Institute for Structural Mechanics
Universitätsstraße 150, 44801 Bochum
Prof. Hung Nguyen Xuan from HUTECH University, Vietnam will hold a guest lecture in the framework of SFB 837 about 'On adaptive polygonal finite elements: An application to collapse plastic analysis'.
Polygons occur extensively in nature. Polygonal finite elements have been applied to a wide range of mechanics problems. They offer more flexibility in mesh design for arbitrary geometries. However, adaptive polygonal finite elements have not been found sufficiently in the literature and furthermore in collapse plastic analysis of solids.
The present research contributes into four crucial points: 1) a spatial decomposition structure obtained from a so-called polytree mesh scheme; 2) Wachspress shape functions at vertex and bubble nodes handled at a primal-mesh level; 3) plastic strain rates and dissipation performed over a dual-mesh level; and 4) a new adaptive primal-mesh strategy driven by the L²-norm-based indicator of strain rates. Investigating both purely cohesive and cohesive-frictional materials. It is proved numerically that the present method performs well for volumetric locking problem. In addition, the optimization formulation of limit analysis is written by the form of second-order cone programming (SOCP) in order to exploit the high efficiency of interior-point solvers. The present method retains a low number of optimization variables and allows us to design and solve the large-scale optimization problems effectively.