scholarly journals Numerical MLPG Analysis of Piezoelectric Sensor in Structures

2014 ◽  
Vol 22 (2) ◽  
pp. 15-20 ◽  
Author(s):  
Peter Staňák ◽  
Ján Sládek ◽  
Vladimír Sládek ◽  
Slavomír Krahulec
Keyword(s):  
Mechanical Response ◽  
Nodal Point ◽  
Piezoelectric Sensor ◽  
Weak Form ◽  
Step Function ◽  
Cylindrical Shape ◽  
Transient Effects ◽  
Piezoelectric Solid ◽  
Mls Approximation ◽  
Local Integral Equations

AbstractThe 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.

scholarly journals Analysis of Piezoelectric Semiconducting Solids by Meshless Method

2015 ◽  
Vol 65 (1) ◽  
pp. 77-92
Author(s):  
P. Staňák ◽  
J. Sládek ◽  
V. Sládek
Keyword(s):  
Nodal Point ◽  
Three Dimensional ◽  
Spherical Shape ◽  
Weak Form ◽  
Step Function ◽  
Various Boundary Conditions ◽  
Mlpg Method ◽  
Piezoelectric Semiconductors ◽  
Local Weak Form ◽  
Local Integral Equations

Abstract In this paper, a meshless local Petrov-Galerkin (MLPG) method is proposed to calculate mechanical and electrical responses of three-dimensional piezoelectric semiconductors under static load. The analyzed solid is discretized by a set of generally distributed nodal points distributed over 3D geometry. Local integral equations (LIEs) are derived from the weak form of governing equations over small local subdomains. The subdomains have a spherical shape with a nodal point located in its centre. A unit step function is used as the test functions in the local weak-form. The moving least-squares (MLS) method is adopted for the approximation of the physical quantities in the LIEs. The proposed MLPG method is verified by using the corresponding results obtained with the finite element method. Numerical examples are presented and discussed for various boundary conditions and loading scenarios to show the performance of the developed MLPG method for analysis piezoelectric semiconducting solids.

scholarly journals Transient Effects of Applying and Removing Strain on the Mechanical Behavior of Rubber

Materials ◽  
2020 ◽  
Vol 13 (19) ◽  
pp. 4333
Author(s):  
Elli Gkouti ◽  
Burak Yenigun ◽  
Aleksander Czekanski
Keyword(s):  
Mechanical Response ◽  
Experimental Tests ◽  
Step Function ◽  
Applied Strain ◽  
Stress And Strain ◽  
Transient Effects ◽  
Viscoelastic Materials ◽  
Partial Removal ◽  
The Relationship ◽  
Over Time

For viscoelastic materials, the relationship between stress and strain depends on time, where the applied strain (or stress) can be expressed as a step function of time. In the present work, we investigated two temporary effects in the response of viscoelastic materials when a given strain is applied and then removed. The application of strain causes a stress response over time, also known as relaxation. By contrast, recovery is the response that occurs following the removal of an applied stress or strain. Both stress and relaxation constitute transient stages of a viscoelastic material exposed to a permanent force. In the current work, we performed several experimental tests to record the recovery in response to the total or partial removal of the strain. By observing and analyzing the mechanical response of the material to strain, we deduced that recovery is a procedure not only related to creep but also to relaxation. Hence, we created a model that simulates the behavior of viscoelastic materials, contributing to the prediction of relevant results concerning different conditions.

THE INTERPOLATING ELEMENT-FREE GALERKIN (IEFG) METHOD FOR TWO-DIMENSIONAL ELASTICITY PROBLEMS

2011 ◽  
Vol 03 (04) ◽  
pp. 735-758 ◽  
Author(s):  
HONGPING REN ◽  
YUMIN CHENG
Keyword(s):  
Least Squares ◽  
Shape Function ◽  
Weak Form ◽  
New Method ◽  
Moving Least Squares ◽  
Two Dimensional ◽  
Element Free Galerkin ◽  
Elasticity Problems ◽  
Mls Approximation ◽  
Element Free

In this paper, a new method for deriving the moving least-squares (MLS) approximation is presented, and the interpolating moving least-squares (IMLS) method proposed by Lancaster is improved. Compared with the IMLS method proposed by Lancaster, a simpler formula of the shape function is given in the improved IMLS method in this paper so that the new method has higher computing efficiency. Combining the shape function constructed by the improved IMLS method with Galerkin weak form of the elasticity problems, the interpolating element-free Galerkin (IEFG) method for the two-dimensional elasticity problems is presented, and the corresponding formulae are obtained. In the IEFG method, the boundary conditions can be applied directly which makes the computing efficiency higher than the conventional EFG method. Some numerical examples are presented to demonstrate the validity of the method.

scholarly journals The Meshless Analysis of Scale-Dependent Problems for Coupled Fields

Materials ◽  
2020 ◽  
Vol 13 (11) ◽  
pp. 2527
Author(s):  
Jan Sladek ◽  
Vladimir Sladek ◽  
Pihua H. Wen
Keyword(s):  
Weak Form ◽  
Algebraic Equations ◽  
Governing Equations ◽  
Electric Field Gradients ◽  
Test Function ◽  
Field Gradients ◽  
Mlpg Method ◽  
Physical Fields ◽  
Local Weak Form ◽  
Local Integral Equations

The meshless local Petrov–Galerkin (MLPG) method was developed to analyze 2D problems for flexoelectricity and higher-grade thermoelectricity. Both problems were multiphysical and scale-dependent. The size effect was considered by the strain and electric field gradients in the flexoelectricity, and higher-grade heat flux in the thermoelectricity. The variational principle was applied to derive the governing equations within the higher-grade theory of considered continuous media. The order of derivatives in the governing equations was higher than in their counterparts in classical theory. In the numerical treatment, the coupled governing partial differential equations (PDE) were satisfied in a local weak-form on small fictitious subdomains with a simple test function. Physical fields were approximated by the moving least-squares (MLS) scheme. Applying the spatial approximations in local integral equations and to boundary conditions, a system of algebraic equations was obtained for the nodal unknowns.

scholarly journals Impact Mechanical Response of a 2-2 Cement-Based Piezoelectric Sensor Considering the Electrode Layer Effect

Sensors ◽  
2017 ◽  
Vol 17 (9) ◽  
pp. 2035 ◽  
Author(s):  
Taotao Zhang ◽  
Keping Zhang ◽  
Wende Liu ◽  
Yangchao Liao
Keyword(s):  
Mechanical Response ◽  
Piezoelectric Sensor ◽  
Electrode Layer ◽  
Layer Effect

scholarly journals An Improved Interpolating Element-Free Galerkin Method Based on Nonsingular Weight Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
F. X. Sun ◽  
C. Liu ◽  
Y. M. Cheng
Keyword(s):  
Least Squares ◽  
Shape Function ◽  
Weak Form ◽  
Moving Least Squares ◽  
Weight Functions ◽  
Element Free Galerkin Method ◽  
Element Free Galerkin ◽  
Node Distribution ◽  
Mls Approximation ◽  
Element Free

Based on the moving least-squares (MLS) approximation, an improved interpolating moving least-squares (IIMLS) method based on nonsingular weight functions is presented in this paper. Then combining the IIMLS method and the Galerkin weak form, an improved interpolating element-free Galerkin (IIEFG) method is presented for two-dimensional potential problems. In the IIMLS method, the shape function of the IIMLS method satisfies the property of Kroneckerδfunction, and there is no difficulty caused by singularity of the weight function. Then in the IIEFG method presented in this paper, the essential boundary conditions are applied naturally and directly. Moreover, the number of unknown coefficients in the trial function of the IIMLS method is less than that of the MLS approximation; then under the same node distribution, the IIEFG method has higher computational precision than element-free Galerkin (EFG) method and interpolating element-free Galerkin (IEFG) method. Four selected numerical examples are presented to show the advantages of the IIMLS and IIEFG methods.

Crack Analysis in Piezoelectric Semiconductors

2014 ◽  
Vol 627 ◽  
pp. 269-272 ◽  
Author(s):  
Jan Sladek ◽  
Vladimir Sladek
Keyword(s):  
Piezoelectric Materials ◽  
Electric Displacement ◽  
Weak Form ◽  
Test Function ◽  
Crack Problems ◽  
Unit Function ◽  
Piezoelectric Semiconductors ◽  
Local Weak Form ◽  
Local Integral Equations ◽  
Electric Loads

Mechanical and electric loads are considered for 2-d crack problems in conducting piezoelectric materials. The electric displacement in conducting piezoelectric materials is influenced by the electron density and it is coupled with the electric current. The coupled governing partial differential equations (PDE) for stresses, electric displacement field and current are satisfied in a local weak-form on small fictitious subdomains. Nodal points are spread on the analyzed domain and each node is surrounded by a small circle for simplicity. Local integral equations are derived for a unit function as the test function on circular subdomains. All field quantities are approximated by the moving least-squares (MLS) scheme.

Stability Analysis of Composite Shafts Considering Internal Damping and Coupling Effect

2020 ◽  
Vol 20 (11) ◽  
pp. 2050118
Author(s):  
Kwangchol Ri ◽  
Poknam Han ◽  
Inchol Kim ◽  
Wonchol Kim ◽  
Hyonbok Cha
Keyword(s):  
Degrees Of Freedom ◽  
Coupling Effect ◽  
Lagrange Equation ◽  
Nodal Point ◽  
Single Layer ◽  
Beam Theory ◽  
Weak Form ◽  
Internal Damping ◽  
Proposed Model ◽  
Equivalent Modulus

A mathematical model is proposed to analyze the stability of composite shafts, considering the internal damping, transverse shear deformation and Poisson’s coupling effect at the same time. The strain–displacement relations are described using the Timoshenko beam theory, and the strain energy and kinetic energy are expressed using the weak form quadrature element method (QEM), for which each nodal point has 4 degrees of freedom. Then, the motion equation of the system is established using the Lagrange equation. The instability thresholds of the composite shaft are determined using the proposed model. The results were compared with those calculated by the equivalent modulus beam theory (EMBT), equivalent single layer theory (ESLT) and simplified homogenized beam theory (SHBT). Good agreement has been achieved. Therefore, the proposed model can be effectively used for the dynamic analysis of composite shafts.

scholarly journals Longitudinally Invariant Elastic Structures Analyzed by the Meshless Mlpg Method Using 2.5D Approach

2015 ◽  
Vol 61 (2) ◽  
pp. 67-84
Author(s):  
P. Stanak ◽  
A. Tadeu ◽  
J. Sladek ◽  
V. Sladek
Keyword(s):  
Nodal Point ◽  
Computational Effort ◽  
Domain Model ◽  
Elastic Response ◽  
Homogeneous Material ◽  
Invariant Structure ◽  
Mlpg Method ◽  
Longitudinal Coordinate ◽  
The Fourier Transform ◽  
Local Integral Equations

Abstract This paper presents a general 2.5D meshless MLPG methodology for the computation of the elastic response of longitudinally invariant structure subjected to the incident wave field. A numerical frequency domain model is established using the Fourier transform in time and longitudinal coordinate domains. This allows for significant reduction of computational effort required. In the MLPG method the Moving-Least Squares (MLS) scheme is employed for the approximation of the spatial variation of displacement field. No finite elements are required for the approximation or integration of unknowns. A small circular subdomain is introduced around each nodal point in the analyzed domain. Local integral equations derived from the governing equations are specified on these subdomains. Continuously non-homogeneous material properties are varying in the cross-section of the analyzed structure. A simple patch test is introduced to assess the accuracy and the convergence of developed numerical model. At the end of the paper, numerical examples illustrate the applicability of the proposed numerical formulation.

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