Computer Programs

NAME OR DESIGNATION OF PROGRAM, COMPUTER, DESCRIPTION OF PROBLEM OR FUNCTION, METHOD OF SOLUTION, RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM, TYPICAL RUNNING TIME, UNUSUAL FEATURES OF THE PROGRAM, RELATED AND AUXILIARY PROGRAMS, STATUS, REFERENCES, MACHINE REQUIREMENTS, LANGUAGE, OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED, OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS, NAME AND ESTABLISHMENT OF AUTHOR, MATERIAL, CATEGORIES

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Program name | Package id | Status | Status date |
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BUCKLE | NESC0667/01 | Tested | 01-APR-1977 |

Machines used:

Package ID | Orig. computer | Test computer |
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NESC0667/01 | IBM 360 series | IBM 360 series |

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3. DESCRIPTION OF PROBLEM OR FUNCTION

BUCKLE is a one-dimensional

computer code compiled to calculate the change in ovality, of an

initially oval, closed-end finite length tube, as a function of

time, temperature, neutron flux and uniform external pressure.

The basic concept employed in BUCKLE is that a tube, which is

slightly out-of-round, tends to become more out-of-round with time

when subjected to net uniform external pressure. The timewise

change in ovality occurs as a consequence of creep deformations

arising from tangential compressive and tangential bending

stresses produced by uniform external pressures acting on an

initially oval tube.

BUCKLE is a one-dimensional

computer code compiled to calculate the change in ovality, of an

initially oval, closed-end finite length tube, as a function of

time, temperature, neutron flux and uniform external pressure.

The basic concept employed in BUCKLE is that a tube, which is

slightly out-of-round, tends to become more out-of-round with time

when subjected to net uniform external pressure. The timewise

change in ovality occurs as a consequence of creep deformations

arising from tangential compressive and tangential bending

stresses produced by uniform external pressures acting on an

initially oval tube.

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4. METHOD OF SOLUTION

BUCKLE employs two mathematical models with an incremental approach to calculate the change in ovality of an initially oval tube, as a function of time. One mathematical model describes the interrelationships between membrane and bending stresses, strain, and ovality of a symmetrical cross section of a hollow cylinder. The second mathematical model describes the interrelationships between stress and strain rate as a function of temperature, neutron flux and time. Although the analytical mechanics model is one-dimensional, stress biaxiality and material anisotropy effects are indirectly included through the selection of the stress coefficient in the creep equation model.

The computational procedure is based on the assumption that for a sufficiently small interval of time, the strain-producing stresses are essentially constant throughout the time interval. At the end of each time interval, the incremental creep strain that occurred during the time interval is used to calculate an incremental change in the ovality of the tube. This increment of ovality is added to the tube ovality existing at the beginning of the time interval. This new value of ovality is then used to recalculate the shell membrane and bending stresses which are used to calculate a new increment of creep strain in the subsequent time interval. If the time intervals are sufficiently small, the solution obtained is approximate and will tend to converge to the real solution. The repetitive calculations are terminated by a specified time limit or when the ovality and/or combined stresses equal specified values.

An option was added with Edition B to employ either a strain hardening or time hardening rule in the creep calculations.

Factors considered in the calculation include: tube dimensions, temperature-dependent material properties, external pressure, and the time-variable internal pressure, temperature and neutron flux.

BUCKLE employs two mathematical models with an incremental approach to calculate the change in ovality of an initially oval tube, as a function of time. One mathematical model describes the interrelationships between membrane and bending stresses, strain, and ovality of a symmetrical cross section of a hollow cylinder. The second mathematical model describes the interrelationships between stress and strain rate as a function of temperature, neutron flux and time. Although the analytical mechanics model is one-dimensional, stress biaxiality and material anisotropy effects are indirectly included through the selection of the stress coefficient in the creep equation model.

The computational procedure is based on the assumption that for a sufficiently small interval of time, the strain-producing stresses are essentially constant throughout the time interval. At the end of each time interval, the incremental creep strain that occurred during the time interval is used to calculate an incremental change in the ovality of the tube. This increment of ovality is added to the tube ovality existing at the beginning of the time interval. This new value of ovality is then used to recalculate the shell membrane and bending stresses which are used to calculate a new increment of creep strain in the subsequent time interval. If the time intervals are sufficiently small, the solution obtained is approximate and will tend to converge to the real solution. The repetitive calculations are terminated by a specified time limit or when the ovality and/or combined stresses equal specified values.

An option was added with Edition B to employ either a strain hardening or time hardening rule in the creep calculations.

Factors considered in the calculation include: tube dimensions, temperature-dependent material properties, external pressure, and the time-variable internal pressure, temperature and neutron flux.

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5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM

The assumptions used in formulating the analytical mechanics model necessarily place certain restrictions on the code's applicability to problems of buckling instability. These limitations are as follows:

(a) BUCKLE does not provide the capability to calculate creep-buckling for a perfectly round tube. The analysis for such a case typically uses the reduced modulus method wherein the modulus is determined from isochronous creep curves.

(b) The time increment used in BUCKLE must be small enough so that approximate convergence to a real solution is obtained. The convergence is generally adequate when the time increment is less than 2% of the collapse time. For short collapse times, a time interval of less than 1% should be used.

(c) The stress-deflection equations used in BUCKLE are based on linear elastic theory. For engineering purposes, the creep-collapse time will be given with sufficient accuracy by this simplified theory which neglects plasticity. Creep-buckling analyses, however, should not be attempted when the stresses exceed the yield strength of the tubing.

(d) BUCKLE does not provide the capability to calculate creep-buckling for a tube which is subjected to an eccentric axial load in addition to a uniform pressure load.

Other methods must be used for the analysis in such cases.

The assumptions used in formulating the analytical mechanics model necessarily place certain restrictions on the code's applicability to problems of buckling instability. These limitations are as follows:

(a) BUCKLE does not provide the capability to calculate creep-buckling for a perfectly round tube. The analysis for such a case typically uses the reduced modulus method wherein the modulus is determined from isochronous creep curves.

(b) The time increment used in BUCKLE must be small enough so that approximate convergence to a real solution is obtained. The convergence is generally adequate when the time increment is less than 2% of the collapse time. For short collapse times, a time interval of less than 1% should be used.

(c) The stress-deflection equations used in BUCKLE are based on linear elastic theory. For engineering purposes, the creep-collapse time will be given with sufficient accuracy by this simplified theory which neglects plasticity. Creep-buckling analyses, however, should not be attempted when the stresses exceed the yield strength of the tubing.

(d) BUCKLE does not provide the capability to calculate creep-buckling for a tube which is subjected to an eccentric axial load in addition to a uniform pressure load.

Other methods must be used for the analysis in such cases.

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7. UNUSUAL FEATURES OF THE PROGRAM

The form of the analytical creep

model used in BUCKLE is one of the standard forms generally used

to describe creep behavior. Other analytical creep models may be

equally suitable for calculating creep strains. The user may

choose to specify, via input data cards, other creep equations or

select coefficients so as to obtain the best fit to data

applicable to his material.

The form of the analytical creep

model used in BUCKLE is one of the standard forms generally used

to describe creep behavior. Other analytical creep models may be

equally suitable for calculating creep strains. The user may

choose to specify, via input data cards, other creep equations or

select coefficients so as to obtain the best fit to data

applicable to his material.

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NESC0667/01, included references:

- P.J. Pankaskie:BUCKLE - An Analytical Computer Code for Calculating Creep

Buckling of an Initially Oval Tube

BNWL-1784 (May 1974).

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NESC0667/01

File name | File description | Records |
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BUCKLE | BUCKLE SOURCE - FORTRAN IV EBCDIC | 594 |

BUCKLE | SAMPLE PROBLEM INPUT | 34 |

BUCKLE | SAMPLE PROBLEM OUTPUT | 2170 |

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- I. Deformation and Stress Distributions, Structural Analysis and Engineering Design Studies

Keywords: buckling, creep, deformation, neutron flux, pressure, temperature, tubes.