Analysis of the stress singularity field at a vertex in 3D-bonded structures having a slanted side surface

Abstract

a b s t r a c tThe stress singularity that occurs at a vertex in a joint with a slanted side surface is investigated. The orders of stress singularity at a vertex and at a point on stress singularity lines for various material properties are determined using eigenanalysis. The stress distribution on an interface and the intensity of stress singularity at the vertex are investigated using BEM. It is shown that the order of stress singularity at the vertex in the joints can be reduced by slanting a side surface so as to decrease the angle between the interface and the side surface. The results of BEM analysis reveal that the distribution of stress on the interface is influenced by the slanted side surface. Finally, the 3D intensities of the singularity for stress components which are continuous at the interface are newly defined and determined for various material combinations.

On ensuring structural integrity for configurations with stress singularities: a review

“…Recent reviews of such asymptotic identifications are available . Additional recent asymptotic identifications are also available …”

“…Often these additional identifications are for more complex local configurations than those in the references in the cited reviews: sometimes they simply fill in a gap in the literature. For classical elasticity with local configurations comprised of isotropic and piecewise homogeneous, linear elastic materials, all the stress singularities asymptotically identified that have been found to date since 2004 are discussed in the studies . Examples of stress singularities identified since 2004 for anisotropic elastic materials are given in the previous studies ; for functionally graded elastic materials; for finite strain in elastic materials; and for varying size scales …”

Restrictions on the stress components in the edge points of the homogeneous elastic body

“…The solution in the classical case is constructed by various methods: operational calculus (Williams, 1952, Cook & Erdogan, 1972, Sinclair, 2004, functions of a complex variable (Parton & Perlin, 1981), Erie functions and integral equations (Cook & Erdogan, 1972;Andreev, 2014), separation of variables and expansion in series into various functions (Shannon et al, 2014(Shannon et al, , 2015Galadzhiev et al, 2011;He & Kotousov 2016), etc. The authors who are using numerical methods: finite element method (Koguchi & Muramoto, 2000;Barut et al, 2001;Xu & Sengupta, 2004;Lee et al, 2006;Xu et al, 2016;Dimitrov et al, 2001), finite element method in combination with by searching for eigenvalues by the Arnold method (Apel et al, 2002), the method of boundary elements and the method of boundary states (Mittelstedt & Becker, 2006;Koguchi & Da Costa, 2010 ), implementing the asymptotic idea by unlimited refinement of the FE-grid at the region near the special points or by constructing special finite elements. Many authors of asymptotic solutions in the study of the stress state near singular points (Williams, 1952;Koguchi & Muramoto, 2000;Wu, 2006, Koguchi & Da Costa, 2010He & Kotousov, 2016) are looking for singularity indices -parameters for solving the characteristic equations of the corresponding homogeneous problems.…”

Stress State at the Vertex of a Composite Wedge, One Side of Which Slides Without Friction Along a Rigid Surface

“…Authors of numerical approaches realize the asymptotic idea through unlimited grid model refinement of the area close to the singular point. Also there are studies by finite element method in Koguchia and Muramoto (2000), Xu and Tong(2016)), method of boundary elements in Mittelstedt (2005), Koguchi (2010), method of boundary conditions in Ryazantseva (2015). Mathematical problems, concerning the justification of asymptotic methods for studying of mechanics problems of a deformable solid body with singular points, were considered and successfully resolved in studies Kondratiev (1967), Mazya(1976).…”