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# Accession Number:

## AD0608205

# Title:

## AUTOMATED DERIVATION AND INTEGER REPRESENTATION OF TOTAL POTENTIAL DIFFERENTIAL EQUATION EXPANSIONS FOR ASSUMED TRIGONOMETRIC SERIES WITH AN APPLICATION TO THE POST-BUCKLING BEHAVIOR OF CIRCULAR CYLINDRICAL SHELLS,

# Descriptive Note:

# Corporate Author:

## STANFORD UNIV CALIF

# Report Date:

## 1964-07-01

# Pagination or Media Count:

##
63.0

# Abstract:

## Many problems in applied mechanics defy exact solution because of the non-linear nature of the descriptive differential equations. In such cases, a solution is often obtained through assumption of appropriate trigonometric or power series, and expansion and collection of coefficients of like trigonometric terms or powers of the variable. The resulting set of non-linear algebraic equations is then used to obtain the solution. In this paper, algorithms are presented for deriving these equations with the aid of a digital computer. The equations are then stored by means of an integer representation. A Newton-Raphson algorithm for solving the integerform equations is also presented. The method is illustrated by re-deriving the solution for post-buckling behavior of thin-walled circular cylindrical shells under axial compression. The time required for computations is short with a Burroughs B5000 computer the total potential expression was derived in approximately two minutes and the major stable portion of the loadshortening curve was found in ten minutes. Author

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#