A Boundary Integral Approach to Attachment/Spherical Shell Interaction

In pressure vessel applications, the accurate evaluation of the state of stress in the vicinity of nozzles or rigid attachments is of vital importance to the structural integrity of the vessel. Consequently, a number of investigations have paid attention to the problem and, through analytical and numerical approaches, provided information concerning the effect of system parameters, such as shell curvature and attachment geometry, on stress concentration and effective shell stiffness. While analytical solutions have only been able to provide information to axisymmetric problems, finite element approaches have been widely used as an attractive alternative. In evaluating the latter, one can identify the high computational cost that accompanies analyses dealing with complex systems. In this study, the performance of a boundary integral scheme is assessed as a possible analytical and/or numerical tool in dealing with spherical shells interacting with attachments. Such method hopes to achieve a close to analytical solutions representation of the stress state in the vicinity of the attachment that is accompanied by significant reduction in the computational cost. To achieve this, a set of integral equations, which satisfy the edge constraints, are reduced to a system of algebraic equations. These integral equations utilize singular solutions obtained for deep (nonshallow) spherical shells, which in turn are more representative of the shell domain. Explicit comparisons, on the basis of representative shell-attachment interaction problems, between the finite element and boundary integral computational techniques are conducted in order to assess the performance and efficiency of the new method. Finally, shell stiffnesses in the form of insert translations and rotations are presented in dimensionless form.