev shape function approach for free vibration analysis of laminated composite arbitrary quadrilateral plates with hole

“…In these studies, the researchers easily modeled the boundary conditions by using these displacement functions. In addition, the differential quadrature method [29][30][31][32][33][34][35][36][37], strong form finite elements based differential quadrature method [38][39][40], Non-Uniform Rational B-Splines (NURBS) method [41][42][43][44][45], pb-2 Ritz method [46], variable kinematic Ritz method combining Carrera unified expression with pb-2 Ritz method [47], finite element method [48] were also used to analyze the vibration characteristic of arbitrary plate. Also, the studies were conducted to analyze the vibration of thick plate by using the three-dimensional theory of elasticity [49].…”