טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentKlepach Doron
SubjectInfluence of Membrane Stresses on Postbuckling of
Rectangular Plates Using a Nonlinear Elastic
3-D Cosserat Brick Element
DepartmentDepartment of Mechanical Engineering
Supervisor Professor Emeritus Miles Rubin


Abstract

This thesis has two main objectives.  The first is to examine the influence of membrane stresses on postbuckled deformations of nonlinear elastic isotropic rectangular plates. The second is to examine the accuracy of a new 3-D Cosserat eight noded brick element (Nadler and Rubin, 2003) which was developed within the context of the theory of a Cosserat point. The equations of the Cosserat element include both material and geometric nonlinearities. A number of example problems are considered which examine predictions of the Cosserat element for plates with simply supported and clamped edges subjected normal compressive loads on opposing ends and to shear loads. Comparison is also made with results from the commercial codes ANSYS and ADINA. In all cases, the Cosserat element behaves well even though only one element is used through the plate's thickness and even when the aspect ratio of the element is large. The approximate nonlinear postbuckling solution by Timoshenko and Gere for a square plate is shown to be more limited than originally expected. Specific examples show that when the plate is compressed and local equilibrium is satisfied, the mode shape changes from the small deformation shape to a more complicated shape that limits the development of large membrane stresses. In particular, an unexpected snap through phenomena is predicted for simply supported edges with no lateral deformation.  These results suggest that the Cosserat element is robust, can perform well under extreme conditions and is capable of modeling combinations of three-dimensional bodies with attached thin structures.