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Steel and Composite Structures
  Volume 6, Number 4, August 2006 , pages 319-333

Bending and buckling of a rectangular porous plate
K. Magnucki, M. Malinowski and J. Kasprzak

    A rectangular plate made of a porous material is thernsubject of the work. Its mechanical properties varyrncontinuously on the thickness of a plate. Arnmathematical model of this plate, which bases onrnnonlinear displacement functions taking into accountrnshearing deformations, is presented. The assumedrndisplacement field, linear geometrical and physicalrnrelationships permit to describe the total potentialrnenergy of a plate. Using the principle ofrnstationarity of the total potential energy the set ofrnfive equilibrium equations for transversely and inrnplane loaded plates is obtained. The derivedrnequations are used for solving a problem of a bendingrnsimply supported plate loaded with transversernpressure. Moreover, the critical load of a bi-axiallyrnin-plane compressed plate is found. In both casesrninfluence of parameters on obtained solutions such asrna porosity coefficient or thickness ratio isrnanalysed. In order to compare analytical results arnfinite element model of a porous plate is built usingrnsystem ANSYS. Obtained numerical results are inrnagreement with analytical ones.
Key Words
    non-homogeneous plate; elastic buckling; rectangular plate.
K. Magnucki; Institute of Applied Mechanics, Poznan University of Technology, ul. Piotrowo 3, PL. 60-965 Poznan, PolandrnInstitute of Rail Vehicles \"TABOR\" ul. Warszawska 181, PL. 61-055 Poznan, PolandrnM. Malinowski; Institute of Mechanical Engineering and Machine Operation, University of Zielona Gora, Zielona Gora, PolandrnJ. Kasprzak; Institute of Applied Mechanics, Poznan University of Technology, Poznan, Poland

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