William Ranson

Pipe-anchor discontinuity analysis utilizing power series solutions, Bessel functions, and Fourier series

Abstract One of the paradigmatic classes of problems that frequently arise in piping stress analysis discipline is the effect of local stresses created by supports and restraints attachments. Over the past 20 years, concerns have been identified by both regulatory agencies in the nuclear power industry and others in the process and chemicals industries concerning the effect of various stiff clamping arrangements on the expected life of the pipe and its various piping components. In many of the commonly utilized geometries and arrangements of pipe clamps, the elasticity problem becomes the axisymmetric stress and deformation determination in a hollow cylinder (pipe) subjected to the appropriate boundary conditions and respective loads per se. One of the geometries that serve as a pipe anchor is comprised of two pipe clamps that are bolted tightly to the pipe and affixed to a modified shoe-type arrangement. The shoe is employed for the purpose of providing an immovable base that can be easily attached either by bolting or welding to a structural steel pipe rack. Over the past 50 years, the computational tools available to the piping analyst 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 driving force in engineering. The employment of symbolic calculus that is currently available through numerous software packages makes closed form solutions very economical. This paper briefly traces the solutions over the past 50 years to a variety of axisymmetric stress problems involving hollow circular cylinders employing a Fourier series representation. In the present example, a properly chosen Fourier series represent the mathematical simulation of the imposed axial displacements on the outside diametrical surface. A general solution technique is introduced for the axisymmetric discontinuity stresses resulting from an anchor restraint on a selected of pipe geometry. These solutions can be economically implemented on todays 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 the general axisymmetric solution technique to other geometries and applied loads are also discussed while the numerical and graphical results are tendered.

Planar surface reconstruction using circle generator laser light

A method is presented for finding the spatial position and orientation of a planar surface using a laser light source that generates structured light in the form of concentric circles. The purpose of the work is to provide the foundation for mapping regular and irregular surfaces for use in spatial surface reconstruction. The results of this work will lead to practical applications in the evaluation of pre- and post-surface deformation, and the reconstruction and representation of higher ordered surfaces. The latter having application as an alternative approach for capturing surfaces in direct geometric terms as opposed to the copious data discretization methods employed in surface reconstruction today.

Structural Aging Monitoring via Web-Based Nondestructive Evaluation (NDE) Technology

To assist owners and operators in real-time on-site monitoring and damage assessment of aging structures, we propose an “aging structure monitoring system” using direct measurements and web-based transmission technology. Such a system from field detection of surface or subsurface cracks to computer modeling/analysis/verification of simulated fatigue crack growth with ultimate delivery of remaining life prediction, is designed to have four major components: (1) The system is capable of transmitting from the field via internet to the office computer direct measurement data that are being collected in the field by personnel using handheld optical scanners to read bar-code-like strain gages either laser bonded (permanent marking) or adhesively bonded to selected critical high stress areas of the surface of a structure. (2) The office computer has a customized database that stores not only relevant geometric and material property data with variability information, but also a history of prior loadings, cumulated strain (plastic) measurements and fatigue crack length or crack tip opening displacement measurements. Such database is constantly being updated and enhanced with variability estimates subsequent to an event on a continouus or periodic inspection basis. (3) Using a minimum of four commercially-available finite-element method (FEM) packages, e.g., ABAQUS, ANSYS, LS-DYNA, and MPAVE, a numerical simulation experiment is conducted on real time using a fracture mechanics and fatigue damage theory-based deterministic model and the direct measurement data. This model is capable of predicting remaining lives for selected future loading scenarios. (4) The results of the FEM simulations are verified via a web-based statistically designed experiment using DATAPLOT where an uncertainty-bounded estimate of the remaining lives of the structure for selected loadings is delivered in real time to the field for decision making. Significance and limitations of this web-based direct-measurement approach to fatigue modeling are discussed.Copyright

Crack Detection and Monitoring Crack Growth in Fastener Holes Using the DMI Optical SR-2 Strain Measurement Technology

Results are presented for crack initiation detection and crack growth monitoring using DMI SR-1 Strain Gages and DMI SR-2 Reader in two Northrop Grumman aluminum test coupons subjected to cyclic loading. Results demonstrate the utility of the technology to detect cracks and crack growth in holes. The DMI SR-1 strain gage is applied so that it frames the hole in the test coupon. This results in strain measurements at tangents to hole and associated shear strains. A differential strain reading between gage lengths on parallel and opposing sides of a hole, resulting from discontinuities in the material surrounding a hole, indicates crack initiation and as the crack grows the differential reading increases.© 2007 ASME

Optical Strain Gage Measurement of Accumulated Damage Around Geometrical Discontinuities Such as in Pipes and Pressure Vessels

The optical strain gage technologies are used to measure strain and evaluate accumulated damage around a geometrical discontinuity such as holes, notches or fillets that exist in pipes and pressure vessels. Results are presented for coupons undergoing stress. The results are consistent with theory. The DMI technologies optically observe record and measure the deformation of a target affixed to the surface of the part undergoing stress in a region of expected maximum strain or a region physically and mathematically linked to the region of maximum strain. Data is acquired from its proprietary target (strain gage) or 2D Data Matrix mark used as a target/strain gage. The deformation of the mark/strain gage as the object undergoes deformation is mathematically described by total strain equal to the elastic and plastic strain components. This equation can be rewritten to express strain life in terms of plastic strain. The measured plastic component of strain is directly related to the damage.Copyright