APPENDIX D: PETROS 2: A NEW FINITE-DIFFERENCE METHOD AND PROGRAM FOR THE CALCULATION OF LARGE ELASTIC-PLASTIC DYNAMICALLY-INDUCED DEFORMATIONS OF GENERAL THIN SHELLS.

Abstract : The equations of motion, strain-displacement relations, and the constitutive relations for a thin Kirchoff shell of arbitrary shape are derived in tensor notation. Taken into account are arbitrarily-large deformations, and material which exhibits elastic, elastic-plastic, strain hardening, and/or strain-rate sensitive behavior: also the shell may be subject to arbitrary initial velocities and/or transient external forces. The governing differential and algebraic equations then are recast into finite-difference form. These finite-difference equations have been employed to write a FORTRAN IV computer program called PETROS 2. Applications to illustrate various features of this formulation and program are presented. Included herein is the PETROS 2 program together with sample problem input and solution data. Subroutines which will handle shells having the following initial geometries are included: (1) cone, (2) cylinder, and (3) flat plate. The user may readily provide a similar initializing subroutine to permit analyzing a shell of some other initial shape. This report contains appendix D to the main report, AD-708 773.