Thick-walled cylinder analyses

Partially Plastic Thick-Walled Cylinders. As the internal pressure is increased above the yield pressure, P, plastic deformation penetrates the wad of the cylinder so that the inner layers are stressed plasticady while the outer ones remain elastic. A rigorous analysis of the stresses and strains in a partiady plastic thick-waded cylinder made of a material which work hardens is very compHcated. However, if it is assumed that the material yields at a constant value of the yield shear stress (Fig. 4a), that the elastic—plastic boundary is cylindrical and concentric with the bore of the cylinder (Fig. 4b), and that the axial stress is the mean of the tangential and radial stresses, then it may be shown (10) that the internal pressure, needed to take the boundary to any radius r such that is given by... 

Bursting tests have been carried out on neatly a hundred thick-walled cylinders made of carbon, low alloy, and stainless steels, together with some nonferrous materials. The diameter ratio of the cylinders varied from 1.75 to 5.86, and some tests were carried out at 660°C. An analysis of the results (19) showed that 90% of the cylinders burst within 15% of the value given by equation 17. 

Each of these steps depends on the process before. The software suite starts with the material selection, in which also an individual material can be dehned. Fiber orientations and the number of plies can be selected in a following step. All material parameters must be chosen before the analysis can start. Six structural analysis modules can be differentiated with the CDS software suite. These solid mechanic modules are thick-walled cylinder, thin plate, thin plate impact-fastener modeling, thick plate, discontinuous tile modeling and compliant beam interlayer analysis. The CDS software suite allows changing the parameters of the manufacturing process or the laminate structure in real time. Four result sections for those parameter changes are provided by the software the effective properties, thermal-processing response, stress-strain results and the failure response. The CDS software suite is a complete analysis tool kit which is easy to use for the client. The software also allows export into an external simulation tool. 

LAMi THiORY OF STRESS ANALYSIS FOR THICK-WALLED CYLINDERS... 

Lome Theory of Stress Analysis for Thick-walled Cylinders... 

Kotulla B. et al. Three-dimensional analysis of stresses and crack development in prestressed thick-walled cylinders, 6th Conference on SMIRT, Paris, Paper H3/1, 1981. Cheung K. C. An assessment of long-term structural behaviour of an asymmetric multicavity PCRV, 6th Conference on SMIRT, Paris, August 1981, Paper H3/9, 1981. 

While it is beyond the scope of this introductory text to fully develop and solve a wide variety of multidimensional stress analysis problems in viscoelasticity, we provide here a classic example to illustrate the use of the correspondence principle to derive a viscoelastic solution from a practical problem in elasticity. We choose here the problem of a Thick Walled Cylinder, often referred to as the Lame Solution. In the following, we first generate the elasticity solution to the classic Lame problem, then extend this elasticity solution to that for a reinforced thick walled cylinder. Subsequently, we use the latter solution to develop the viscoelastic solution via the correspondence principle. 

The experimental evaporator (micro two-phase jets generator) is shown on Fig. 10 -11. The heater block of the evaporator includes a hole machined directly in the centre of the copper cylinder with thick walls and is used for the installation of a nickel sintered powder evaporator. Some thermocouples are disposed inside the copper block to control the heat flow to the evaporator from the electric heater disposed on its outer surface. To minimize heat losses, the heater block was insulated. Heat input to the evaporator was calculated by conduction analysis using thermocouples that were placed at a known distance apart in the copper heater block. 

The dimensionless quantities defined above for a plane wall can also be used for a cylinder or sphere by replacing the space variable x by r and the half-thickness L by the outer radius r. Note that the characieristic length in the definition of the Biot number is taken to be the half-thickness L for the plane wall, and the radius for the long cylinder and sphere instead of 1//A used in lumped system analysis. 

Analysis (a) This short cylinder can physically bo formed by the intersection of a long cylinder of radius = 5 cm and a plane wall of thickness 2L = 12 cm. 

Standard engineering analysis can be used. Consider a cylinder of inside radius r, outside radius it, and length L containing a fluid under pressure p. The circumferential or hoopwise load in the wall (r = thickness) is proportional to the pressure times radius = pr, and the... 

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