Boundary element analysis of static plane problems in size-dependent consistent couple stress elasticity. (1st November 2021)

• Record Type: Journal Article
• Authors: Lei, Jun; Ding, Pengsheng; Zhang, Chuanzeng
• Is Part Of: Engineering analysis with boundary elements. Volume 132(2021)
• Page Start: 399
• Page End: 415
• Publication Date: 2021-11-01
• Subjects: Couple stress theory -- Boundary element method -- Size-dependence -- Stress concentration -- Multiple holes -- Static problems; 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.2021.08.014
• Languages: English
• ISSNs: 0955-7997

Abstract

Abstract: Based on a consistent couple stress elasticity theory, a two-dimensional (2D) boundary element method (BEM) is developed to solve the boundary value problems in the couple stress elastic materials. The displacement boundary integral equations (BIEs) are applied to compute the mechanical quantities on the boundary. The integral representations for the generalized strains and stresses at internal points are also presented together with the explicit expressions for the high-order fundamental solutions. The collocation method is adopted for the spatial discretization of the BIEs. Some special numerical and semi-analytical techniques are provided for the evaluation of weakly and strongly singular integrals. The sinh transformation is used to deal with the nearly singular integrals for near-boundary internal points or boundary nodes in thin structures. An error-controlled integration scheme is adopted for computing the non-singular integrals to improve the accuracy. Three representative 2D boundary value problems in the consistent couple stress elasticity theory are studied by the developed BEM. The correctness and accuracy of the present BEM results are verified by comparison with the corresponding analytical results. Then, multiple flat elliptical holes in a plate are numerically studied to show the interaction effects on the stress concentration.