Model order reduction for large-scale structures with local nonlinearities
In solid mechanics, linear structures often exhibit (local) nonlinear behavior when close to failure. For instance, the elastic deformation of a structure becomes plastic after being deformed beyond recovery. To properly assess such problems in a real-life application, we need fast and multi-query evaluations of coupled linear and nonlinear structural systems, whose approximations are not straight forward and often computationally expensive. In this work, we propose a linear-nonlinear domain decomposition, where the two systems are coupled through the solutions on the linear-nonlinear interface. After necessary sensitivity analysis, e.g. for structures with a high dimensional parameter space, we adopt a non-intrusive method, e.g. Gaussian processes regression (GPR), to solve for the solution on the interface. We then utilize different model order reduction techniques to address the linear and nonlinear problems individually. To accelerate the approximation, we employ again the non-intrusive GPR for the nonlinearity, while intrusive model order reduction methods, e.g. the conventional reduced basis (RB) method or the static-condensation reduced- basis-element (SCRBE) method, are employed for the solution in the linear subdomain. We provide several numerical examples to demonstrate the effectiveness of our method.
ROM_Local nonlinearity.pdf
Postprint
openaccess
1.35 MB
Adobe PDF
f8b6ffcc86fda0304b4b49b802f64a12
MOR_local_nonlinear.pdf
openaccess
1.33 MB
Adobe PDF
e135d60e6c801975d5e1367f1dd2f729