01440nas a2200133   4500008004100000245010900041210006900150300001200219490000700231520087600238100002001114700002101134856015101155       2019                        eng d00aReduced Basis Approaches for Parametrized Bifurcation Problems held by Non-linear Von Kármán Equations0 aReduced Basis Approaches for Parametrized Bifurcation Problems h  a112-1350 v813 a<p>This work focuses on the computationally efficient detection of the buckling phenomena and bifurcation analysis of the parametric Von Kármán plate equations based on reduced order methods and spectral analysis. The computational complexity—due to the fourth order derivative terms, the non-linearity and the parameter dependence—provides an interesting benchmark to test the importance of the reduction strategies, during the construction of the bifurcation diagram by varying the parameter(s). To this end, together the state equations, we carry out also an analysis of the linearized eigenvalue problem, that allows us to better understand the physical behaviour near the bifurcation points, where we lose the uniqueness of solution. We test this automatic methodology also in the two parameter case, understanding the evolution of the first buckling mode.</p>1 aPichi, Federico1 aRozza, Gianluigi  uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85068973907&doi=10.1007%2fs10915-019-01003-3&partnerID=40&md5=a09af83ce45183d6965cdb79d87a919b