Mesh‐free models for static analysis of smart laminated composite beams

Abstract

Summary This paper is concerned with the development of mesh‐free models for the static analysis of smart laminated composite beams. The overall smart composite beam is composed of a laminated substrate composite beam and a piezoelectric layer attached partially or fully at the top surface of the substrate beam. The piezoelectric layer acts as the distributed actuator layer of the smart beam. A layer‐wise displacement theory and an equivalent single‐layer theory have been used to derive the models. Several cross‐ply substrate beams are considered for presenting the numerical results. The responses of the smart composite beams computed by the present new mesh‐free model based on the layer‐wise displacement theory excellently match with those obtained by the exact solutions. The mesh‐free model based on the equivalent single‐layer theory cannot accurately compute the responses due to transverse actuation by the piezoelectric actuator. The models derived here suggest that the mesh‐free method can be efficiently used for the numerical analysis of smart structures. Copyright © 2016 John Wiley & Sons, Ltd.

Free vibration of the piezoelectric laminated composite beams under the elastic foundation

“…The dynamic analysis of piezoelectric laminated composite and sandwich beams has been analyzed by a coupled refined layerwise theory that including a high-order polynomial, an exponential expression and a layerwise term containing the electric field [23]. A smart composite beam that a laminated substrate composite beam and a piezoelectric layer attached partially or fully at the top surface of the substrate beam has been concerned under a layer-wise displacement theory and an equivalent single-layer theory [24]. The multi-layered piezoelectric cantilevers are studied based on the Airy stress function method, and then the exact solutions of the static governing equations are found [25].…”

A New Meshless Fragile Points Method (FPM) With Minimum Unknowns at Each Point, For Flexoelectric Analysis Under Two Theories with Crack Propagation. Part I: Theory and Implementation

“…Abdollahi et al [25] proposed a meshfree method with a C ∞ continuous basis function using Local Maximum Entropy (LME) approximants. After that, the Element-Free Galerkin (EFG) Method based on the Moving Least Squares (MLS) approximation which can generate C 1 continuos functions through an appropriate choice of the weight functions, was applied to composite beam analysis with flexoelectricity [26][27][28], as well as 2D strain gradient [29] and flexoelectric analysis [15]. The Meshless Local Petrov-Galerkin (MLPG) Method is also established based on the MLS approximation for trial functions, whereas multiple test functions (e.g., weight function, local fundamental solution, Heaviside function, etc.)…”