Analysis of dynamic stress concentration problems employing spline-based wavelet Galerkin method. (September 2015)

• Record Type: Journal Article
• Authors: Tanaka, Satoyuki; Sannomaru, Shogo; Imachi, Michiya; Hagihara, Seiya; Okazawa, Shigenobu; Okada, Hiroshi
• Is Part Of: Engineering analysis with boundary elements. Volume 58(2015:Sep.)
• Page Start: 129
• Page End: 139
• Publication Date: 2015-09
• Subjects: Wavelet Galerkin method -- Meshfree method -- Dynamic analysis -- X-FEM -- Stress intensity factor; Boundary element methods -- Periodicals; Engineering mathematics -- Periodicals; Équations intégrales de frontière, Méthodes des -- Périodiques; Mathématiques de l'ingénieur -- Périodiques; Boundary element methods; Engineering mathematics; Periodicals; 620.00151
• DOI: 10.1016/j.enganabound.2015.04.003
• Languages: English
• ISSNs: 0955-7997

Abstract

Abstract: Two-dimensional (2D) dynamic stress concentration problems are analyzed using the wavelet Galerkin method (WGM). Linear B-spline scaling/wavelet functions are employed. We introduce enrichment functions for the X-FEM to represent a crack geometry. In the WGM, low-resolution scaling functions are periodically located across the entire analysis domain to approximate deformations of a body. High-resolution wavelet functions and enrichment functions including crack tip singular fields are superposed on the scaling functions to represent the severe stress concentration around holes or crack tips. Heaviside functions are also enriched to treat the displacement discontinuity of the crack face. Multiresolution analysis of the wavelet basis functions plays an important role in the WGM. To simulate the transients, the wavelet Galerkin formulation is discretized using a Newmark- β time integration scheme. A path independent J -integral is adopted to evaluate the dynamic stress intensity factor (DSIF). We solve dynamic stress concentration problems and evaluate DSIF of 2D cracked solids. The accuracy and effectiveness of the proposed method are discussed through the numerical examples.