Large deflection and initial instability analysis of anisotropic plates by the generalized finite element method

Paulo De Tarso Rocha De Mendonça,Clovis Sperb De Barcellos,Marx Ribeiro

doi:10.1590/1679-78255394

Paulo De Tarso Rocha De Mendonça, Clovis Sperb De Barcellos + Show 1 more

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https://doi.org/10.1590/1679-78255394

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Abstract

Abstract This paper presents investigations laminated plates under moderately large transverse displacements and initial instability, through the Generalized Finite Element Methods - GFEM. The von Karman plate hypothesis are used along with Kirchhoff and Reissner-Mindlin kinematic plate bending models to approximate transverse displacements and critical buckling loads. The generalized approximation functions are either C 0or C k continuous functions, with k being arbitrarily large. It is well known that in GFEM, when both the partition of unity (PoU) and the enrichments functions are polynomials, the stiffness matrices are singular or ill conditioned, which causes additional difficulties in applications that requires the solution of algebraic eigenvalues problems, like in the determination of natural frequencies of vibration or the initial buckling loads. Some investigations regarding this problem are presently addressed and some aspects and advantages of using C k -GFEM are observed. In addition, comparisons are presented between the classical GFEM and the Stable-GFEM (SGFEM) with regard to the evaluation of the initial critical buckling loads. The numerical experiments use reference values from analytical and numerical results obtained in the open literature.

Highlights

Anisotropic laminated plates are amongst the most commonly used types of structural elements in aeronautical and naval industry
The same can be stated about benchmark problems with singularities, whose GFEM response have been already intensively investigated in the literature
The current paper presents a comparison between two types of GFEM, C 0 and C k, in response of Mindlin and Kirchhoff kinematic models under moderately large displacements, modeled under the von Kármán theory

Summary

Introduction

Anisotropic laminated plates are amongst the most commonly used types of structural elements in aeronautical and naval industry They are often subjected to in-plane compressive and shear loads which, when combined with their slenderness, make prone to geometric instability by buckling, where various parameters such as thickness, layer stack, loading type, boundary conditions and geometry affect its ability to maintain structural integrity. Through some kinematic hypotheses, allow the three-dimensional fields to be approximated by two-dimensional ones, reducing the complexity and the number of variables required to estimate its mechanical behavior. These simplifications lead to important mathematical consequences, such as:.

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