Numerical estimation of stress intensity factors in cracked functionally graded piezoelectric materials – A scaled boundary finite element approach

2018 ◽  
Vol 206 ◽  
pp. 301-312 ◽  
Author(s):  
A.L.N. Pramod ◽  
Ean Tat Ooi ◽  
Chongmin Song ◽  
Sundararajan Natarajan
Keyword(s):  
Finite Element ◽  
Piezoelectric Materials ◽  
Functionally Graded ◽  
Numerical Estimation ◽  
Intensity Factors ◽  
Finite Element Approach ◽  
Functionally Graded Piezoelectric Materials ◽  
Element Approach ◽  
Functionally Graded Piezoelectric ◽  
Scaled Boundary Finite Element

Interaction Integrals for Fracture Analysis of Functionally Graded Piezoelectric Materials

2008 ◽  
Author(s):  
B. N. Rao
Keyword(s):  
Piezoelectric Materials ◽  
Crack Tip ◽  
Functionally Graded ◽  
Piezoelectric Medium ◽  
Intensity Factors ◽  
Interaction Integral ◽  
Functionally Graded Piezoelectric Materials ◽  
Electric Displacement Intensity Factor ◽  
Functionally Graded Piezoelectric ◽  
Asymptotic Fields

This paper presents domain form of interaction integrals based on three independent formulations for computation of stress intensity factors and electric displacement intensity factor for cracks in functionally graded piezoelectric materials. Conservation integrals of J–type are derived based on the governing equations for piezoelectric media and the crack tip asymptotic fields of homogeneous piezoelectric medium as auxiliary fields. Each of the formulation differs in the way auxiliary fields are imposed in the evaluation of interaction integral and each of them results in a consistent form of interaction integral in the sense that extra terms naturally appears in their derivation to compensate for the difference in the chosen crack tip asymptotic fields of homogeneous and functionally graded piezoelectric medium. The additional terms play an important role of ensuring domain independence of the presented interaction integrals. Comparison of numerically evaluated intensity factors through the three consistent formulations with those obtained using displacement extrapolation method is presented by means of an example.

Geometrical nonlinear characteristics of functionally graded structure using functionally graded piezoelectric materials

2018 ◽  
Vol 22 (2) ◽  
pp. 370-401
Author(s):  
CK Susheel ◽  
Anshul Sharma ◽  
Rajeev Kumar ◽  
Vishal S Chauhan
Keyword(s):  
Finite Element ◽  
Piezoelectric Materials ◽  
Functionally Graded ◽  
Element Formulation ◽  
Static And Dynamic Analysis ◽  
Graded Structure ◽  
Functionally Graded Piezoelectric Materials ◽  
Linear Algebraic Equations ◽  
Functionally Graded Piezoelectric ◽  
Functionally Graded Structure

In the present article, a parametric study on the geometric nonlinear static and dynamic analysis of thin functionally graded structure sandwiched between functionally graded piezoelectric materials is presented. The properties of functionally graded material are graded in the thickness direction according to a power law distribution and variation of electric field is assumed to be quadratic across the thickness of functionally graded piezoelectric materials layers. The structure is modeled using finite element modeling. The finite element formulation is derived using Hamilton’s principle using full geometric nonlinearities. This is done by using Green-Lagrangian strains instead of von-Karman strains which are usually used by most researchers while conducting similar studies. The ensued non-linear algebraic equations are then solved using the modified Newton–Raphson method. A fuzzy logic controller is used to attenuate the vibration occurring in the host structure.

scholarly journals A Coupling Electromechanical Inhomogeneous Cell-Based Smoothed Finite Element Method for Dynamic Analysis of Functionally Graded Piezoelectric Beams

2019 ◽  
Vol 2019 ◽  
pp. 1-16
Author(s):  
Bin Cai ◽  
Liming Zhou
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Piezoelectric Materials ◽  
Continuous System ◽  
Functionally Graded ◽  
Gaussian Integration ◽  
Functionally Graded Piezoelectric Materials ◽  
Smoothed Finite Element Method ◽  
Functionally Graded Piezoelectric ◽  
Element Method

To accurately simulate the continuous property change of functionally graded piezoelectric materials (FGPMs) and overcome the overstiffness of the finite element method (FEM), we present an electromechanical inhomogeneous cell-based smoothed FEM (ISFEM) of FGPMs. Firstly, ISFEM formulations were derived to calculate the transient response of FGPMs, and then, a modified Wilson-θ method was deduced to solve the integration of the FGPM system. The true parameters at the Gaussian integration point in FGPMs were adopted directly to replace the homogenization parameters in an element. ISFEM provides a close-to-exact stiffness of the continuous system, which could automatically and more easily generate for complicated domains and thus significantly decrease numerical errors. The accuracy and trustworthiness of ISFEM were verified as higher than the standard FEM by several numerical examples.

The Higher Order Crack Tip Fields for Interfacial Crack between Linear Functionally Graded and Homogeneous Piezoelectric Materials

2014 ◽  
Vol 1015 ◽  
pp. 97-100
Author(s):  
Yao Dai ◽  
Xiao Chong ◽  
Ying Chen
Keyword(s):  
Piezoelectric Materials ◽  
Electric Displacement ◽  
Interfacial Crack ◽  
Crack Tip ◽  
Higher Order ◽  
Functionally Graded ◽  
Linear Functions ◽  
Intensity Factors ◽  
Crack Tip Fields ◽  
Functionally Graded Piezoelectric Materials

The higher order crack-tip fields for an anti-plane crack situated in the interface between functionally graded piezoelectric materials (FGPMs) and homogeneous piezoelectric materials (HPMs) are presented. The mechanical and electrical properties of the FGPMs are assumed to be linear functions of y perpendicular to the crack. The crack surfaces are supposed to be insulated electrically. By using the method of eigen-expansion, the higher order stress and electric displacement crack tip fields for FGPMs and HPMs are obtained. The analytic expressions of the stress intensity factors and the electric displacement intensity factors are derived.

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