TAILIEUCHUNG - Lifetime-Oriented Structural Design Concepts- P18

Tham khảo tài liệu 'lifetime-oriented structural design concepts- p18', công nghệ thông tin, đồ họa - thiết kế - flash phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 468 4 Methodological Implementation e adapt. 3-Pt-Gauss-Integration 1 e adapt. Simpson-Integration 1 1 e adapt. 4-Pt-Gauss-Integration 2 3 4 5 6 . e adapt. Combination NC-Gauss Fig. . Strain e from equation for the integral Fig. . Number of integration points used in the numerical integration of Numerical Methods 469 which can be rewritten as fë x y 32 2 x2 1 x 2 - rx 1 x 2 y x 2 x 7 6 x 2 x y2 1 x 2 y4 y6 . By integrating the function fe x y analytically in the integration range x G 1 and y G 1 the integration value f6 x y dx Jx y is obtained. The numerical results are shown in Figures and . p-Version of the XFEM By using the XFEM with bi-linear shape functions to compute the displacements of the tension test shown in Figure the resulting displacements ux around the crack tip are shown in Figure for the deformed system. The black line indicates the asymptotic displacements of the crack surfaces in the vicinity of the crack tip. It can be seen from the figure that the approximation of the displacement field results in big differences to the analytical solution. Furthermore a constriction is noticeable which occurs at the position where the crack cuts the edge of the crack tip element. The results can be improved by using a refinement of the element mesh h-version or h-extension as well as higher order polynomials for the shape functions p-version or p-extension . Using a h-extension will improve the results but the constriction is still visible but closer to the crack tip while using a p-version for the shape functions results in the displacements 470 4 Methodological Implementation Fig. . Displacements ux for the deformed system using bilinear shape functions Fig. . Displacements ux for the deformed system left using bi-quadratic shape functions right using quadratic hierarchical shape functions shown in figure . .

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