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 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 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.

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.

AN INTERPOLATING LOCAL PETROV–GALERKIN METHOD FOR POTENTIAL PROBLEMS

2014 ◽  
Vol 06 (01) ◽  
pp. 1450009 ◽  
Author(s):  
L. CHEN ◽  
C. LIU ◽  
H. P. MA ◽  
Y. M. CHENG
Keyword(s):  
Present Method ◽  
Shape Function ◽  
Three Dimensional ◽  
Weak Form ◽  
Step Function ◽  
Kriging Interpolation ◽  
Heaviside Step Function ◽  
Discrete Equations ◽  
Potential Problems ◽  
Local Weak Form

In this paper, based on the moving Kriging interpolation (MKI), the meshless interpolating local Petrov–Galerkin (ILPG) method is presented to solve two- and three-dimensional potential problems. In the present method, the shape function constructed by the MKI has the property of the Kronecker δ function. Then in the ILPG method the essential boundary conditions can be implemented directly. The discrete equations are obtained using the local symmetric weak form. The Heaviside step function is used as the test function in each sub-domain to avoid some domain integral in the symmetric weak form, which will greatly improve the effectiveness of the present method. The ILPG method in this paper is a truly meshless method, which does not require a mesh either for obtaining shape function or for numerical integration in the local weak form. Several numerical examples of potential problems show that the ILPG method has higher computational efficiency and convergence rate than the MLPG method.

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

2020 ◽  
Author(s):  
Jan Sladek ◽  
Vladimir Sladek ◽  
Pihua H. Wen
Keyword(s):  
Weak Form ◽  
Governing Equations ◽  
Electric Field Gradients ◽  
Test Function ◽  
Coupled Fields ◽  
Field Gradients ◽  
Mlpg Method ◽  
Integral Equa ◽  
Physical Fields ◽  
Local Weak Form

The meshless Petrov-Galerkin (MLPG) method is developed to analyse 2-D problems for flexoelectricity and thermoelectricity. Both problems are multiphysical and scale dependent. The size-effect is considered by the strain- and electric field-gradients in the flexoelecricity and higher-grade heat flux in the thermoelectricity. The variational principle is applied to de-rive the governing equations considered constitutive equations. The order of derivatives in governing equations is higher than in equations obtained from classical theory. The coupled governing partial differential equations (PDE) are satisfied in a local weak-form on small fic-titious subdomains with a simple test function. Physical fields are approximated by the mov-ing least-squares (MLS) scheme. Applying the spatial approximations in local integral equa-tions a system of algebraic is obtained for the nodal unknowns.

Convergent Overdetermined-RBF-MLPG for Solving Second Order Elliptic PDEs

2013 ◽  
Vol 5 (1) ◽  
pp. 78-89 ◽  
Author(s):  
Ahmad Shirzadi ◽  
Leevan Ling
Keyword(s):  
Error Analysis ◽  
Basis Function ◽  
Numerical Approximation ◽  
Weak Form ◽  
Elliptic Pdes ◽  
Double Precision ◽  
Step Functions ◽  
Mlpg Method ◽  
Local Weak Form ◽  
Good Agreement

AbstractThis paper deals with the solvability and the convergence of a class of unsymmetric Meshless Local Petrov-Galerkin (MLPG) method with radial basis function (RBF) kernels generated trial spaces. Local weak-form testings are done with step-functions. It is proved that subject to sufficiently many appropriate testings, solvability of the unsymmetric RBF-MLPG resultant systems can be guaranteed. Moreover, an error analysis shows that this numerical approximation converges at the same rate as found in RBF interpolation. Numerical results (in double precision) give good agreement with the provided theory.

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.

Meshless TL and UL Approaches for Large Deformation Analysis

2010 ◽  
Vol 139-141 ◽  
pp. 893-896 ◽  
Author(s):  
Yuan Tong Gu
Keyword(s):  
Large Deformation ◽  
Computational Efficiency ◽  
Metal Forming ◽  
Weak Form ◽  
Superior Performance ◽  
Deformation Analysis ◽  
Large Deformation Analysis ◽  
Updated Lagrangian ◽  
Local Weak Form ◽  
Large Deformation Problems

To accurately and effectively simulate large deformation is one of the major challenges in numerical modeling of metal forming. In this paper, an adaptive local meshless formulation based on the meshless shape functions and the local weak-form is developed for the large deformation analysis. Total Lagrangian (TL) and the Updated Lagrangian (UL) approaches are used and thoroughly compared each other in computational efficiency and accuracy. It has been found that the developed meshless technique provides a superior performance to the conventional FEM in dealing with large deformation problems for metal forming. In addition, the TL has better computational efficiency than the UL. However, the adaptive analysis is much more efficient using in the UL approach than using in the TL approach.

Sign in / Sign up

Export Citation Format

Share Document