PSI - Issue 23

Michal Jedlička et al. / Procedia Structural Integrity 23 (2019) 445– 450 Michal Jelička, Václav Rek, Ji ří Vala / Structural Integrity Procedia 00 (2019) 000 – 000

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large number of equally spaced integration nodes of standard Gaussian quadrature (e.g. 64 Gauss integration nodes for a hexahedron). The better but more complicated approach relies on the use of an available mesh generator to form the tetrahedral mesh within an element, considering the position and shape of the respective type of discontinu ity. This internal mesh does not lead to an increase of the number of degrees of freedom, only provides partial values of a particular element volume for the numerical quantification of the corresponding energy functionals, where inte grands represent density of some energy. Alternatively, it provides possible positions of integration nodes for quan tification of stresses (but not necessary) for both linear and nonlinear analysis, too.

Fig. 1. a) A specified crack, b) forcing a fully cracked finite element.

Fig. 2. Implementation of the phantom node method.

Fig. 3. a) Illustration of various approaches to numerical integration: a) the Gaussian integration with 64 nodes; b) the method of internal meshing of elements.

Fig. 4. Two adjacent finite elements a) with a specified crack, b) with an artificial computational crack.