Investigation in weighted function and optimization of isoparametric singular boundary elements' size in 3-d crack problem

✍ Scribed by Yongyuan Zhang; Wei Feng

• Publisher: Elsevier Science
• Year: 1987
• Tongue: English
• Weight: 607 KB
• Volume: 26
• Category: Article
• ISSN: 0013-7944
• DOI: 10.1016/0013-7944(87)90102-0

✦ Synopsis

In this paper, there are several measures being used to simplify the analytic method and improve the computational accuracy. We have emphatically studied: (1) An explicit weighted function expression in isoparametric singular 3EM. (2) A reasonable collocation of &nodes isoparametric boundary elements and application of transition elements. (3) Optimization of the sizes of isoparametric singular elements. The study shows: (i) the deduced explicit weighted function expression of S-nodes isoparametric BEM is good at setting up a general method of computing the SIF of 3-D crack problem under complex load. (ii)The reasonable collocation of isoparametric boundary elements and the optimization of the size of the singular boundary elements obviously improved the accuracy of numerical computation. NOTATION crack depth half-length of crack stress intensity factor parametric angle of the ellipse a normal force applied at P Young's modulus Poisson's ratio opening displacement a point on the crack surface a point on the crack front a small area of the crack surface around the point P a normal stress function of P SIF at P' resulting from forces F applied at P weight function at P' depending upon P Rice's weight function potential engery relative size of isoparametric singular boundary elements Cartesian coordinates Local coordinates I -19.11% -14.30% .