Use of GENOPT and BIGBOSOR4 to optimize weld lands in axially compressed stiffened cylindrical shells and evaluation of the optimized designs by STAGS David Bushnell, retired Robert P. Thornburgh U.S. Army Research Laboratory, Langley Research Center

A cylindrical shell with embedded T-stiffened weld lands

SUMMARY OF TALK Purpose of the work What is a “T-stiffened weld land”? Decision variables for optimization The “huge torus” model of a shell of revolution About GENOPT and BIGBOSOR4 Two-phase optimization problem Optimization of the “acreage” cylindrical shell Optimization of the T-stiffened weld land Evaluation of the optimized design by STAGS

Purposes of the work A “quick and dirty” tool was needed to optimize T-stiffened weld lands embedded in cylindrical shells A paper was needed that provides enough detail so that the reader can use GENOPT/BIGBOSOR4 to optimize other shell structures. Examples are needed showing how to use a general-purpose finite element program such as STAGS to evaluate optimized designs produced by GENOPT/BIGBOSOR4

What is a “T-stiffened weld land”?

Decision variables for the optimization of a T- stiffened weld land

“huge torus” model of a cylindrical shell

“Huge torus” model of 180 degrees of a cylindrical shell with T-stiffened weld lands every 120 degrees

Cross section of “huge torus” model showing how the shell segments in the BIGBOSOR4 model would be numbered in an example that has T-stiffened weld lands embedded in the “acreage” cylindrical shell at 60-degree intervals

About BIGBOSOR4 and GENOPT BIGBOSOR4 is essentially the same as BOSOR4 except that it will handle many more shell segments than BOSOR4. GENOPT is described in the next several slides.

PURPOSES OF GENOPT Convert an analysis into a user-friendly analysis Make the step into the world of automated optimization easy

PROPERTIES OF GENOPT An analysis of a fixed design is “automatically” converted into an optimization of that design concept. GENOPT can be applied in any field. It is not limited to structural analysis. User-specified data names and one-line definitions appear throughout the output. Hence the input and output is in the jargon of the GENOPT-user’s field. GENOPT is a FORTRAN program that writes other FORTRAN programs.

ARCHITECTURE OF GENOPT The program system generated by GENOPT has the “BEGIN”, “DECIDE”, “MAINSETUP”, “OPTIMIZE”, “SUPEROPT”, “CHANGE”, “CHOOSEPLOT”, “CLEANUP” architecture typical of other software written by the first author for specific applications (BOSOR4, BIGBOSOR4, BOSOR5, PANDA2)

TWO TYPES OF USER GENOPT USER: Uses GENOPT to create a user-friendly system of programs for optimizing a class of objects. In this paper the generic class is called “weldland” END USER: Uses the user-friendly system of programs created by the GENOPT user to optimize objects in the class covered by the GENOPT USER’s program system. In this paper the specific member of the “weldland” class is called “wcold”.

ROLE OF THE GENOPT USER(1) Choose a generic class of problems for which a user- friendly analysis and/or optimization program is needed. Decide which phenomena (behaviors) may affect the design. These are called “behavioral constraints”. Examples: stress, buckling, modal vibration, displacement, clearance. Establish the objective of the optimization. Examples: minimum weight, minimum cost, minimum surface rms error, etc.

ROLE OF THE GENOPT USER(2) Organize the input data. Simple constants? Arrays?, Tabular data?, Decision variables? For each input datum choose: (a) a meaningful name, (b) a clear one-line definition, (c) supporting “help” paragraph(s). Write or “borrow” algorithms to predict various behaviors, such as buckling, modal vibration, and stress, that may affect the evolution of the design during optimization cycles. Test the new user-friendly program system. Interact with the END USER.

ROLE OF THE END USER(1) Choose a specific problem that fits within the generic class established by the GENOPT USER. Choose an initial design with appropriate loads and an allowable and a factor of safety for each behavior. Choose appropriate decision variables with appropriate lower and upper bounds. Choose linked variables and linking expressions (equality constraints), if any. (These are chosen by the END USER in the processor called “DECIDE”).

ROLE OF THE END USER(2) Choose inequality constraints, if any. (To be chosen by the END USER in “DECIDE”). During optimization use enough restarts, iterations, and “CHANGE” commands in the search for a global optimum design. (This is now done automatically by “SUPEROPT”). Interact with the GENOPT USER. Check the optimum design via general-purpose programs and/or tests.

THE GENOPT MENU OF COMMANDS(1) Command for the GENOPT USER and the END USER: GENOPTLOG (activates the GENOPT menu of commands). Commands for the GENOPT USER: GENTEXT (GENOPT USER generates a prompt file with “help” paragraphs. GENTEXT produces FORTRAN program fragments, some complete FORTRAN programs, and two “skeletal” FORTRAN subroutines to be “fleshed out” later by the GENOPT user.) GENPROGRAMS (GENOPT USER generates executable elements: BEGIN, DECIDE, MAINSETUP, OPTIMIZE, CHANGE, STORE, CHOOSEPLOT, DIPLOT). INSERT (GENOPT USER adds parameters, if necessary). CLEANGEN (GENOPT user cleans up GENeric case files).

THE GENOPT MENU OF COMMANDS(2) Commands for the END USER: BEGIN (END USER provides initial design, material properties, loads, allowables, and factors of safety). DECIDE (END USER chooses decision variables, bounds, linked variables, inequality constraints, and escape variables). MAINSETUP (END USER sets up strategy parameters for simple analysis of a fixed design or optimization). OPTIMIZE (END USER performs the analysis or optimization). SUPEROPT (END USER tries to find a “global” optimum). CHANGE (END USER changes some variables).

THE GENOPT MENU OF COMMANDS(3) CHOOSEPLOT (END USER chooses which decision variables to plot versus design iterations). DIPLOT (END USER obtains postscript plot files for margins and/or decision variables and the objective versus design iterations). CLEANSPEC (END USER cleans up SPECific case files).

SEVEN ROLES THAT VARIABLES PLAY 1. A possible decision variable for optimization, typically a dimension of a structure. 2. A constant parameter (cannot vary as the design evolves), typically a control integer or material property, but not a load, allowable, or factor of safety, which are asked for later. 3. A parameter characterizing the environment, such as a load component or a temperature. 4. A quantity that describes the response (behavior) of the structure to its environment, (e.g. maximum stress, buckling load, natural frequency, maximum displacement). 5. An allowable, such as maximum allowable stress. 6. A factor of safety. 7. The objective, for example, weight.

Glossary of variable names and one-line definitions created by the GENOPT user for the generic case called “weldland”

Part of output from the specific case called “wcold”. The variable names and one-line definitions created by the GENOPT user show up in the output seen by the end user.

Part of the weldland.PRO file created automatically by GENOPT for the generic case called “weldland”

GENPROGRAMS CREATES THESE EXECUTABLE FILES BEGIN(end user supplies starting design, loads, etc.) DECIDE(end user chooses decision variables, bounds, equality and inequality constraints, etc.) MAINSETUP(end user chooses analysis type, which behaviors to process, how many design iterations, etc.) CHANGE(end user can change values of variables.) AUTOCHANGE (automatic random change in decision variables; used by SUPEROPT.)

GENPROGRAMS CREATES THESE EXECUTABLE FILES (continued) CHOOSEPLOT (end user chooses what variables to plot v. design iterations.) OPTIMIZE (end user launches the mainprocessor run, either analysis of a fixed design or optimization or design sensitivity analysis.) STORE (variables, margins, objective for all design iterations are stored for display in the *.OPP file.)

A two-phase optimization is required First the “acreage” cylindrical shell must be optimized. This is a cylindrical shell with internal stringers and internal rings of rectangular cross section. The effect of cold-bending fabrication is included in the optimization loop. Next, a typical T-stiffened weld land to be embedded in the “acreage” must be optimized. During this second phase the “acreage” properties are held constant.

Phase 1: optimization of “nasacoldbend” acreage cylindrical shell by PANDA2

Phase 2: Optimization of the T-stiffened weld land by GENOPT/BIGBOSOR4

Phase 2: T-stiffened weld land optimized by GENOPT/BIGBOSOR4

General buckling from “wcold” model

Critical general buckling mode from STAGS

A slightly higher general buckling mode from STAGS

Critical general buckling mode from Thornburgh’s STAGS model

Local buckling from “nasacoldbend/PANEL3” model

Local buckling mode from Thornburgh’s STAGS model

Weld land plate/T-stiffener buckling from “wcold” model

Weld land plate/T-stiffener buckling mode from Thornburgh’s STAGS model

T-stiffener crippling from “nasacoldbend/PANEL3” model

T-stiffener crippling from STAGS model

T-stiffener rolling from “nasacoldbend/PANEL3” model

T-stiffener rolling from STAGS model

Load-displacement curves from STAGS models

Load-displacement curves from STAGS models for the case in which T-stringer slenderness is constrained.

Conclusions The optimized T-stiffened weld lands are verified by various STAGS models. It is best to optimize including constraints on the slenderness of the T-stringers. The behavior is insensitive to the number of T- stiffened weld lands in the cylindrical shell. The long paper is detailed enough so that it can serve as a “user’s manual” for the use of GENOPT/BIGBOSOR4 in other contexts.