tailieunhanh - dohrmann Episode 1 Part 5

Tham khảo tài liệu 'dohrmann episode 1 part 5', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | this example that these constraints cause the element to be too stiff. It was found that a reformulated EUST9 element which uses single point integration mean quadrature for the deviaXoric strain energy improves the element performance but offers no clear advantage over UST8. The enhanced uniform strain element EUST11 only has four constraints that restrict the motion of virtual mid-face nodes 5 . 8 see Eqs. 16-19 . In addition deformations may vary bilinearly along the element edges. Plots of the energy norm for the different element types are shown in Figure 7 for V . The results for the eleven-node enhanced uniform strain element EUST11 are clearly more accurate than the others. The slope much less than unity for CST4 indicates that the meshes are not of sufficient refinement for asymptotic convergence to occur. Example 2 The second example considers a problem in which the displacements of all nodes on the boundary are specified. For the 2D problem nodes on the boundaries Xi 0 and Xi hl i 1 2 are subjected to the enforced displacements 1 21 22 23 a x X 2xiX2 2 21 22 23 a xf - 22 22221 77 78 where a is a constant and the plane strain assumption is applied. The nodal displacements on the boundaries Xi 0 and Xi hi 1 2 3 for the 3D problem are specified as 111 21 22 23 a x X3 - 2x 2x X2 2xiX3 5x2x3 79 2 21 22 23 a xj x - 222 22223 22221 52321 80 3 21 22 23 a 2i -I-22 - 223 22321 22322 52122 81 The elasticity solutions to the 2D and 3D boundary value problems are given by Eqs. 77-81 as well. The total strain energies for the 2D and 3D problems are given respectively by Utot IQhMhị Ga2 3 82 and utot 6hih2h3 5 hi hĩ h2 3 ỉi7i2 h2h3 ỡữ2 83 One can confirm that the elasticity solutions have no volumetric strain. That is È È È 84 ƠX1 ux ux Consequently the exact value of the volumetric strain energy UVO1 is zero. Calculated values of Utot for the 2D plane strain problem are shown in Table 4. In addition to the 2D elements mentioned previously Table 4 includes

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