tailieunhanh - Nonlinear Finite Elements for Continua and Structures Part 14

Tham khảo tài liệu 'nonlinear finite elements for continua and structures part 14', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 66 o QUAD4 ASMD QBI ASQBI ASOI ADS and and OI Pian-Sumihara Figure 16. Convergence of displacement and energy error norms V plane strain To assess the coarse mesh accuracy of the elements the normalized end displacements point A if Fig. 14 for the 1x4 element mesh are shown in Table 6. A coarse 1x4 element mesh of skewed elements was also run and the normalized end displacements point A in Fig. 17 are shown in Table 7. Pian-Sumihara is slightly better than ASQBI for the skewed elements but the difference is minor. L 4 12 typ. Pt. A 67 Figure 17. Skewed coarse mesh with 0 Table 6. dyFEM dyAnalytical at point A of mesh in Fig. 14 rectangular elements Material QUAD4 ASMD QBI ASQBI and OI and ADS Pian-Sumihara ASOI 1 2 Table 7. dyFEM dyAnalytical at point A of mesh in Fig. 17 skewed elements Material QUAD4 ASMD ASQBI Pian- Sumihara ASOI ADS 1 2 Circular Hole in Plate. This problem was considered to evaluate the performance of these elements in a different setting. A plate with a hole solved by R. C. J. Howland 1930 is shown in Fig. 18. The solution is in the form of an infinite series and gives the stress field around the circular hole in the center of an axially loaded plane stress plate of finite width and of infinite length. The series converges only within a circular region around the hole. The diameter of this circular area is equal to the plate width. The displacement field is not given so convergence of the displacement norm could not be checked. 68 The shaded area indicates For the finite element meshes the plate length was taken to be twice the plate width. The nodes at which the load is applied are outside the region in which the analytical solution converges so the analytical solution could not be used to determine the load distribution on the end of the plate. The nodal forces were therefore calculated by .

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