An efficient mixed variational reduced order model formulation for non-linear analyses of elastic shells

The Koiter-Newton method had recently demonstrated a superior performance for non-linear analyses of structures, compared to traditional path-following strategies. The method follows a predictor-corrector scheme to trace the entire equilibrium path. During a predictor step a reduced order model is constructed based on Koiter's asymptotic post-buckling theory which is followed by a Newton iteration in the corrector phase to regain the equilibrium of forces. In this manuscript, we introduce a robust mixed solid-shell formulation to further enhance the efficiency of stability analyses in various aspects. We show that a Hellinger-Reissner variational formulation facilitates the reduced order model construction omitting an expensive evaluation of the inherent fourth order derivatives of the strain energy. We demonstrate that extremely large step sizes with a reasonable out-of-balance residual can be obtained with substantial impact on the total number of steps needed to trace the complete equilibrium path. More importantly, the numerical effort of the corrector phase involving a Newton iteration of the full order model is drastically reduced thus revealing the true strength of the proposed formulation. We study a number of problems from engineering and compare the results to the conventional approach in order to highlight the gain in numerical efficiency for stability problems

Weakly Enforced Boundary Conditions for the NURBS-Based Finite Cell Method

In this paper, we present a variationally consistent formulation for the weak enforcement of essential boundary conditions as an extension to the finite cell method, a fictitious domain method of higher order. The absence of boundary fitted elements in fictitious domain or immersed boundary methods significantly restricts a strong enforcement of essential boundary conditions to models where the boundary of the solution domain coincides with the embedding analysis domain. Penalty methods and Lagrange multiplier methods are adequate means to overcome this limitation but often suffer from various drawbacks with severe consequences for a stable and accurate solution of the governing system of equations. In this contribution, we follow the idea of NITSCHE [29] who developed a stable scheme for the solution of the Laplace problem taking weak boundary conditions into account. An extension to problems from linear elasticity shows an appropriate behavior with regard to numerical stability, accuracy and an adequate convergence behavior. NURBS are chosen as a high-order approximation basis to benefit from their smoothness and flexibility in the process of uniform model refinement

Solving Bit-Vector Equations of Fixed and Non-Fixed Size

This report is concerned with solving equations on fixed andnon-fixed size bit-vector terms. We define an equational transformationsystem for solving equations on terms where all sizes ofbit-vectors and extraction positions are known. This transformationsystem suggests a generalization for dealing with bit-vectorsof unknown size and unknown extraction positions. Both solversadhere to the principle of splitting bit-vectors only on demand,thereby making them quite effective in practice

Phase-field boundary conditions for the voxel finite cell method: surface-free stress analysis of CT-based bone structures

The voxel finite cell method employs unfitted finite element meshes and voxel quadrature rules to seamlessly transfer CT data into patient-specific bone discretizations. The method, however, still requires the explicit parametrization of boundary surfaces to impose traction and displacement boundary conditions, which constitutes a potential roadblock to automation. We explore a phase-field based formulation for imposing traction and displacement constraints in a diffuse sense. Its essential component is a diffuse geometry model generated from metastable phase-field solutions of the Allen-Cahn problem that assumes the imaging data as initial condition. Phase-field approximations of the boundary and its gradient are then employed to transfer all boundary terms in the variational formulation into volumetric terms. We show that in the context of the voxel finite cell method, diffuse boundary conditions achieve the same accuracy as boundary conditions defined over explicit sharp surfaces, if the inherent length scales, i.e., the interface width of the phase-field, the voxel spacing and the mesh size, are properly related. We demonstrate the flexibility of the new method by analyzing stresses in a human femur and a vertebral body

Determining the Novel Pathogen Neodothiora populina as the Causal Agent of the Aspen Running Canker Disease in Alaska

Neodothiora populina Crous, G.C. Adams & Winton was determined to be a new pathogen of trembling aspen (Populus tremuloides) growing in Alaska, based on completion of Koch’s Postulates in replicated forest and growth chamber inoculation trials. The pathogen is responsible for severe damage and widespread rapid mortality of sapling to mature aspen (≥ 80 years) in the boreal forests of interior Alaska, due to large diffuse annual (1–2 years) cankers. Isolation of the pathogen was challenging, and identification based on cultural characters was difficult. Fruiting bodies were not found on wild diseased trees, but erumpent pycnidia were found in bark overlying cankers on several stems inoculated with pure cultures

Nesting Biology of Lesser Canada Geese, Branta canadensis parvipes, along the Tanana River, Alaska

Lesser Canada Geese (Branta canadensis parvipes) are widespread throughout interior regions of Alaska and Canada, yet there have been no published studies documenting basic aspects of their nesting biology. We conducted a study to determine reproductive parameters of Lesser Canada Geese nesting along the Tanana River near the city of Fairbanks, in interior Alaska. Fieldwork was conducted in May of 2003, and consisted of locating nests along the riparian corridor between Fairbanks and Northpole, Alaska. Nests were found on gravel islands and shore habitats along the Tanana River, and were most commonly observed among driftwood logs associated with patches of alder (Alnus spp.) and willow (Salix spp.). Peak of nest initiation was 3-8 May, with a range from 27 April to 20 May; renesting was likely. Clutches ranged in size from 2 to 7 eggs and averaged 4.6 eggs. There was a negative correlation between clutch size and date of nest initiation. Egg size (mean mass = 128 g) was similar to other medium-sized Canada Geese. A positive correlation between egg size and clutch size was likely related to female age. Nineteen of 28 nests (68%) were active when visited; nests located on islands with nesting Mew Gulls (Larus canus) were more likely to be active than nests located elsewhere. Evidence at nest sites implicated Bald Eagles (Haliaeetus leucocephalus) and Red Foxes (Vulpes vulpes) as nest predators

Widespread Mortality of Trembling Aspen (Populus tremuloides) Throughout Interior Alaskan Boreal Forests Resulting from a Novel Canker Disease

Over the past several decades, growth declines and mortality of trembling aspen throughout western Canada and the United States have been linked to drought, often interacting with outbreaks of insects and fungal pathogens, resulting in a “sudden aspen decline” throughout much of aspen’s range. In 2015, we noticed an aggressive fungal canker causing widespread mortality of aspen throughout interior Alaska and initiated a study to quantify potential drivers for the incidence, virulence, and distribution of the disease. Stand-level infection rates among 88 study sites distributed across 6 Alaska ecoregions ranged from \u3c 1 to 69%, with the proportion of trees with canker that were dead averaging 70% across all sites. The disease is most prevalent north of the Alaska Range within the Tanana Kuskokwim ecoregion. Modeling canker probability as a function of ecoregion, stand structure, landscape position, and climate revealed that smaller-diameter trees in older stands with greater aspen basal area have the highest canker incidence and mortality, while younger trees in younger stands appear virtually immune to the disease. Sites with higher summer vapor pressure deficits had significantly higher levels of canker infection and mortality. We believe the combined effects of this novel fungal canker pathogen, drought, and the persistent aspen leaf miner outbreak are triggering feedbacks between carbon starvation and hydraulic failure that are ultimately driving widespread mortality. Warmer early-season temperatures and prolonged late summer drought are leading to larger and more severe wildfires throughout interior Alaska that are favoring a shift from black spruce to forests dominated by Alaska paper birch and aspen. Widespread aspen mortality fostered by this rapidly spreading pathogen has significant implications for successional dynamics, ecosystem function, and feedbacks to disturbance regimes, particularly on sites too dry for Alaska paper birch

Stand up Paddle Surfing-An Aerobic Workout and Balance Training

AbstractOriginating from an ancient Hawaiian tradition Stand Up Paddle Surfing (SUP) is a growing pastime and sports activity in which a person stands upright on a surfboard and propels it using a single paddle. During paddling the board constantly is in an unstable condition forcing paddlers to focus on keeping balance and simultaneously propelling the board by paddling. Therefore it is expected that SUP can be a high impact aerobic workout and balance training. A total of 68 subjects performed on-water and SUP ergometer trials, during ergometer trials heart rate (HR) was permanently measured and balance was assessed before and after all trials (ergometer and on-water) using a single leg hop test on a Win Pod electronic baropedometric platform. Results of the balance tests - though for a relatively small number of participants - showed that after ergometer trials a significant improvement in stability occurred whereas it was only significant for the right foot's anteroposterior movement after on-water trials. The result of the exercise-test illustrated that the HR of beginners stays in the aerobic zone which makes SUP suitable for endurance training