Shape optimization for 2-D mixed-mode fracture using Extended FEM (XFEM) and Level Set Method (LSM)

• Published in: Structural and multidisciplinary optimization Vol. 44; no. 2; pp. 165 - 181
• Main Authors: Edke, Mangesh S., Chang, Kuang-Hua
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01.08.2011; Springer Nature B.V
• Subjects: Algorithms; Computational Mathematics and Numerical Analysis; Connecting rods; Crack propagation; Crack tips; Design optimization; Design parameters; Engineering; Engineering Design; Finite element method; Minimum weight; Propagation; Research Paper; Sensitivity analysis; Service life; Shape optimization; Theoretical and Applied Mechanics; Design sensitivity analysis; Fracture mechanics; Extended finite element method; Shape optimization
• DOI: 10.1007/s00158-010-0616-5
• ISSN: 1615-147X

Weight and service life are often the two most important considerations in design of structural components. This research incorporates a novel crack propagation analysis technique into shape optimization framework to support design of 2-D structural components under mixed-mode fracture for: (1) maximum service life, subject to an upper limit on volume, and (2) minimum weight subject to specified minimum service life. In both cases, structural performance measures are selected as constraints and CAD dimensions are employed as shape design variables. Fracture parameters, such as crack growth rate and crack growth direction are computed using extended finite element method (XFEM) and level set method (LSM). XFEM employs special enrichment functions to incorporate the discontinuity of structural responses caused by the crack surfaces and crack tip fields into finite element approximation. The LSM utilizes level set functions to track the crack during the crack propagation analysis. As a result, this method does not require highly refined mesh around the crack tip nor re-mesh to conform to the geometric shape of the crack when it propagates, which makes the method extremely attractive for crack propagation analysis. An accurate and efficient semi-analytical design sensitivity analysis (DSA) method is developed for calculating gradients of fracture parameters. Two different approaches—a batch-mode, gradient-based, nonlinear algorithm and an interactive what-if analysis—are used for optimization. An engine connecting rod example is used to demonstrate the feasibility of the proposed method.