Eine Plattform für die Wissenschaft: Bauingenieurwesen, Architektur und Urbanistik
Eine Plattform für die Wissenschaft: Bauingenieurwesen, Architektur und Urbanistik
On solving 3D elasticity problems for inhomogeneous region with cracks, pores and inclusions
Abstract Studying stress concentration and stress intensity factors (SIFs), being of importance for multiple scientific and engineering applications, we focus on developing an efficient means for accurate, robust and stable evaluation of these quantities. 3D elasticity problems for a piece-wise homogeneous region (finite or infinite), containing cracks, pores and inclusions, are considered. The combination of singular and hypersingular boundary integral equations, specially tailored for such problems, is used as start point. The boundary is represented by four-vertex, in general curvilinear, boundary elements. An element is transformed into a plane trapezoid by a transformation with Jacobian expanded into a power series in local coordinates. In particular cases, the trapezoidal element may be a parallelepiped, rectangle, square or triangle. Higher order approximation of the density, accounting for its asymptotic behavior near a crack edge, is employed to increase the accuracy of SIF evaluation. We show that using power-type asymptotics results in recurrent equations. They reduce evaluation of influence coefficients to arithmetic operations with relatively small number of starting integrals over the element. In the case of zero exponent, an element is ordinary (non-singular). Then, the number of starting integrals is at most 3 and we present analytical formulae for their evaluation. In the case of an arbitrary exponent, the number of starting integrals is at most 8 and they are evaluated numerically. In the case of square-root asymptotics, important for fracture mechanics, hydraulic fracturing and mining applications, the number of starting integrals is 5, and we show that they can be evaluated by using the highly efficient algorithms suggested. Then the approach developed provides drastic (an order) accuracy increase for SIF evaluation under practically insignificant growth of the computation cost as compared with using ordinary elements only. The remarkable feature of the method developed is that being of higher order accuracy it evaluates the influence coefficients almost analytically in many practically important cases involving ordinary elements and singular edge elements. Known benchmark solutions serve us to check the accuracy and stability of the method and to make conclusions on a reasonable form and on the sizes of edge elements. The examples demonstrate the potential of the method for solving problems under consideration.
On solving 3D elasticity problems for inhomogeneous region with cracks, pores and inclusions
Abstract Studying stress concentration and stress intensity factors (SIFs), being of importance for multiple scientific and engineering applications, we focus on developing an efficient means for accurate, robust and stable evaluation of these quantities. 3D elasticity problems for a piece-wise homogeneous region (finite or infinite), containing cracks, pores and inclusions, are considered. The combination of singular and hypersingular boundary integral equations, specially tailored for such problems, is used as start point. The boundary is represented by four-vertex, in general curvilinear, boundary elements. An element is transformed into a plane trapezoid by a transformation with Jacobian expanded into a power series in local coordinates. In particular cases, the trapezoidal element may be a parallelepiped, rectangle, square or triangle. Higher order approximation of the density, accounting for its asymptotic behavior near a crack edge, is employed to increase the accuracy of SIF evaluation. We show that using power-type asymptotics results in recurrent equations. They reduce evaluation of influence coefficients to arithmetic operations with relatively small number of starting integrals over the element. In the case of zero exponent, an element is ordinary (non-singular). Then, the number of starting integrals is at most 3 and we present analytical formulae for their evaluation. In the case of an arbitrary exponent, the number of starting integrals is at most 8 and they are evaluated numerically. In the case of square-root asymptotics, important for fracture mechanics, hydraulic fracturing and mining applications, the number of starting integrals is 5, and we show that they can be evaluated by using the highly efficient algorithms suggested. Then the approach developed provides drastic (an order) accuracy increase for SIF evaluation under practically insignificant growth of the computation cost as compared with using ordinary elements only. The remarkable feature of the method developed is that being of higher order accuracy it evaluates the influence coefficients almost analytically in many practically important cases involving ordinary elements and singular edge elements. Known benchmark solutions serve us to check the accuracy and stability of the method and to make conclusions on a reasonable form and on the sizes of edge elements. The examples demonstrate the potential of the method for solving problems under consideration.
On solving 3D elasticity problems for inhomogeneous region with cracks, pores and inclusions
Jaworski, Dawid (Autor:in) / Linkov, Aleksandr (Autor:in) / Rybarska-Rusinek, Liliana (Autor:in)
Computers and Geotechnics ; 71 ; 295-309
01.01.2015
15 pages
Aufsatz (Zeitschrift)
Elektronische Ressource
Englisch
On solving 3D elasticity problems for inhomogeneous region with cracks, pores and inclusions
| Online Contents | 2016
On solving 3D elasticity problems for inhomogeneous region with cracks, pores and inclusions
| British Library Online Contents | 2016
| Engineering Index Backfile | 1966