BEM for Static and Dynamic Fracture Analysis in Thin Piezoelectric Structures

2013 ◽  
Vol 816-817 ◽  
pp. 149-152
Author(s):  
Hong Jun Zhong ◽  
Hong Yan Wang ◽  
Jun Lei ◽  
Wei Dong Gu
Keyword(s):  
Singular Integrals ◽  
Integration Method ◽  
Domain Boundary ◽  
Fracture Analysis ◽  
Thin Structures ◽  
Analytical Integration ◽  
Piezoelectric Structure ◽  
Nearly Singular Integrals ◽  
Quadratic Element ◽  
Piezoelectric Structures

A 2D time-domain boundary element method (BEM) is developed to study the fracture problems in thin piezoelectric structure. The nearly singular integrals arisen in thin structures are calculated in two ways. One is based on a nonlinear coordinate transformation for curve-quadratic element, and the other one is an analytical integration method for straight quadratic element. Numerical examples are presented to verify the effectiveness and stability of the present BEM in thin piezoelectric structure.

scholarly journals Analytical Modeling and Simulation of S-Drive Piezoelectric Actuators

Actuators ◽  
2021 ◽  
Vol 10 (5) ◽  
pp. 87
Author(s):  
Nicholas A. Jones ◽  
Jason Clark
Keyword(s):  
Element Model ◽  
Mechanical Efficiency ◽  
Compact Model ◽  
High Frequency Response ◽  
Macro Scale ◽  
Piezoelectric Structure ◽  
Modern Manufacturing ◽  
Manufacturing Techniques ◽  
Piezoelectric Structures ◽  
Improve Device

This paper presents a structural geometry for increasing piezoelectric deformation, which is suitable for both micro- and macro-scale applications. New and versatile microstructure geometries for actuators can improve device performance, and piezoelectric designs benefit from a high-frequency response, power density, and efficiency, making them a viable choice for a variety of applications. Previous works have presented piezoelectric structures capable of this amplification, but few are well-suited to planar manufacturing. In addition to this manufacturing difficulty, a large number of designs cannot be chained into longer elements, preventing them from operating at the macro-scale. By optimizing for both modern manufacturing techniques and composability, this structure excels as an option for a variety of macro- and micro-applications. This paper presents an analytical compact model of a novel dual-bimorph piezoelectric structure, and shows that this compact model is within 2% of a computer-distributed element model. Furthermore it compares the actuator’s theoretical performance to that of a modern actuator, showing that this actuator trades mechanical efficiency for compactness and weight savings.

scholarly journals Efficient Computation of Highly Oscillatory Fourier Transforms with Nearly Singular Amplitudes over Rectangle Domains

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1930
Author(s):  
Zhen Yang ◽  
Junjie Ma
Keyword(s):  
Adaptive Mesh Refinement ◽  
Numerical Experiments ◽  
Singular Integrals ◽  
Fourier Transforms ◽  
Adaptive Mesh ◽  
Oscillatory Integrals ◽  
Efficient Computation ◽  
New Approach ◽  
Highly Oscillatory ◽  
Nearly Singular Integrals

In this paper, we consider fast and high-order algorithms for calculation of highly oscillatory and nearly singular integrals. Based on operators with regard to Chebyshev polynomials, we propose a class of spectral efficient Levin quadrature for oscillatory integrals over rectangle domains, and give detailed convergence analysis. Furthermore, with the help of adaptive mesh refinement, we are able to develop an efficient algorithm to compute highly oscillatory and nearly singular integrals. In contrast to existing methods, approximations derived from the new approach do not suffer from high oscillatory and singularity. Finally, several numerical experiments are included to illustrate the performance of given quadrature rules.

scholarly journals A Generation of Special Triangular Boundary Element Shape Functions for 3D Crack Problems

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Guizhong Xie ◽  
Fenglin Zhou
Keyword(s):  
Boundary Element ◽  
Crack Front ◽  
Singular Integrals ◽  
Triangular Element ◽  
Crack Problems ◽  
Nearly Singular Integrals ◽  
Triangular Elements ◽  
Displacement Extrapolation Method ◽  
Element Shape ◽  
Displacement Extrapolation

This paper focuses on tackling the two drawbacks of the dual boundary element method (DBEM) when solving crack problems with a discontinuous triangular element: low accuracy of the calculation of integrals with singularity and crack front element must be utilized to model the square-root property of displacement. In order to calculate the integrals with higher order singularity, the triangular elements are segmented into several subregions which consist of subtriangles and subpolygons. The singular integrals in those subtriangles are handled by the singularity subtraction technique in the integration space and can be regularized and accurately calculated. For the nearly singular integrals in those subpolygons, the element subdivision technique is employed to improve the calculation accuracy. In addition, considering the location of the crack front in the element, special crack front elements are constructed based on a 6-node discontinuous triangular element, in which the displacement extrapolation method is introduced to obtain the stress intensity factors (SIFs) without consideration of orthogonalization of the crack front mesh. Several numerical results are investigated to fully verify the validation of the presented approach.

Computation of nearly singular integrals in 3D BEM

2014 ◽  
Vol 48 ◽  
pp. 32-42 ◽  
Author(s):  
Yaoming Zhang ◽  
Xiaochao Li ◽  
Vladimir Sladek ◽  
Jan Sladek ◽  
Xiaowei Gao
Keyword(s):  
Singular Integrals ◽  
Nearly Singular Integrals
Sign in / Sign up

Export Citation Format

Share Document