BOSOR5 can handle segmented and branched, elasticplastic shells of revolution with discrete ring stiffeners, meridional discontinuities, and multimaterial construction. BOSOR5 also includes creep. The shell wall can be made up of as many as six layers, each of which is a different nonlinear (elasticplastic) material. In the prebuckling analysis largedeflection axisymmetric behavior is presumed. Bifurcation buckling loads are computed corresponding to axisymmetric or nonaxisymmetric buckling modes.
The strategy for solving the nonlinear prebuckling problem is such that the user obtains reasonably accurate answers even if he or she uses very large load or time steps. This strategy is based on a subincremental iteration method in which the size of the subincrement is automatically determined so that the change in stress is less than a certain prescribed percentage of the effective stress at each material point in the shell wall. Discrete rings of arbitrary cross section are considered to be assemblages of thin rectangular elements.
The input is interactive, as with BOSOR4 (BIGBOSOR4). BOSOR5 has been checked by means of numerous runs in which the results have been compared to other analyses and to tests. BOSOR5 does not supersede BOSOR4 or BIGBOSOR4 because it has no modal vibration capability, nor can it handle nonaxisymmetrically loaded shells.
Graphic from Pressure Vessels and Piping: Design Technology – 1982, A Decade of Progress, S.Y. Zamrik and D. Dietrich, editors, published by ASME; Chapter 2.4 “Plastic Buckling” by David Bushnell, pp. 47117.
For a gallery of the kind of problem that can be solved by BOSOR5, see the slide show. This slide show is primarily composed of pictures taken from the long, illustrated abstracts of papers about BOSOR5 and results generated from executions of BOSOR5.
NOTE: BOSOR5 does NOT supersede BOSOR4 or BIGBOSOR4. BOSOR4/BIGBOSOR4 is restricted to the study of shells made of material that is linear elastic. BOSOR5 is more restricted than BOSOR4/BIGBOSOR4 in the type of analysis that BOSOR5 can do, but BOSOR5 will handle elasticplastic material and creep.
Abstracts and Papers

Bifurcation Buckling Of Shells of Revolution Including Large Deflections, Plasticity and Creep, David Bushnell, Lockheed Palo Alto Research Laboratory, 3251 Hanover Street, Palo Alto, California 94304 USA. International Journal of Solids and Structures, Vol. 10, pp. 12871305, 1974.
A summary is first presented of the conceptual difficulties and paradoxes surrounding plastic bifurcation buckling analysis. Briefly discussed are nonconservativeness, loading rate during buckling, and the discrepancy of buckling predictions with use of J2 flow theory vs J2 deformation theory. The axisymmetric prebuckling analysis, including large deflections, elasticplastic material behavior and creep is summarized. Details are given on the analysis of nonsymmetric bifurcation from the deformed axisymmetric state. Both J2 flow theory and J2 deformation theory are described. The treatment, based on the finitedifference energy method, applies to layered segmented and branched shells of arbitrary meridional shape composed of a number of different elasticplastic materials. Numerical results generated with a computer program based on the analysis are presented for an externally pressurized cylinder with conical heads.

Comparisons Of Test and Theory for Nonsymmetric ElasticPlastic Buckling of Shells of Revolution, David Bushnell, Lockheed Palo Alto Research Laboratory, 3251 Hanover Street, Palo Alto, California 94304 USA. Gerard D. Galletly, Dept. of Mechanical Engineering, The University, Liverpool L693BX, England. International Journal Solids Structures, Vol. 10, pp. 12711286, 1974.
Experimental and analytical buckling pressures are presented for very carefully fabricated thin cylindrical shells with 45, 60 and 75° conical heads and for cylindrical shells with torispherical heads pierced by axisymmetric cylindrical nozzles of various thicknesses and diameters. Nonsymmetric buckling occurs at pressures for which some of the material is loading plastically in the neighborhoods of stress concentrations caused by meridional slope discontinuities. The buckling pressures for the conecylinder vessels are predicted within 2.6 per cent and for the pierced torispherical vessels within 4.4 per cent with use of BOSOR5, a computer program based on the finite difference energy method in which axisymmetric large deflections, nonlinear material properties and nonsymmetric bifurcation buckling are accounted for. The predicted buckling pressures of the pierced torispherical specimens are rather sensitive to details of the analytical model in the neighborhood of the juncture between the nozzle and the head. The buckling pressures of the conecylinder vessels can be accurately predicted by treatment of the wall material as elastic, enforcement of the full compatibility conditions at the juncture in the prebuckling analysis, and release of the rotation compatibility condition in the bifurcation (eigenvalue) analysis.

BOSOR5 – A Computer Program for Buckling of ElasticPlastic Complex Shells of Revolution Including Large Deflections and Creep: Vol. 1: User’s Manual, Input Data , David Bushnell, Lockheed Palo Alto Research Laboratory, 3251 Hanover Street, Palo Alto, California 94304 USA. Lockheed Missiles & Space Company, Inc. Report LMSCD407166, December, 1974.
This volume contains the instructions to the user for constructing data decks for the BOSOR5 computer program. BOSOR5 runs on the UNIVAC 1108 and the CDC 6600. (2011 NOTE: BOSOR5 runs on LINUX.) It is divided into three separate programs, a preprocessor, a mainprocessor, and a postprocessor. These programs may be run as one job in a run stream or separately. The program includes a restart capability. BOSOR5 can handle segmented and branched shells with discrete ring stiffeners, meridional discontinuities, and multimaterial construction. The shell wall can be made up of as many as six layers, each of which is of a different nonlinear material. In the prebuckling analysis axisymmetric behavior is presumed. Bifurcation buckling loads are computed corresponding to axisymmetric or nonaxisymmetric buckling modes. The strategy for solving the nonlinear prebuckling problem is such that the user obtains reasonably accurate answers even if he or she uses very large load or time steps. BOSOR5 has been checked by means of numerous runs in which the results have been compared to other analyses and to tests.

BOSOR5 – A Program for Buckling of ElasticPlastic Complex Shells of Revolution Including Large Deflections And Creep, David Bushnell, Lockheed Palo Alto Research Laboratory, 3251 Hanover Street, Palo Alto, California 94304 USA. Computers & Structures, Vol. 6, pp. 221239. 1976.
BOSOR5 can handle segmented and branched shells with discrete ring stiffeners, meridional discontinuities, and multimaterial construction. The shell wall can be made up of as many as six layers, each of which is a different nonlinear material. In the prebuckling analysis largedeflection axisymmetric behavior is presumed. Bifurcation buckling loads are computed corresponding to axisymmetric or nonaxisymmetric buckling modes. The strategy for solving the nonlinear prebuckling problem is such that the user obtains reasonably accurate answers even if he uses very large load or time steps. BOSOR5 has been checked by means of numerous runs in which the results have been compared to other analyses and to tests.

Buckling of ElasticPlastic Shells of Revolution with Discrete ElasticPlastic Ring Stiffeners, David Bushnell, Lockheed Palo Alto Research Laboratory, 3251 Hanover Street, Palo Alto, California 94304 USA. Int. J. Solids Structures, 1976, Vol. 12, pp. 5166.
The theory is summarized for axisymmetric prebuckling and nonsymmetric bifurcation buckling of ringstiffened shells of revolution. The analysis is based on finite difference energy minimization in which moderately large meridional rotations, elasticplastic effects, and primary or secondary creep are included. This theory is implemented in a computer program called BOSOR5, for the analysis of segmented and branched ringstiffened shells of revolution of multimaterial construction. Comparisons between test and theory are given for axisymmetric collapse and nonsymmetric bifurcation buckling of 69 machined ringstiffened aluminum cylinders submitted to external hydrostatic pressure. Because most of the cylinders fail at an average stress that corresponds to the knee of the stressstrain curve, the analytical predictions are not very sensitive to modeling particulars such as nodal point density or boundary conditions. Agreement between test and theory is improved if the analytical model reflects the fact that the shell and rings intersect over finite axial lengths.

A Strategy for the Solution of Problems Involving Large Deflections, Plasticity and Creep, David Bushnell, Lockheed Palo Alto Research Laboratory, 3251 Hanover Street, Palo Alto, California 94304 USA. International Journal for Numerical Methods in Engineering, Vol. 11, 683708, 1977.
A strategy for solving problems involving simultaneously occurring large deflections, elasticplastic material behavior, and primary creep is described. The incremental procedure involves a double iteration loop at each load level or time. In the inner loop the material properties are held constant and the nonlinear equilibrium equations are solved by the NewtonRaphson method. These equations are formulated in terms of the tangent stiffness. In the outer loop the plastic and creep strains are determined and the tangent stiffness properties are updated with use of a subincremental algorithm. The magnitude of each time subincrement is determined such that the change in effective stress is less than a preset percentage of the effective stress. The strategy is implemented in a computer program, BOSOR5, for the analysis of shells of revolution. Examples are given of elasticplastic deformations of a centrally loaded flat plate and elasticplasticcreep deformations of a beam in bending. The major benefits of the subincremental technique are the increased reliability with which problems involving nonlinear plastic and timedependent material behavior can be solved and the greatly relaxed requirement on the number of load or time increments needed for satisfactory results.

Plastic Buckling, David Bushnell, Lockheed Palo Alto Research Laboratory, 3251 Hanover Street, Palo Alto, California 94304 USA. Pressure Vessels and Piping: Design Technology – 1982, A Decade of Progress, S.Y. Zamrik and D. Dietrich, editors, published by ASME; Chapter 2.4, pp. 47117. 1982.
The phenomenon of plastic buckling is first illustrated by the behavior of a fairly thick cylindrical shell, which under axial compression deforms at first axisymmetrically and later nonaxisymmetrically. Thus, plastic buckling encompasses two modes of behavior, nonlinear collapse at the maximum point in a load versus deflection curve and bifurcation buckling.

Computerized Analysis of ShellsGoverning Equations, David Bushnell, Lockheed Palo Alto Research Laboratory, 3251 Hanover Street, Palo Alto, California 94304 USA. Computers & Structures, Vol. 18, pp 471536, 1984.
This paper opens with a general discussion of terms in an energy function that might be the basis from which equations governing stress, stability, and vibration analyses are derived. The energy expression includes strain energy of the shell and discrete stiffeners, kinetic energy of the shell and stiffeners, constraint conditions with Lagrange multipliers, and other terms arising from the change in direction of applied loads during deformation. Brief discussions are included of the coupling effect between bending and extensional energy needed for the analysis of layered composite shells or elasticplastic shells, nonlinear terms, and the form that the energy expression takes upon discretization of the structure.

BOSOR5 – Program for Buckling of Complex, Branched Shells of Revolution Including Large Deflections, Plasticity and Creep, David Bushnell, Lockheed Missiles & Space Company, Palo Alto, CA, USA. Structural Analysis Systems – Vol. 2, A. NikuLari, editor, Pergamon, pp. 2554, 1986.
 Long abstract
 Full paper
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 Runstream
 Imposed End Shortening
 General Geometry Warning!
 Ellipsoidal Geometry Warning!
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 Nonlinear Axisymmetric Collapse Warning!
 More information about the BOSOR5 runstream
BOSOR5 performs axisymmetric collapse and nonaxisymmetric bifurcation buckling including elasticplastic material behavior and creep. It does not supersede BOSOR4, as it has no modal vibration capability or linear nonaxisymmetric stress analysis capability.