Reduced Basis Approaches for Parametrized Bifurcation Problems held by Non-linear Von Kármán Equations
Reduced Basis Approaches for Parametrized Bifurcation Problems held by Non-linear Von Kármán Equations
复制标题
非线性冯卡门方程参数化分岔问题的简化基方法
DOI：
10.1007/s10915-019-01003-3
复制
发表时间：
2018
影响因子：
2.5
通讯作者：
G. Rozza
中科院分区：
文献类型：
--
作者：
F. Pichi;G. Rozza
本文基于降阶方法和谱分析方法，对参数化Von Kármán板方程的屈曲现象和分叉分析进行了有效的计算检测。由于四阶导数项，非线性和参数依赖性的计算复杂性，提供了一个有趣的基准测试的重要性，减少战略，在建设的分歧图，通过改变参数（S）。为此，连同状态方程，我们也进行了分析的线性特征值问题，使我们能够更好地了解附近的分岔点，我们失去了唯一性的解决方案的物理行为。我们测试这种自动方法也在两个参数的情况下，了解第一屈曲模式的演变。
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.