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UID:0-354@aerospace.technion.ac.il

DTSTART;TZID=Asia/Jerusalem:20181219T163000

DTEND;TZID=Asia/Jerusalem:20181219T173000

DTSTAMP:20230527T135421Z

URL:https://aerospace.technion.ac.il/events/column-buckling-with-non-ideal
 -boundary-conditions/

SUMMARY:Column Buckling with Non-Ideal Boundary Conditions
DESCRIPTION:Lecturer:Tomer Meir\n Faculty:Department of Aerospace Engineeri
 ng\n Institute:Technion – Israel Institute of Technology\n Location:Clas
 sroom 165\, ground floor\, Library\, Aerospace Eng.\n Zoom: \n Abstract: \
 n Details: \n Buckling of a slender elastic column under static compressiv
 e load is a fundamental and classical problem in structural stability. It 
 has been examined over more than 250 years\, starting with Euler and up to
  present day. For combinations of the ideal boundary conditions – simple
 \, clamped\, sliding and free -- exact analytical solutions for critical l
 oads are available. In real structures however\, end fixations of columns 
 are not ideal but rather restrained by elastic end supports\, two at each 
 end. For elastic supports\, critical loads have been determined numericall
 y for several cases\, yet a comprehensive stability analysis covering all 
 possible combinations of elastic end conditions is still missing. Mathemat
 ically\, the buckling loads are obtained as roots of transcendental equati
 ons that include four constants of the end restraint springs.\nThe present
  research aims at a complete (once and for all) mapping of the buckling lo
 ads for entire possible combinations of elastic boundary conditions. Speci
 fically\, compact design charts\, in a user-friendly format\, are presente
 d along with several elegant formulae for buckling loads within definite l
 imits of validity. In addition\, we extend the findings for elastic buckli
 ng into the plastic range\, where pre-buckling stresses are higher than th
 e yield stress. Analysis is within the framework of Euler buckling theory 
 of homogeneous columns with constant bending stiffness.\nWe start with an 
 earlier reformulation of the governing transcendental equation where the f
 our spring constants are regrouped into just three parameters: two equival
 ent spring parameters and one nondimensional measure of supports asymmetry
 . The equation is then factorized into two distinct branches that are exam
 ined separately.  New closed form expressions are derived for several cas
 es and numerical charts are supported by accurate asymptotic expansions. C
 omparison with available solutions confirms the efficiency of suggested ap
 proach to the buckling problems.\nA detailed sensitivity analysis reveals 
 the nonlinear effect of elastic end supports and ends asymmetry on the buc
 kling load. Among the cases examined in detail are rigid body instability\
 , weak columns (applicable to MEMS)\, symmetric torsional springs and mult
 iple roots. Also discussed are the buckling energy partition and influence
  of supports age deterioration.
CATEGORIES:Seminars
LOCATION:Classroom 165\, ground floor\, Library\, Aerospace Eng.

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DTSTART:20181028T010000

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