SOLID-SHELL FINITE ELEMENT MODELS FOR EXPLICIT SIMULATIONS OF CRACK PROPAGATION IN THIN STRUCTURES

Crack propagation in thin shell structures due to cutting is conveniently simulated using explicit finite element approaches, in view of the high nonlinearity of the problem. Solidshell elements are usually preferred for the discretization in the presence of complex material behavior and degradation phenomena such as delamination, since they allow for a correct representation of the thickness geometry. However, in solid-shell elements the small thickness leads to a very high maximum eigenfrequency, which imply very small stable time-steps. A new selective mass scaling technique is proposed to increase the time-step size without affecting accuracy. New ”directional” cohesive interface elements are used in conjunction with selective mass scaling to account for the interaction with a sharp blade in cutting processes of thin ductile shells

Topology Optimization of Convective Cooling System Designs

This research investigates an approach to finding the optimal geometry of convective cooling system structures for the enhancement of cooling performance. To predict the cooling effect of convective heat transfer, flow analysis is performed by solving the Brinkman-penalized Navier-Stokes equation, and the temperature profile is obtained from the homogenized thermal-transport equation. For accurate and cost-effective analysis, stabilized finite element methods (FEM) and the adjoint sensitivity method for the multiphysics system are implemented. Several stabilization methods with different definitions of their stabilization tensors and the Newton-Raphson iteration method are introduced to solve the governing equations. This study investigates numerical instabilities, such as velocity and pressure oscillation at the fluid-solid interfaces, which result from the fact that the non body-conforming mesh for the topology optimization method fails to capture the sharp change in velocity gradient with a high Reynolds number flow. These oscillations are not problematic at the system analysis level, but prevent the design from converging to an optimized shape at the design optimization level, creating element-scale cavities near the solid boundaries. Several stabilization methods are examined for their ability to alleviate the instabilities. The Galerkin/least-square method produces less oscillation in most cases but it is insufficient in resolving the convergence issue. The density and sensitivity filters do not effectively suppress the cavities at the design optimization level, while a move-limit scheme easily prevents this instability without significant increase in computational cost. The topology optimization method is applied to the convective cooling system design, by using the same configuration that was successfully used in designing the Navier-Stokes flow system. The main design purpose is to design a flow channel to maximize cooling efficiency. A numerical issue concerning the behavior of the Brinkman penalization is presented with example designs. The optimizer frequently ignores the Brinkman penalization and creates infeasible designs. To resolve this issue, a multi-objective function that also minimizes pressure drop is suggested. As design examples, 2D and 3D cooling channels are designed by the multi-objective function, and the effect of Reynolds and Prandtl number change is discussed.Ph.D.Mechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/91462/1/kjun_1.pd

A Virtual Element Method for elastic and inelastic problems on polytope meshes

We present a Virtual Element Method (VEM) for possibly nonlinear elastic and inelastic problems, mainly focusing on a small deformation regime. The numerical scheme is based on a low-order approximation of the displacement field, as well as a suitable treatment of the displacement gradient. The proposed method allows for general polygonal and polyhedral meshes, it is efficient in terms of number of applications of the constitutive law, and it can make use of any standard black-box constitutive law algorithm. Some theoretical results have been developed for the elastic case. Several numerical results within the 2D setting are presented, and a brief discussion on the extension to large deformation problems is included