Review Review: Constrained finite strip method developments and applications in cold-formed steel design Zhanjie Li a , Jean C. Batista Abreu a , Jiazhen Leng a , Sándor Ádány b , Benjamin W. Schafer a,n a Department of Civil Engineering, Johns Hopkins University, Baltimore, Maryland, USA b Department of Structural Mechanics, Budapest University of Technology and Economics, Budapest, Hungary article info Available online 6 November 2013 Keywords: Constrained finite strip method Modal identification Local buckling Distortional buckling Buckling mode interaction abstract The stability of thin-walled members is decidedly complex. The recently developed constrained Finite Strip Method (cFSM) provides a means to simplify thin-walled member stability solutions through its ability to identify and decompose mechanically meaningful stability behavior, notably the formal separation of local, distortional, and global deformation modes. The objective of this paper is to provide a review of the most recent developments in cFSM. This review includes: fundamental advances in the development of cFSM; applications of cFSM in design and optimization; identifying buckling modes and collapse mechanisms in shell finite element models; and, additional stability research initiated by the cFSM methodology. A brief summary of the cFSM method, in its entirety, is provided to explain the method and highlight areas where research remains active in the fundamental development. The application of cFSM to cold-formed steel member design and optimization is highlighted as the method has the potential to automate generalized strength prediction of thin-walled cold-formed steel members. Extensions of cFSM to shell finite element models is also highlighted, as this provides one path to bring the useful identification features of cFSM to general purpose finite element models. A number of alternative methods, including initial works on a constrained finite element method, initiated by cFSM methods, are also detailed as they provide insights on potential future work in this area. Research continues on fundamentals such as methods for generalizing cFSM to arbitrary cross-sections, improved design and optimization methods, and new ideas in the context of shell finite element method applications. & 2013 Elsevier Ltd. All rights reserved. Contents 1. Introduction .......................................................................................................... 3 2. The constrained finite strip method ....................................................................................... 3 2.1. Classic FSM .................................................................................................... 3 2.2. Signature curve stability analysis ................................................................................... 4 3. cFSM formulation ..................................................................................................... 4 3.1. Modal decomposition and identification for simply supported ends ....................................................... 5 3.2. General boundary conditions stability analysis ........................................................................ 5 3.3. Modal identification for general end boundary conditions ............................................................... 5 3.4. Stiffness matrix options in FSM and cFSM ............................................................................ 6 3.5. New shear modes in cFSM ........................................................................................ 7 4. cFSM in cold-formed steel research ....................................................................................... 8 4.1. cFSM in design of cold-formed steel members ........................................................................ 8 4.2. ‘FSM at cFSM buckling length’ approach ............................................................................. 8 4.3. ‘cFSM with correction factors’ approach.............................................................................. 8 4.4. cFSM in shape optimization of cold-formed members .................................................................. 9 4.4.1. Unconstrained optimization ................................................................................ 9 Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/tws Thin-Walled Structures 0263-8231/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.tws.2013.09.004 n Corresponding author. Tel.: þ1 410 16 6265; fax: þ1 410 516 7473. E-mail addresses: lizhanjie@jhu.edu (Z. Li), jbatist1@jhu.edu (J.C. Batista Abreu), jleng1@jhu.edu (J. Leng), sadany@epito.bme.hu (S. Ádány), schafer@jhu.edu (B.W. Schafer). Thin-Walled Structures 81 (2014) 2–18