Journal off Pressure Vessel Technology Notch-Stress Analysis by FE Submodeling

1 This paper presents experiences in detailed finite element analyses of pressure vessel components with respect to load-carrying capacity and fatigue strength. The application of the submodeling technique for shell-to-solid models is discussed. The finite-element method (FEM) has become the most accurate and most efficient instrument of structural analysis in pressure vessel design. Shell elements are widely used for analyzing large three-dimensional structures such as vessels with adjacent pipes and supports. The application of these elements leads to a reduction of modeling and computing time in comparison with volume (solid) models. The properties of shell elements make it possible to separate membrane and bending stress components easily from each other and to assess the load-carrying capacity of the given structure by using, for example, the system of stress categories according to the ASME Code. The separation of global and local membrane components remains a problem. Nevertheless, there are serious difficulties in the modeling of differences in structural stiffness (e.g., nozzle-to-vessel connections with different wall thickness) and the inclusion of constructive details such as weld seams, grooves, knuckles, or flanged-out connections. Recent work It is possible to involve most constructive details in the FE model by using volume elements (solids). The limits will be set by the capacity of the computer with respect to memory/ disk space (admissible number of main degrees of freedom in the FE model) and to acceptable computing times. The analysis of complete three-dimensional solid models can easily become much too time-consuming. The advantages of both shell and solid FE models can be combined by using the submodeling technique (cut-boundary displacement method, specified boundary displacement method) which is implemented in most commercial FE programs. It is based on St. Venant's principle, which states that Fig. 1 Shell-to-solid model of a nozzle-cylinder intersection if an actual distribution of forces is replaced by a statically equivalent system, the distribution of stress and strain is altered only near the regions of load application, as described in the ANSYS Users Manual (1994). It is important to place the cut boundaries at a sufficient distance from a stress concentration. Figure 2 provides a comparison of stress concentration factors a = a eq /a M (maximum equivalent stress o" eq referred to the circumferential membrane stress of the cylinder a M = pDIXT) as a function of the diameter ratio for a cylinder (mean diameter D and wall thickness T) with a small hole (diameter d) submitted to internal pressure loading p. The solid model cannot be meshed fine enough to reflect the notch stresses for very small holes (low d/D ratios) correctly. The shell-to-solid submodel allows a much finer mesh in the region of stress concentration with the same number of degrees of freedom (DOF). Elements with quadratic shape functions were used in all the exemplary analyses. It is obvious that the theoretical value of 2.5 for very small holes is well approximated by the shell-to-solid submodel. Another question is to what extent peak stresses must have reduced within the submodel to yield correct results. Equation

Orientational Effects and Random Mixing in 1-Alkanol + Alkanone Mixtures

1-Alkanol + alkanone systems have been investigated through the data analysis of molar excess functions, enthalpies, isobaric heat capacities, volumes and entropies, and using the Flory model and the formalism of the concentrationconcentration structure factor (SCC(0)). The enthalpy of the hydroxyl-carbonyl interactions has been evaluated. These interactions are stronger in mixtures with shorter alcohols (methanol-1-butanol) and 2-propanone or 2-butanone. However, effects related to the self-association of alcohols and to solvation between unlike molecules are of minor importance when compared with those which arise from dipolar interactions. Physical interactions are more relevant in mixtures with longer 1-alkanols. The studied systems are characterized by large structural effects. The variation of the molar excess enthalpy with the alcohol size along systems with a given ketone or with the alkanone size in solutions with a given alcohol are discussed in terms of the different contributions to this excess function. Mixtures with methanol show rather large orientational effects. The random mixing hypothesis is attained to a large extent for mixtures with 1-alkanols ≠ methanol and 2-alkanones. Steric effects and cyclization lead to stronger orientational effects in mixtures with 3-pentanone, 4-heptanone, or cyclohexanone. The increase of temperature weakens orientational effects. Results from SCC(0) calculations show that homocoordination is predominant and support conclusions obtained from the Flory model.Ministerio de Ciencia e Innovación, under Project FIS2010-1695