|
|
||
|
|
|
|
See:
http://0-www.worldcat.org.novacat.nova.edu/identities/lccn-no2002-30680
http://www.facebook.com/people/Charles-C-Rankin/1140678630
Personal
Charles was a great man, loved by many for his great sense of humor, respected by many for his towering intellect and superb accomplishments in the field of structural mechanics. He will remain forever in the minds and hearts of his many friends and colleagues.
Technical Contributions
Charles Rankin is known for his salient fundamental contributions over more than 30 years to the field of solid and structural mechanics. All of these contributions have been formulated by Charles and implemented into his general-purpose nonlinear static and dynamic finite element code called STAGS (STructural Analysis of General Shells), widely used especially at NASA Langley Research Center. Charles was no mere programmer implementing into a code the mechanics theories of others; he developed these theories mainly by himself. Many of Charles’ fundamental contributions are now finding their way into the most widely used commercial structural computer programs such as MSC_NASTRAN, ANSYS and ABAQUS. In this way Charles’ important original contributions will for the foreseeable future have a major impact on research and engineering in academia, government and industry.
Specifically Charles Rankin’s technical contributions are as follows:
1. Formulation of a finite-element-independent co-rotational theory and its implementation into the STAGS computer program in the 1980s [18, 29, 31, 33] that was original with Charles and that has just recently been and is now being introduced into widely used commercial computer codes. This method permits the simulation of highly nonlinear phenomena in thin-walled structures such as the reliable determination via Newton’s method of far post-buckling static and dynamic equilibrium states of stiffened, composite shell structures universally used by the aerospace industry. Charles’ unique co-rotational formulation avoids finite-element “lockup”. It has been especially well received by the developers of commercial structural computer codes because it operates outside the finite element kernels that differ not only from code to code but also from finite element to finite element within each commercial software package. Unique to STAGS is an extension to large strain for various selected strain measures [5, 7], again in a process that is virtually independent of the details of the finite element kernal. A Google search with use of the string, “corotational finite element”, produces about 74000 results, indicating that this original contribution of Charles has now become an important standard in computational mechanics the world over.
2. Formulation (with Eduard Riks) and implementation into STAGS of an arc-length method that permits the traversal of limit points from pre-buckling to post-buckling of imperfect shells under destabilizing loads [16, 21, 24, 25]. Charles optimized the solution stepping algorithm for the reliable determination of the nonlinear equilibrium state at each successive loading step. This strategy includes the unique ability to switch solutions paths and continue “in the path direction” of a particular buckling eigenvector in order to enable a more reliable and accurate investigation of post-buckling behavior. Charles’ unique strategy permits the accurate prediction of “mode-jumping” [19, 23], a dynamic phenomenon in which a given post-buckled state evolves dynamically, at a given load level, into an entirely different, non-neighboring, post-buckled state. STAGS is the first general-purpose computer program to include these sophisticated formulations and strategies that are now finding their way into the major commercial codes.
3. Formulation and implementation into STAGS of an algorithm to determine multiple bifurcation eigenvalues and eigenvectors from nonlinearly determined rather than from linearly determined pre-buckled equilibrium states. This original contribution by Charles is essential for the successful simulation of “mode jumping” [8, 19, 23], a phenomenon that is especially prominent in compressed stiffened thin shells of the type universally used by the aerospace industry. It is also essential for the determination of the behavior of an axially compressed imperfect stiffened cylindrical shell loaded well beyond its initial buckling load to ultimate failure in its far post-buckled state.
4. Formulation and implementation of a solution strategy that permits the successive introduction into a given nonlinear finite element model of a shell structure a sequence of buckling modal imperfections [8]. This strategy, original with Charles, is required in order to determine static and dynamic nonlinear post-buckled equilibrium states of thin shells with closely spaced bifurcation points in the nonlinear regime, for the determination of secondary and tertiary (and so on) equilibrium bifurcations, and for successful nonlinear continuation beyond these secondary and tertiary bifurcations [8, 13]. This very complex nonlinear behavior is typical of extremely light-weight stiffened thin shell structures such as the huge external tank of the Space Shuttle and optimally designed aircraft fuselages. Charles’ unique strategy is crucial if the ultimate failure of such thin shell structures is to be determined reliably. Numerous comparisons in the literature between test and the theory implemented in STAGS demonstrate the accuracy of predictions by STAGS.
5. Formulation and implementation of a strategy that permits successive smooth transitions from static to transient and from transient to static analyses of a given structure during execution of a sequence of nonlinear computer runs sometimes required for the complete determination of the ultimate failure of a thin shell structure [8]. A crucial aspect of this strategy is the use of advanced static arc-length methods to enable the reliable return to a converged nonlinear static equilibrium state from a nonlinear transient state by means of appropriate load relaxation.
6. Formulation and implementation of a strategy that permits the simulation of unzipping of a through crack in a shell possibly with multiple crack tips and turning of a crack during loading [9, 26, 28, 30]. This unique and sophisticated strategy requires the use of a combination of advanced arc-length procedures and load-relaxation return to nonlinear static equilibrium, all done seamlessly in STAGS without user intervention. STAGS is the only code to report the actual energy release rate during the entire crack growth process. This crack tip behavior simulation capability, originally unique to STAGS, is crucial for solution of the problem of fatigue failure and catastrophic delamination in composite and metallic aircraft fuselages [2, 4, 9, 15]. Charles’ formulations are now finding their way into ABAQUS, primarily via Charles’ service on the ABAQUS Fracture Customer Review Team.
7. Formulation and implementation of a “sandwich” finite element that efficiently accounts for soft, shear-deformable cores and stiff face sheets [11, 36]. The STAGS sandwich element makes clever use of existing shell elements for the face sheets, and adds a separation between the face sheets. The space is filled with an 8-node solid element whose displacement field is taken from the face sheets; this process allows for a very high order resolution of the dominant shear field between the face sheets. An additional important aspect of the sandwich element is that one is able to raise the through-the-thickness order by stacking phantom face sheets within the core to provide a more flexible displacement field. Phantom face sheets are shell elements with no stiffness, with a displacement field driven by the core shear field.
8. The development of unique nonlinear material models in separate “material modules” which are independent of the rest of the software. This formulation makes it straightforward to introduce into large commercial finite element codes various composite-response progressive failure models that include many different failure threshold and growth criteria [14, 22, 28]. Notable among these models created by Charles is the simulation of composite fatigue delamination in a mixed-mode setting [2] and advanced decohesion finite elements for the simulation of composite delamination [4]: an initial version implemented into STAGS in 1999 and revised and improved since then. These sophisticated models have been implemented in ABAQUS.
Biography
Charles Rankin received his PhD in Molecular Physics from the University of Chicago in 1968 and his BS in Chemistry from the University of North Carolina in 1964. It is unusual that his degrees are in a different field than that of his major technical contributions, demonstrating his exceptional ability not only to learn and master new disciplines but also to rise to the top of his new field of endeavor.
Charles worked at Lockheed (now Lockheed Martin) practically his entire career. He retired from the Lockheed Martin Advanced Technology Center, Palo Alto, in 2003 and worked at Rhombus Consultants Group in Palo Alto from 2003 until July 2012. From 1983 on he devoted most of his time to the continuing development of the STAGS computer program, primarily under contract with the NASA Langley Research Center in Hampton, Virginia. During this time he received several Lockheed Martin recognition awards and NASA Group Achievement Awards relating to work on Aging Aircraft Structural Integrity and work on the Space Shuttle External Tank. He was at the height of his powers until he was hospitalized with advanced cancer in July 2012 from which he died on August 11, 2012.
During the last ten years of his life Charles served on the AIAA Structures Technical Committee. For almost ten years (2003 – 2012) he was a member of the ABAQUS Fracture Customer Review Team. For eight years (2004 – 2012) he served on the NASA Engineering and Safety Center (NESC) Structures Technical Discipline Team. He served as a member of the NESC Space Shuttle External Tank Intertank Stringer Cracking Investigation Team in 2011 and participated in the International Workshop on Structural Integrity of Aging Airplanes in 1992. He served three times on a board for evaluation of a student’s defense of a PhD dissertation or MS thesis.
Charles was always an avid hiker and served the Sierra Club as a leader of long hikes in the San Francisco Bay area and in the Sierra Nevada of California.
Page 175 / 220