Pipe Anchor Discontinuity Analysis: Axisymmetric Closed Form Solutions Utilizing Bessel's Functions Fourier Series

摘要

One of the paradigmatic classes of problems that frequently arises in elasticity is the axisymmetric stress and deformation determination in a hollow cylinder (pipe). Over the past fifty years, the computational tools wvailable to the piping engineer have changed dramatically and thereby have caused the implementation of solutions to the basic problems of elasticity to change likewise. The need to obtain closed form elasticity solutions, however, has always been a drivign force in industry. The utilization of symbolic calculus that is currently available through a number o fwoftware packages makes closed form soutions over the past fifty years to a variety of axisymmetric stress problems involving hollow circular cylinders employing a Fourier series representation fo the imposed internal pressures and restrained displacemetns. A general solution technique is introduced fo rthe axisymmetric discontinuity stresses resulting from an anachor restraint on a series of pipe geometries. These solutions can be economically implemented on today's symbolic calculus software packages with no loss in solution accuracy when compared to often more expensive techniques such as the finite element method. Verification of the axisymmetric solution technique is illustrated by the comparison of results for the closed form solutions versus those approximated by the finite element technique. Extensions of th general axisymmetric solution technique to other geometries and applied loads are also discussed while the numerical and graphical results are tendered.