The free vibration analysis of a circular plate made up of a porous material integrated by piezoelectric actuator patches has been studied. The plate is assumed to be thin and its shear deformations have been neglected. The porous material properties vary through the plate thickness according to some given functions. Using Hamilton's variational principle and the classical plate theory (CPT) the governing motion equations have been obtained. Simple and clamped supports have been considered for the boundary conditions. The differential quadrature method (DQM) has been used for the discretizations required for numerical analysis. The effect of some parameters such as thickness ratio, porosity, piezoelectric actuators, variation of piezoelectric actuators-to-porous plate thickness ratio, pores distribution and pores compressibility on the natural frequency, radial and circumferential stresses has been illustrated. The results have been compared with the similar ones in the literature.

Free vibration analysis of saturated porous FG circular plates integrated with piezoelectric actuators via differential quadrature method

Extended isogeometric analysis for dynamic fracture in multiphase piezoelectric/piezomagnetic composites

Modeling of mechanical behavior of plates has been accomplished in the past decades, with different numerical strategies including the finite element and meshfree methods, and with a range of plate theories including the first-order shear deformation theory (FSDT). In this paper, we propose an efficient numerical meshfree approach to analyze static bending and free vibration of functionally graded (FG) plates. The kinematics of plates is based on a novel simple FSDT, termed as S-FSDT, which is an effective four-variable refined plate theory. The S-FSDT requires C 1 -continuity that is satisfied with the basis functions based on moving Kriging interpolation. Some major features of the approach can be summarized: (a) it is less computationally expensive due to having fewer unknowns; (b) it is naturally free from shear-locking; (c) it captures the physics of shear-deformation effect present in the conventional FSDT; (d) the essential boundary conditions can straightforwardly be treated, the same as the FEM; and (e) it can deal with both thin and thick plates. All these features will be demonstrated through numerical examples, which are to confirm the accuracy and effectiveness of the proposed method. Additionally, a discussion on other possible choices of correlation functions used in the model is given.

A simple FSDT-based meshfree method for analysis of functionally graded plates

A novel extended 4-node quadrilateral finite element (XCQ4) based on a consecutive-interpolation procedure (CIP) with continuous nodal stress for accurately modeling singular stress fields near crack tips of two-dimensional (2D) cracks in solids is presented In contrast to the traditional approaches, the approximation functions constructed based on the CIP involve both nodal values and averaged nodal gradients as interpolation conditions Our objective is to exhibit a pioneering extension of the recently developed CQ4 element enhanced by enrichment to precisely model 2D elastic crack problems, taking advantages of the strengths and making use all the desirable features of both techniques, the CIP and the local enriched partition of unity method The stress intensity factors (SIFs) are estimated using the interaction integral The accuracy and performance of the proposed XCQ4 and its numerical properties are illustrated by numerical examples, considering both single and mixed-mode problems with complicated configurations Compared with reference solutions available in the literature and the conventional XQ4 results, it is found that the accuracy of the XCQ4 is high Studies on the convergence rate of the SIFs in relative errors also reveal a better performance of the XCQ4 over the classical XQ4 The fracture parameters are found to be stable for different areas of integration paths around the crack tip Further applications of the developed XCQ4 to other complex problems are potential

An extended consecutive-interpolation quadrilateral element (XCQ4) applied to linear elastic fracture mechanics

Analysis of transient dynamic fracture parameters of cracked functionally graded composites by improved meshfree methods

SUMMARY

We propose two strategies of novel adaptive numerical integration based on mapping techniques for solving the complicated problems of domain integration encountered in meshfree methods. Several mapping methods are presented in detail that map a complex integration domain to much simpler ones, for example, squares, triangles or circles. The techniques described in the paper can be applied to both global and local weak forms, and the highly nonlinear meshfree integrands are evaluated with controlled accuracy. The necessity of the clumsy procedure of background mesh or cell structures used for integration purpose in existing meshfree methods is avoided, and many meshfree methods that require the domain integration can now become ‘truly meshfree’. Various numerical examples in two dimensions are considered to demonstrate the applicability and the effectiveness of the proposed methods and it shows that the accuracy is improved significantly. Their obtained results are compared with analytical solutions and other approaches and very good agreements are found. Additionally, some three-dimensional cases applied by the present methods are also examined. Copyright © 2012 John Wiley & Sons, Ltd.

Donat Racz

Papers

Novel adaptive meshfree integration techniques in meshless methods