Tham khảo tài liệu 'volume 08 - mechanical testing and evaluation part 2', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Fig. 25 Finite element model of a strip under tension and containing a hole. Source Ref 24 Along the vertical line of symmetry each nodal point is permitted to move vertically but not laterally. Along the horizontal line of symmetry each node is permitted to move laterally but not vertically. These constitute the constraints on the problem. At each of the nodal points along the upper surface equal loads are applied that add up to the total applied load. Alternatively uniform small displacements in the vertical direction can be applied to each node along the upper surface. This constitutes the loading for the problem. The material behavior is represented by elastic modulus E and Poisson ratio V in the constitutive equations Eq 23a 23b and 23c. Results of solution of the simultaneous equations for all elements are shown in Fig. 26. Note that the axial stress 5y along the horizontal plane through the hole has a peak value at the edge of the hole. Also a small lateral stress distribution ax occurs along the horizontal plane of symmetry. Note that along the vertical centerline the axial stress is zero at the hole and then increases to the applied stress while the lateral stress is compressive. Fig. 26 Stress distributions calculated for the model shown in Fig. 25. Source Ref 24 To evaluate failure by yielding the stresses in each element of the model can be substituted into Eq 24. The resulting stress magnitude is called the von Mises stress and can be compared to the material yield strength ơo to determine if yielding will occur. For example Fig. 27 shows a contour plot of the von Mises stress for the problem shown in Fig. 25. Note that yielding would occur first at the inside of the hole and propagate along a 45 plane illustrated by the band of high von Mises stress. Fig. 27 Contour plot of von Mises stress for the model in Fig. 25. Source Ref 24 As another example a finite element analysis of the contact bearing load described previously in Fig. 22 is shown in Fig. .
