scholarly journals On the modification of the method of mechanical quadrature for SIE in crack problems under step-like loads

2014 ◽  
Author(s):  
A. N. Galybin
Keyword(s):  
Mechanical Quadrature ◽  
Crack Problems

Wavelet Finite Element Method Analysis of Bending Plate Based on Hermite Interpolation

2013 ◽  
Vol 389 ◽  
pp. 267-272 ◽  
Author(s):  
Peng Shen ◽  
Yu Min He ◽  
Zhi Shan Duan ◽  
Zhong Bin Wei ◽  
Pan Gao
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Thin Plate ◽  
Hermite Interpolation ◽  
Energy Functional ◽  
Field Function ◽  
Wavelet Finite Element Method ◽  
Wavelet Finite Element ◽  
Crack Problems ◽  
Element Method

In this paper, a new kind of finite element method (FEM) is proposed, which use the two-dimensional Hermite interpolation scaling function constructed by tensor product as the basis interpolation function of field function, and then combine with the energy functional with related mechanics and variational principle, the wavelet finite element equations for solving elastic thin plate unit that constructed in this paper are derived. Then the bending problem of thin plate is solved very quickly and availably through the matlab program. The numerical example in this paper indicates the correctness and validity of this method, and has high calculation precision and convergence speed. Moreover, it also provides a reliable method to solve the free vibration problem of thin plate and the pipe crack problems.

An Effective Numerical Approach for Multiple Void-Crack Interaction

2005 ◽  
Vol 73 (4) ◽  
pp. 525-535 ◽  
Author(s):  
Xiangqiao Yan
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Elastic Plate ◽  
Homogeneous Problem ◽  
Crack Problem ◽  
General System ◽  
Numerical Approach ◽  
Displacement Discontinuity ◽  
Crack Problems ◽  
Element Method

This paper presents a numerical approach to modeling a general system containing multiple interacting cracks and voids in an infinite elastic plate under remote uniform stresses. By extending Bueckner’s principle suited for a crack to a general system containing multiple interacting cracks and voids, the original problem is divided into a homogeneous problem (the one without cracks and voids) subjected to remote loads and a multiple void-crack problem in an unloaded body with applied tractions on the surfaces of cracks and voids. Thus the results in terms of the stress intensity factors (SIFs) can be obtained by considering the latter problem, which is analyzed easily by means of the displacement discontinuity method with crack-tip elements (a boundary element method) proposed recently by the author. Test examples are included to illustrate that the numerical approach is very simple and effective for analyzing multiple crack/void problems in an infinite elastic plate. Specifically, the numerical approach is used to study the microdefect-finite main crack linear elastic interaction. In addition, complex crack problems in infinite/finite plate are examined to test further the accuracy and robustness of the boundary element method.

A High-Accuracy Mechanical Quadrature Method for Solving the Axisymmetric Poisson's Equation

2017 ◽  
Vol 9 (2) ◽  
pp. 393-406 ◽  
Author(s):  
Hu Li ◽  
Jin Huang
Keyword(s):  
Three Dimensional ◽  
High Accuracy ◽  
Poisson’S Equation ◽  
Two Dimensional ◽  
Quadrature Method ◽  
Poisson's Equation ◽  
Mechanical Quadrature ◽  
Asymptotic Error ◽  
Accuracy Order ◽  
Mechanical Quadrature Method

AbstractIn this article, we consider the numerical solution for Poisson's equation in axisymmetric geometry. When the boundary condition and source term are axisymmetric, the problem reduces to solving Poisson's equation in cylindrical coordinates in the two-dimensional (r,z) region of the original three-dimensional domain S. Hence, the original boundary value problem is reduced to a two-dimensional one. To make use of the Mechanical quadrature method (MQM), it is necessary to calculate a particular solution, which can be subtracted off, so that MQM can be used to solve the resulting Laplace problem, which possesses high accuracy order and low computing complexities. Moreover, the multivariate asymptotic error expansion of MQM accompanied with for all mesh widths hi is got. Hence, once discrete equations with coarse meshes are solved in parallel, the higher accuracy order of numerical approximations can be at least by the splitting extrapolation algorithm (SEA). Meanwhile, a posteriori asymptotic error estimate is derived, which can be used to construct self-adaptive algorithms. The numerical examples support our theoretical analysis.

Sign in / Sign up

Export Citation Format

Share Document