Analysis of Thermo-Piezoelectricity Problems by Meshless Method

Sládek, J.; Sládek, V.

doi:10.2478/v10147-011-0030-z

Cited by 8 publications

(5 citation statements)

References 33 publications

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“…The meshless Local Petrov-Galerkin (MLPG) method (Atluri and Zhu, 1998;Atluri, 2004) is considered to be one of the most popular meshless methods. The MLPG has been successfully applied to various problems related to piezoelectricity, including 2-D problems (Sladek, et al, 2006), thermopiezoelectricity (Sladek et al, 2010a) and piezoelectric rectangular and laminated plates (Sladek et al, 2010b;Sladek et al, 2012b). An investigation of magnetoelectric effects in composites with piezoelectric and piezomagnetic layers has been recently conducted by Sladek et al (2012a).…”

Section: Introductionmentioning

confidence: 98%

Numerical MLPG Analysis of Piezoelectric Sensor in Structures

Sládek¹,

Sládek²,

Krahulec³

2014

Slovak Journal of Civil Engineering

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The paper deals with a numerical analysis of the electro-mechanical response of piezoelectric sensors subjected to an external non-uniform displacement field. The meshless method based on the local Petrov-Galerkin (MLPG) approach is utilized for the numerical solution of a boundary value problem for the coupled electro-mechanical fields that characterize the piezoelectric material. The sensor is modeled as a 3-D piezoelectric solid. The transient effects are not considered. Using the present MLPG approach, the assumed solid of the cylindrical shape is discretized with nodal points only, and a small spherical subdomain is introduced around each nodal point. Local integral equations constructed from the weak form of governing PDEs are defined over these local subdomains. A moving least-squares (MLS) approximation scheme is used to approximate the spatial variations of the unknown field variables, and the Heaviside unit step function is used as a test function. The electric field induced on the sensor is studied in a numerical example for two loading scenarios.

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Section: Introductionmentioning

confidence: 98%

Numerical MLPG Analysis of Piezoelectric Sensor in Structures

Sládek¹,

Sládek²,

Krahulec³

2014

Slovak Journal of Civil Engineering

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“…This area is extensively explored in engineering structures, due to its temperature-dependent characteristics. Several articles have tackled the thermopiezoelectric contact problem with friction [5,[9][10][11][12][13], thermo-elasto-visco-plasticity [14][15][16], and thermo-visco-elasticity [17,18]. These studies are rooted in variations in constitutive laws and contact conditions [19][20][21][22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Existence and Uniqueness of Weak Solutions to Frictionless-Antiplane Contact Problems

Fadlia,

Dalah,

Torres

2024

Mathematics

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We investigate a quasi-static-antiplane contact problem, examining a thermo-electro-visco-elastic material with a friction law dependent on the slip rate, assuming that the foundation is electrically conductive. The mechanical problem is represented by a system of partial differential equations, and establishing its solution involves several key steps. Initially, we obtain a variational formulation of the model, which comprises three systems: a hemivariational inequality, an elliptic equation, and a parabolic equation. Subsequently, we demonstrate the existence of a unique weak solution to the model. The proof relies on various arguments, including those related to evolutionary inequalities, techniques for decoupling unknowns, and certain results from differential equations.

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“…Thus, a coupling of thermo-electro-mechanical fields is needed to be taken into account if a temperature load is considered in a piezoelectric solid. Several models of fully coupled thermo-piezoelectricity has been developed for determining static responses under combined thermal, electric and mechanical excitations, see (Liu et al, 2014;Shang et al, 2002;Sládek et al, 2010;Tiersten, 1971). Recently, contact problems involving thermo-piezoelectric materials (Baiz et al, 2018;Benaissa et al, 2015Benaissa et al, , 2016 have been studied.…”

Section: Introductionmentioning

confidence: 99%

Numerical analysis of a frictional contact problem for thermo-electro-elastic materials

Ouafik¹

2020

Journal of Theoretical and Applied Mechanics

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A numerical method is presented for a mathematical model which describes the frictional contact between a thermo-electro-elastic body and a conductive foundation. The contact is described by Signorini's conditions and Tresca's friction law including electrical and thermal conductivity conditions. Our aim is to present a detailed description of the numerical modelling of the problem. To this end, we introduce a discrete scheme based on the finite element method. Under some regularity assumptions imposed on the true solution, optimal order error estimates are derived for the linear element solution. This theoretical result is illustrated numerically.

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Analysis of Thermo-Piezoelectricity Problems by Meshless Method

Cited by 8 publications

References 33 publications

Numerical MLPG Analysis of Piezoelectric Sensor in Structures

Numerical MLPG Analysis of Piezoelectric Sensor in Structures

Existence and Uniqueness of Weak Solutions to Frictionless-Antiplane Contact Problems

Numerical analysis of a frictional contact problem for thermo-electro-elastic materials

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