Presentation is loading. Please wait.

Presentation is loading. Please wait.

Mechanics-based modal identification of thin-walled members with multi-branched cross-sections by: S. Ádány and B.W. Schafer McMat 2005 2005 Joint ASME/ASCE/SES.

Similar presentations


Presentation on theme: "Mechanics-based modal identification of thin-walled members with multi-branched cross-sections by: S. Ádány and B.W. Schafer McMat 2005 2005 Joint ASME/ASCE/SES."— Presentation transcript:

1 Mechanics-based modal identification of thin-walled members with multi-branched cross-sections by: S. Ádány and B.W. Schafer McMat Joint ASME/ASCE/SES Conference on Mechanics and Materials Baton Rouge, Louisiana June 2, 2005

2 motivation mechanical criteria for modal decomposition / identification framework for FSM implementation brief example details of FSM implementation including multi-branched sections concluding thoughts

3 L cr M cr local buckling distortional buckling lateral-torsional buckling stability mode identification in a thin-walled member FEM FSM

4 GBT and modal identification Advantages – modes look “right” – can focus on individual modes or subsets of modes – can identify modes within a more general GBT analysis Disadvantages – development is unconventional/non-trivial, results in the mechanics being partially obscured (opinion) – not widely available for use in programs – Extension to general purpose FE awkward We identified the key mechanical assumptions of GBT and then implemented them in FSM (FEM) to enable these methods to perform GBT-like “modal” solutions. (as Dinar has described!)

5 mechanical assumptions of GBT  modes criteria: #1 membrane restriction #2 non-zero warping #3 no transverse bending #1 #2 #3

6 FSM modal decomposition (identification) Begin with our standard stability (eigen) problem Now introduce a set of constraints consistent with a desired modal definition, this is embodied in R Pre-multiply by R T and we create a new, reduced stability problem that is in a space with restricted degree of freedom, if we choose R appropriately we can reduce down to as little as one “modal” DOF

7 brief example... implemented in open source matlab-based finite strip software

8 decomposition and identification of an I-beam

9

10 #1 #2 #3 u,v: membrane plane stress w,  : thin plate bending FSM implementation details...

11 general displacement vector: d=[U V W  ] T constrained to distortional: d=Rd r, d r =[V] u (i) -v 1,2 relation via membrane assumptions (#1) u (i-1,i) -V i-1,i,i+1 relation considering connectivity u (i-1,i),w (i-1,i) -U i,W i by coord. transformation subset of this: u (i-1,i) -U i,W i relation U i,W i -V i-1,i,i+1 through combining above  i -U i,W i relation through beam analogy (#3) notations: superscript = elements, subscript = nodes, lowercase = local, uppercase = global

12 u (i) -v 1,2 relation FSM shape functions membrane restriction: resulting relation:

13 u (i-1),(i) -V i-1,i,i+1 relation element (i-1): element (i): connectivity:

14 u (i-1),(i) -U i W i relation local-global transform: element (i-1): element (i):

15 U i W i -V i-1,i,i+1 relation local-global transform membrane assumption + connectivity

16 multi-branched: u (i) -v 1,2 relation membrane restriction results in:

17 multi-branched: u (i.1),(i.m) -V i,..,m relation

18 multi-branched: u (i-1),(i) -U i W i relation (cont.) single-branched: multi-branched: The multi-branched case is over-determined (heart of the issue for a multi-branched section):

19 multi-branched: U i W i -V i-1,i,i+1 relation

20 multi-branch case leads to additional constraints on V....

21 concluding thoughts Current general purpose FSM (FEM) methods are uncapable of modal identification / decomposition for thin-walled member stability modes Inspired by GBT, the modes (i.e., G, D, L, O classes of modes) are postulated as mechanical constraints Modal definitions are implemented in an FSM context for singly and multi-branched sections Formal modal definitions enable FSM to perform – Modal decomposition (focus on a given mode) – Modal identification (figure out what you have) Much work remains, and definitions are not perfect

22 acknowledgments Thomas Cholnoky Foundation Hungarian Scientific Research Fund U.S., National Science Foundation

23

24

25  -U,V relation U,W displacements reconciled through  and beam analogy U,W are “support displacements”

26 Q-U,V relation

27 d=Rd r

28 Why bother? modes  strength

29 Thin-walled members

30 FSM K e = K em + K eb Membrane (plane stress)

31 FSM K e = K em + K eb Thin plate bending

32 finite strip method Capable of providing complete solution for all buckling modes of a thin-walled member Elements follow simple mechanics bending w, cubic “beam” shape function thin plate theory membrane u,v, linear shape functions plane stress conditions Drawbacks: special boundary conditions, no variation along the length, cannot decompose, nor help identify “mechanics-based” buckling modes

33 Special purpose FSM can fail too

34 Experiments on cold-formed steel columns 267 columns,  = 2.5,  = 0.84


Download ppt "Mechanics-based modal identification of thin-walled members with multi-branched cross-sections by: S. Ádány and B.W. Schafer McMat 2005 2005 Joint ASME/ASCE/SES."

Similar presentations


Ads by Google