Quantum mechanics

Engineering

Philosophy

Materials science

Shear (geology)

Boundary value problem

Simple (philosophy)

Physics

Finite element method

Nonlinear system

Homogeneous

Mathematics

Epistemology

Mathematical analysis

Geometry

Composite material

Isogeometric analysis

Combinatorics

Structural engineering

Finite Elements in Analysis and Design

This paper presents a novel approach based on isogeometric analysis (IGA) and a simple first-order shear deformation plate theory (S-FSDT) for geometrically nonlinear analysis of homogeneous and non-homogeneous functionally graded plates. Owing to many advantages such as (a) the S-FSDT is free of shear-locking, (b) less one unknown for the S-FSDT as compared with the conventional FSDT, (c) the awkward C1 continuity required for the generalized displacements is treated straightforwardly because of the nature of the higher-order continuity IGA method, the new formulation is thus effective in modeling the geometrical nonlinearities of plates. The S-FSDT is associated with the von Kármán strain for dealing with small strain and moderate rotation. Numerical validation is analyzed and numerical applications are considered. The obtained results are compared with reference solutions to show the accuracy and the effectiveness of the present approach. The effects of different boundary conditions, gradient index, length-to-thickness ratio, geometric shape, etc. on the geometrically nonlinear mechanical responses of functionally graded plates are investigated.

A simple FSDT-based isogeometric analysis for geometrically nonlinear analysis of functionally graded plates