This and the next 6 slides are from:
Wooseok Ji (Aerospace Engineering, University of Michigan), “Static and dynamic response of a sandwich structure under axial compression”, Ph.D. dissertation, 2008
An analytical method for predicting global and wrinkling instabilities of a sandwich beam is presented. The sandwich beam is modeled as a 2D-linear elastic continuum. Field equations representing a solid slightly deformed from a state of initial stress and under conditions of plane strain is adopted in the analysis. The results obtained yield the buckling stress and the associated wavelength. The results have shown that the buckling stress for the anti-symmetrical deformation mode is always lower that that of the symmetrical one. The buckling behavior of the two modes is parameterized according to the ratio of core thickness to the face sheet thickness. The results are compared with previous experimental results, theoretical analyses, and a finite element analysis prediction. Since the present analysis has fewer assumptions than previous analyses, the limitations of previous investigation are discussed for different combination of geometry and material properties. The results presented here, which have been verified by finite element analysis and compared against experimental results, reproduce the buckling behavior accurately for a wide range of material and geometric parameters. The results that have been presented here are a good prediction of the overall behavior of a sandwich beam in a uniaxial compressive load environment regardless of the core modulus and thickness ratio. In particular, for thick face sheets and for relatively stiff cores, the present model is found to be more accurate than previous models that assume beam like behavior for the face sheets and neglect the axial load carrying capability of the core. The results from finite element analysis have verified the findings of the present analytical model. In addition the correct formulation of the 2D elastic sandwich column problem has been presented along with a FE formulation of the problem. The latter has revealed deficiencies in the formulation adopted by popular commercial codes (for example ABAQUS). An analytical prediction of dynamic buckling is also presented in this thesis. Dynamic buckling of a structure under uniaxial impact compression is studied. Fully coupled equations of inplane and out-of-plane motions are solved to find the condition of the onset of dynamic buckling. There exists a critical time for the axial strain to satisfy the emergence of the buckling deformation. The bifurcation condition is derived for the simple Euler-Bernoulli beam as well as the sandwich beam. Experimental studies are also performed to investigate the failure mechanism of the sandwich structure under axial impact loading. The sequential responses of the sandwich specimens reveal that the structure initially experiences the axial deformation only until the buckling deformation emerges at a certain load value corresponding to the critical time. FE analysis is also performed to simulate the dynamic response and it is found that there exist a sudden increase of the bending deformation after numerous superpositions of axial strain waves. The dynamic buckling analysis presented here has numerous potential applications in various fields. The analysis is not dependent on the beam response, but is derived quantitatively so that it is adaptable to various engineering applications.
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