tailieunhanh - Elasticity Part 8

Tham khảo tài liệu 'elasticity part 8', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Sadd Elasticity Final Proof 6 14pm page 199 8-26. Solve the rotating disk problem of Example 8-11 for the case of an annular disk with inner radius a and outer radius b being stress free. Explicitly show that for the case b a the maximum stress is approximately twice that of the solid disk. Two-Dimensional Problem Solution 199 TLFeBOOK This page intentionally left blank TLFeBOOK Sadd Elasticity Final Proof 2 57pm page 201 9 Extension Torsion and Flexure of Elastic Cylinders This chapter investigates particular solutions to the problem of cylindrical bars subjected to forces acting on the end planes. The general problem is illustrated in Figure 9-1 where an elastic cylindrical bar with arbitrary cross-section R and lateral surface S carries general resultant end loadings of force P and moment M. The lateral surface is taken to be free of external loading. The cylindrical body is a prismatic bar and the constant cross-section may be solid or contain one or more holes. Considering the components of the general loading leads to a definition of four problem types including extension torsion bending and flexure. These problems are inherently three-dimensional and thus analytical solutions cannot be generally determined. In an attempt to obtain an approximate solution in central portions of the bar Saint-Venant presumed that the character of the elastic field in this location would depend only in a secondary way on the exact distribution of tractions on the ends of the cylinder and that the principal effects are caused by the force resultants on the ends Saint-Venant s principle . As such he relaxed the original problem by no longer requiring the solution to satisfy pointwise traction conditions on the ends but rather seeking one which had the same resultant loading. This approach is similar to our previous two-dimensional studies of beam problems in Chapter 8. Under these conditions the solution is not unique but provides reasonable results away from .