Browsing by Author "Laursen, Tod A"
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Item Open Access An efficient finite element method for embedded interface problems(2013) Annavarapu, ChandrasekharWe focus on developing a computationally efficient finite element method for interface problems. Finite element methods are severely constrained in their ability to resolve interfaces. Many of these limitations stem from their inability in independently representing interface geometry from the underlying discretization. We propose an approach that facilitates such an independent representation by embedding interfaces in the underlying finite element mesh. This embedding, however, raises stability concerns for existing algorithms used to enforce interfacial kinematic constraints. To address these stability concerns, we develop robust methods to enforce interfacial kinematics over embedded interfaces. We begin by examining embedded Dirichlet problems – a simpler class of embedded constraints. We develop both stable methods, based on Lagrange multipliers,and stabilized methods, based on Nitsche’s approach, for enforcing Dirichlet constraints over three-dimensional embedded surfaces and compare and contrast their performance. We then extend these methods to enforce perfectly-tied kinematics for elastodynamics with explicit time integration. In particular, we examine the coupled aspects of spatial and temporal stability for Nitsche’s approach.We address the incompatibility of Nitsche’s method for explicit time integration by (a) proposing a modified weighted stress variational form, and (b) proposing a novel mass-lumpingprocedure.We revisit Nitsche’s method and inspect the effect of this modified variational form on the interfacial quantities of interest. We establish that the performance of this method, with respect to recovery of interfacial quantities, is governed significantly by the choice for the various method parameters viz.stabilization and weighting. We establish a relationship between these parameters and propose an optimal choice for the weighting. We further extend this approach to handle non-linear,frictional sliding constraints at the interface. The naturally non-symmetric nature of these problems motivates us to omit the symmetry term arising in Nitsche’s method.We contrast the performance of the proposed approach with the more commonly used penalty method. Through several numerical examples, we show that with the pro-posed choice of weighting and stabilization parameters, Nitsche’s method achieves the right balance between accurate constraint enforcement and flux recovery - a balance hard to achieve with existing methods. Finally, we extend the proposed approach to intersecting interfaces and conduct numerical studies on problems with junctions and complex topologies.Item Open Access Correlation of Finite Element Analysis to Impacted Composite Plates(2011) Berry, Jessica LynnThe purpose of this thesis was to examine progressive composite damage models available within LS-DYNA and to correlate the results of these models with drop weight impact testing and with the non-destructive evaluation techniques of shearography, thermography, and ultrasonic testing. The secondary purpose of this study was to assess whether shearography and thermography provide an adequate less expensive replacement to ultrasonic testing. For this investigation, three models were chosen: Chang-Chang, Chang-Chang + Tsai-Wu, and a Faceted Failure Surface
Model. For the experimental impact testing, two sets of specimens were chosen: a 16-ply lay-up and a 32-ply lay-up of carbon fiber pre-preg material. The panel specimens were tested at various impact energies and the displacement and force history of the impactor were recorded. The models showed good correlation for the force history with the experiments. Furthermore, the 16-ply models correlated well with the displacement history. However, due the penalty method implementation, the 32-ply models did not show similar peak displacement output. The damage shown by the models was compared to non-destructive evaluation techniques. The shearography and thermography showed significantly less damage than the ultrasonic scans, and therefore do not provide an adequate replacement to ultrasonic scanning. In looking at correlation between the models and the non-destructive evaluation techniques, the faceted failure surface showed significantly more damage due to its elastic-plastic type formulation.
Item Open Access Data Transfer between Meshes for Large Deformation Frictional Contact Problems(2013) Kindo, Temesgen MarkosIn the finite element simulation of problems with contact there arises
the need to change the mesh and continue the simulation on a new mesh.
This is encountered when the mesh has to be changed because the original mesh experiences severe distortion or the mesh is adapted to minimize errors in the solution. In such instances a crucial component is the transfer of data from the old mesh to the new one.
This work proposes a strategy by which such remeshing can be accomplished in the presence of mortar-discretized contact,
focusing in particular on the remapping of contact variables which must occur to make the method robust and efficient.
By splitting the contact stress into normal and tangential components and transferring the normal component as a scalar and the tangential component by parallel transporting on the contact surface an accurate and consistent transfer scheme is obtained. Penalty and augmented Lagrangian formulations are considered. The approach is demonstrated by a number of two and three dimensional numerical examples.
Item Open Access Effect of van der Waals forces on Retilce Nonflatness in Extreme Ultraviolet Lithography(2010) Gajendran, HarishankerDue to the increasing cost of the enhancement techniques in current projection lithographic techniques and the required time in developing new technology's
as feasible manufacturing technology, EUVL is considered as the leading candidate for production of 45 nm node and less. In EUVL, mask is held electrostatically against chuck. This electrostatic chucking process affects the nonflatness of the mask due to contact interaction and the voltage force between the mask and chuck. A fundamental understanding of chucking phenomenon is required to realize the SEMI P37 and SEMI P40 stringent flatness requirements.
The primary challenge is to understand and characterize the ability of electrostatic chucking phenomenon to acheive consistent and reliable shapes of chucked masks.
The objective of this thesis is to study the effect of initial nonflatness of mask and chuck, chucking voltage, chuck and mask dimension and gravity on the final nonflatness of the mask A finite element model of the mask and chuck with initial nonflat surface is developed. To predict the final nonflatness of the mask frontside with nm accuracy, the contact interaction between mask and chuck is modeled using van der Waals forces. These results are compared with penalty method for the runtime and accuracy of results
Item Open Access Springback Analysis for Rod Bending in Spinal Fusion Surgery Applications(2010) Wallace, TerenceSpinal fusion is quickly becoming a common surgical operation in today's medical field. A major component of spinal fusion surgery is the use of metal rods. These rods, which are made of titanium or stainless steel, must be bent in such a way to hold the spine in the correct configuration. This part of the surgery is very time consuming and tiring for the surgeon, which increases the risk to the patient. A device is being designed that would automatically bend the rods to match a flexible pattern formed by the surgeon. A major consideration in the design of this device is predicting the amount of springback exhibited by the rod when bent. This thesis discusses a method of determining that springback. First, an experimental setup is designed and used to bend surrogate rods to certain angles. This experimental data is compared to a numerical simulation of the bending. The material model in the simulation uses a stress-strain curve derived from tensile test data. It was found that at bend angles less than 60 degrees, the simulation results are accurate enough to predict springback. Therefore, a curve was fit to the data, and the resulting polynomial equation was used to solve for the bend angle to which the rod would need to be bent in order to obtain a desired angle. However, the simulation became inaccurate at higher bend angles. It was found that a mesh finer than that which was used for the simulation resulted in better agreement with the experimental values. In conclusion, it was shown that a numerical simulation could be used to produce accurate springback values in order to develop a prediction algorithm for a rod bending device.
Item Open Access Stable Embedded Grid Techniques in Computational Mechanics(2010) Sanders, JessicaEngineering mechanics problems involving interfaces, whether physical or introduced by numerical methodologies, are commonplace. Just a few examples include fracture and fault mechanics, classical contact-impact, phase boundary propagation, and fluid-structure interaction. This dissertation focuses on issues of numerical stability and accuracy that must be addressed when such interfaces are included in a realistic simulation of a physical system.
We begin by presenting a novel numerical method of fluid/structure interaction that may be applied to the problem of movable devices and ocean waves. The work is done with finite differences, large motion Lagrangian mechanics, and an eye towards creating a model in which complex rigid body dynamics can be incorporated.
We then review the many advantages of embedded mesh techniques for interface representation, and investigate a completely finite element based strategy for embedding domains. The work is seen as a precursor to robust multi-physics simulation capabilities. Special attention must be given to these techniques in terms of stable and convergent representation of surface fluxes. Mesh locking and over-constraint are particularly addressed. We show that traditional methods for enforcing continuity at embedded interfaces cannot adequately guarantee flux stability, and show a less traditional method, known as Nitsche's method, to be a stable alternative. We address the open problem of applying Nitsche's method to non-linear analysis by drawing parallels between the embedded mesh and discontinuous Galerkin (DG) methods, and propose a DG style approach to Nitsche's method. We conclude with stable interfacial fluxes for a continuity constraint for a case of embedded finite element meshes in large deformation elasticity. The general conclusion is drawn that stability must be addressed in the choice of interface treatment in computational mechanics.