A hybrid-mixed finite element formulation for the geometrically exact analysis of three-dimensional framed structures

This paper addresses the development of a hybrid-mixed finite element formulation for the quasi-static geometrically exact analysis of three-dimensional framed structures with linear elastic behavior. The formulation is based on a modified principle of stationary total complementary energy, involving, as independent variables, the generalized vectors of stress-resultants and displacements and, in addition, a set of Lagrange multipliers defined on the element boundaries. The finite element discretization scheme adopted within the framework of the proposed formulation leads to numerical solutions that strongly satisfy the equilibrium differential equations in the elements, as well as the equilibrium boundary conditions. This formulation consists, therefore, in a true equilibrium formulation for large displacements and rotations in space. Furthermore, this formulation is objective, as it ensures invariance of the strain measures under superposed rigid body rotations, and is not affected by the so-called shear-locking phenomenon. Also, the proposed formulation produces numerical solutions which are independent of the path of deformation. To validate and assess the accuracy of the proposed formulation, some benchmark problems are analyzed and their solutions compared with those obtained using the standard two-node displacement/ rotation-based formulation.

Shell curvature as an initial deformation: A geometrically exact finite element approach

An alternative approach for the analysis of arbitrarily curved shells is developed in this paper based on the idea of initial deformations. By `alternative` we mean that neither differential geometry nor the concept of degeneration is invoked here to describe the shell surface. We begin with a flat reference configuration for the shell mid-surface, after which the initial (curved) geometry is mapped as a stress-free deformation from the plane position. The actual motion of the shell takes place only after this initial mapping. In contrast to classical works in the literature, this strategy enables the use of only orthogonal frames within the theory and therefore objects such as Christoffel symbols, the second fundamental form or three-dimensional degenerated solids do not enter the formulation. Furthermore, the issue of physical components of tensors does not appear. Another important aspect (but not exclusive of our scheme) is the possibility to describe exactly the initial geometry. The model is kinematically exact, encompasses finite strains in a totally consistent manner and is here discretized under the light of the finite element method (although implementation via mesh-free techniques is also possible). Assessment is made by means of several numerical simulations. Copyright (C) 2009 John Wiley & Sons, Ltd.

Hybrid and multi-field variational principles for geometrically exact three-dimensional beams

This paper addresses the development of several alternative novel hybrid/multi-field variational formulations of the geometrically exact three-dimensional elastostatic beam boundary-value problem. In the framework of the complementary energy-based formulations, a Legendre transformation is used to introduce the complementary energy density in the variational statements as a function of stresses only. The corresponding variational principles are shown to feature stationarity within the framework of the boundary-value problem. Both weak and linearized weak forms of the principles are presented. The main features of the principles are highlighted, giving special emphasis to their relationships from both theoretical and computational standpoints. (C) 2010 Elsevier Ltd. All rights reserved.

Spontaneous vegetation on overburden piles in the Coal Basin of Santa Catarina, Brazil

The objective of this work was to select indigenous vegetal species for restoration programs aiming at the regeneration of ombrophilous dense forest. Thirty-five spoil piles located in the county of Sideropolis, Santa Catarina, that received overburden disposal for 39 years (1950-1989) were selected for study because they exhibited remarkable spontaneous regrowth of trees compared to surrounding spoil piles. Floristic inventory covered the whole area of the 35 piles, whereas survey on phytosociology and natural regeneration studies were conducted in 70 plots distributed along the 35 piles. Floristic inventory recorded 83 species from 28 botanical families. Herbaceous terricolous plants constituted the predominant species (47.0%), followed by shrubs (26.5%), trees (19.3%), and vines (7.2%). Results from surveys on phytosociology and natural regeneration, focused on shrubs and trees, recorded incipient ecological succession. In addition, the most adapted species recorded on the overburden piles, as ranked by index of natural regeneration (RNT) plus importance value index (IVI), were as follows: Clethra scabra (RNT = 23.93%; IVI = 17.28%), Myrsine coriacea (RNT = 20.93%, IVI = 11.26%), Eupatorium intermedium (RNT 7.56%, IVI 0.40%), Miconia ligustroides (RNT 5.84%, IVI 2.37%), Ossaea amygdaloides (RNT 3.84%, IVI 1.30%), Tibouchina sellowiana (RNT 3.29%, M 1.94%), Eup. inulaefolium (RNT = 2.65%, IVI = 0.80%), and Baccharis dracunculifolia (RNT = 2.28%; IVI = 0.56%). High values of IVI and RNT exhibited by the exotic species Eucalyptus saligna (IVI = 21.73%, RNT = 51.41%) indicated strong competition between exotic and indigenous species. Severe chemical (acidic pH and lack of nutrients) and physical (coarse substrate and slope angle of 40-50 degrees) characteristics displayed by the overburden piles constituted limitations to floristic diversity and size of indigenous trees, indicating the need for substrate reclamation prior to forest restoration.

Finite Element Analysis and Optimization of a Single-Axis Acoustic Levitator

A finite element analysis and a parametric optimization of single-axis acoustic levitators are presented. The finite element method is used to simulate a levitator consisting of a Langevin ultrasonic transducer with a plane radiating surface and a plane reflector. The transducer electrical impedance, the transducer face displacement, and the acoustic radiation potential that acts on small spheres are determined by the finite element method. The numerical electrical impedance is compared with that acquired experimentally by an impedance analyzer, and the predicted displacement is compared with that obtained by a fiber-optic vibration sensor. The numerical acoustic radiation potential is verified experimentally by placing small spheres in the levitator. The same procedure is used to optimize a levitator consisting of a curved reflector and a concave-faced transducer. The numerical results show that the acoustic radiation force in the new levitator is enhanced 604 times compared with the levitator consisting of a plane transducer and a plane reflector. The optimized levitator is able to levitate 3, 2.5-mm diameter steel spheres with a power consumption of only 0.9 W.

Colloidal Processing of Glass-Ceramics for Laminated Object Manufacturing

Green tapes of Li(2)O-ZrO(2)-SiO(2)-Al(2)O(3) (LZSA) parent glass were produced by aqueous tape casting as the starting material for the laminated object manufacturing (LOM) process. The rheological behavior of the powder suspensions in aqueous media, as well as the mechanical properties of the cast tapes, was evaluated. According to xi potential measurements, the LZSA glass powder particles showed acid surface characteristics and an IEP of around 4 when in aqueous media. The critical volume fraction of solids was about 72 wt% (27 vol%), which hindered the processability of more concentrated slurries. The glass particles also showed an anisometric profile, which contributed to an increase in the interactions between particles during flow. Therefore, the suspensions could not be processed at high solids loadings. Aqueous-based glass suspensions were also characterized by shear thickening after the addition of dispersants. Three slurry compositions were formulated, suitable green tapes were cast, and tapes were successfully laminated by LOM to a gear wheel geometry. A higher tensile strength of the green tapes corresponded to a higher tensile strength of the laminates. Thermal treatment was then applied to the laminates: pyrolysis at 525 degrees C, sintering at 700 degrees C for 1 h, and crystallization at 850 degrees C for 30 min. A 20% volumetric shrinkage was observed, but no surface flaws or inhomogeneous areas were detected. The sintered part maintained the curved edges and internal profile after heat treatment.

Residence time distribution in holding tubes using generalized convection model and numerical convolution for non-ideal tracer detection

A procedure is proposed for the determination of the residence time distribution (RTD) of curved tubes taking into account the non-ideal detection of the tracer. The procedure was applied to two holding tubes used for milk pasteurization in laboratory scale. Experimental data was obtained using an ionic tracer. The signal distortion caused by the detection system was considerable because of the short residence time. Four RTD models, namely axial dispersion, extended tanks in series, generalized convection and PER + CSTR association, were adjusted after convolution with the E-curve of the detection system. The generalized convection model provided the best fit because it could better represent the tail on the tracer concentration curve that is Caused by the laminar velocity profile and the recirculation regions. Adjusted model parameters were well cot-related with the now rate. (C) 2010 Elsevier Ltd. All rights reserved.

Impact of seedling removal on regenerating community structure of a seasonal semideciduous forest

(Impact of seedling removal on regenerating community structure of a seasonal semideciduous forest). Transplanting seedlings and saplings from natural forests has been considered an alternative to producing saplings of native species for forest restoration purposes, but the possible impact of this procedure on plant community regeneration has not been investigated. This work evaluates the impact of different treatments of shrub and tree-seedling (up to 30 cm) removal from a seasonal semideciduous forest fragment located in southeastern Brazil on the natural regeneration process. Eighty 2x2 m plots were installed in two habitats (forest edge and interior) and submitted to four seedling-removal treatments (I, II - 100% removal with or without soil mixing; III - 50% removal without soil mixing: and IV - control treatment Without seedling removal). Regeneration density and richness were evaluated before treatment as well as 6, 12 and 18 months later. The results were compared among treatments for each evaluation period and among periods within treatments. There were similarities between edge and interior. The natural regeneration process did not improve with soil mixing. Plots submitted to seedling removal partially recovered plant density; however, these plots had lower species richness when compared to the control and to the initial values before treatment. Seedling removal has a negative impact on the regeneration process of low-density species, thus the use of natural regeneration as a sapling source for forest restoration purposes should focus only on high-density species with well-known regeneration strategies and not on the community as a whole.

Carbon and nitrogen cycling in a tropical Brazilian soil cropped with sugarcane and irrigated with wastewater

Carbon (C) and nitrogen (N) dynamics in agro-systems can be altered as a consequence of treated sewage effluent (TSE) irrigation. The present study evaluated the effects of TSE irrigation over 16 months on N concentrations in sugarcane (leaves, stalks and juice), total soil carbon (TC), total soil nitrogen (TN), NO(3)(-)-N in soil and nitrate (NO(3)(-)) and dissolved organic carbon (DOC) in soil solution. The soil was classified as an Oxisol and samplings were carried out during the first productive crop cycle, from February 2005 (before planting) to September 2006 (after sugarcane harvest and 16 months of TSE irrigation). The experiment was arranged in a complete block design with five treatments and four replicates. Irrigated plots received 50% of the recommended mineral N fertilization and 100% (T100), 125% (T125), 150% (T150) and 200% (T200) of crop water demand. No mineral N and irrigation were applied to the control plots. TSE irrigation enhanced sugarcane yield but resulted in total-N inputs(804-1622 kg N ha(-1)) greater than exported N (463-597 kg N ha(-1)). Hence, throughout the irrigation period, high NO(3)(-) concentrations (up to 388 mg L(-1) at T200) and DOC (up to 142 mg L(-1) at T100) were measured in soil solution below the root zone, indicating the potential of groundwater contamination. TSE irrigation did not change soil TC and TN. (C) 2009 Elsevier B.V. All rights reserved.

Can Eucalyptus invade native forest fragments close to commercial stands?

Some Eucalyptus species are widely used as a plantation crop in tropical and subtropical regions. One reason for this is the diversity of end uses, but the main reason is the high level of wood production obtained from commercial plantings. With the advancement of biotechnology it will be possible to expand the geographical area in which eucalypts can be used as commercial plantation crops, especially in regions with current climatic restrictions. Despite the popularity of eucalypts and their increasing range, questions still exist, in both traditional planting areas and in the new regions: Can eucalypts invade areas of native vegetation, causing damage to natural ecosystems biodiversity? The objective of this study it was to assess whether eucalypts can invade native vegetation fragments in proximity to commercial stands, and what factors promote this invasive growth. Thus, three experiments were established in forest fragments located in three different regions of Brazil. Each experiment was composed of 40 plots (1 m(2) each one), 20 plots located at the border between the forest fragment and eucalypts plantation, and 20 plots in the interior of the forest fragments. In each experimental site, the plots were paired by two soil exposure conditions, 10 plots in natural conditions and 10 plots with soil exposure (no plant and no litter). During the rainy season, 2 g of eucalypts seeds were sown in each plot, including Eucalyptus grandis or a hybrid of E. urophylla x E. grandis, the most common commercial eucalypt species planted in the three region. At 15, 30, 45, 90, 180, 270 and 360 days after sowing, we assessed the number of seedlings of eucalypts and the number of seedlings of native species resulting from natural regeneration. Fifteen days after sowing, the greatest number of eucalypts seedlings (37 m(-2)) was observed in the plots with lower luminosity and exposed soil. Also, for native species, it was observed that exposed soil improved natural germination reaching the highest number of 163 seedlings per square meter. Site and soil exposure were the factors that have the greatest influence on seed germination of both eucalypt and native species. However, 270 days after sowing, eucalypt seedlings were not observed at any of the three experimental sites. The result shows the inability of eucalypts to adapt to condition outside of their natural range. However, native species demonstrated their strong capacity for natural regeneration in forest fragments under the same conditions where eucalypts were seeded. (C) 2011 Elsevier B.V. All rights reserved.

An estimate of biometric parameters in eucalyptus clone plantations in Southern Bahia: an application of the airborne laser scanning (ALS) technology

The application of airborne laser scanning (ALS) technologies in forest inventories has shown great potential to improve the efficiency of forest planning activities. Precise estimates, fast assessment and relatively low complexity can explain the good results in terms of efficiency. The evolution of GPS and inertial measurement technologies, as well as the observed lower assessment costs when these technologies are applied to large scale studies, can explain the increasing dissemination of ALS technologies. The observed good quality of results can be expressed by estimates of volumes and basal area with estimated error below the level of 8.4%, depending on the size of sampled area, the quantity of laser pulses per square meter and the number of control plots. This paper analyzes the potential of an ALS assessment to produce certain forest inventory statistics in plantations of cloned Eucalyptus spp with precision equal of superior to conventional methods. The statistics of interest in this case were: volume, basal area, mean height and dominant trees mean height. The ALS flight for data assessment covered two strips of approximately 2 by 20 Km, in which clouds of points were sampled in circular plots with a radius of 13 m. Plots were sampled in different parts of the strips to cover different stand ages. The clouds of points generated by the ALS assessment: overall height mean, standard error, five percentiles (height under which we can find 10%, 30%, 50%,70% and 90% of the ALS points above ground level in the cloud), and density of points above ground level in each percentile were calculated. The ALS statistics were used in regression models to estimate mean diameter, mean height, mean height of dominant trees, basal area and volume. Conventional forest inventory sample plots provided real data. For volume, an exploratory assessment involving different combinations of ALS statistics allowed for the definition of the most promising relationships and fitting tests based on well known forest biometric models. The models based on ALS statistics that produced the best results involved: the 30% percentile to estimate mean diameter (R(2)=0,88 and MQE%=0,0004); the 10% and 90% percentiles to estimate mean height (R(2)=0,94 and MQE%=0,0003); the 90% percentile to estimate dominant height (R(2)=0,96 and MQE%=0,0003); the 10% percentile and mean height of ALS points to estimate basal area (R(2)=0,92 and MQE%=0,0016); and, to estimate volume, age and the 30% and 90% percentiles (R(2)=0,95 MQE%=0,002). Among the tested forest biometric models, the best fits were provided by the modified Schumacher using age and the 90% percentile, modified Clutter using age, mean height of ALS points and the 70% percentile, and modified Buckman using age, mean height of ALS points and the 10% percentile.

A positive growth response to NaCl applications in Eucalyptus plantations established on K-deficient soils

Contrasting responses of Eucalyptus trees to K fertilizer applications have been reported on soils with low K contents. A complete randomized block experiment was set up in Brazil to test the hypothesis that large atmospheric deposits of NaCl in coastal regions might lead to a partial substitution of K by Na in Eucalyptus physiology and enhance tree growth. Treatments with application of 1.5, 3.0, 4.5 kmol K ha(-1) (K(1.5), K(3.0), 1(4.5, respectively) as KCl, 3.0 kmol K ha(-1) applied as K(2)SO(4), 3.0 kmol Na ha(-1) (Na(3.0)) as NaCl commercialized for cattle feeding, and a mixture of 1.5 kmol K + 1.5 kmol Na ha(-1) (K(1.5) + Na(1.5)) were compared to a control treatment (C) with no K and Na applications. All the plots were fertilized with large amounts of the other nutrients. A positive effect of NaCl applications on the growth of E. grandis trees was observed. NaCl and KCl additions in treatments Na(3.0) and K(3.0) increased above-ground biomass by 56% and 130% three years after planting, respectively, in comparison with the C treatment. By contrast, accumulated litterfall up to age 3 years was not significantly modified. NaCl applications in the Na(3.0) treatment significantly increased Na accumulation in above-ground tree components but did not modify K accumulation, whatever the sampling age. A partial substitution of K by Na in tree physiology, as observed for various agricultural crops, might explain this behaviour. Our results suggest the possibility of applying inexpensive K fertilizers, which are less purified in Na, and explain why high yields are achieved without K fertilizer applications in areas with large dry depositions of marine aerosols. Further investigations are necessary to identify the processes involving Na in Eucalyptus tree physiology. (C) 2009 Elsevier B.V. All rights reserved.

Why don`t our stands grow even faster? Control of production and carbon cycling in eucalypt plantations

The growth of Eucalyptus stands varies several fold across sites, under the influence of resource availability, stand age and stand structure. We describe a series of related studies that aim to understand the mechanisms that drive this great range in stand growth rates. In a seven-year study in Hawaii of Eucalyptus saligna at a site that was not water limited, we showed that nutrient availability differences led to a two-fold difference in stand wood production. Increasing nutrient supply in mid-rotation raised productivity to the level attained in continuously fertilised plots. Fertility affected the age-related decline in wood and foliage production; production in the intensive fertility treatments declined more slowly than in the minimal fertility treatments. The decline in stem production was driven largely by a decline in canopy photosynthesis. Over time, the fraction of canopy photosynthesis partitioned to below-ground allocation increased, as did foliar respiration, further reducing wood production. The reason for the decline in photosynthesis was uncertain, but it was not caused by nutrient limitation, a decline in leaf area or in photosynthetic capacity, or by hydraulic limitation. Most of the increase in carbon stored from conversion of the sugarcane plantation to Eucalyptus plantation was in the above-ground woody biomass. Soil carbon showed no net change. This study and other studies on carbon allocation showed that resource availability changes the fraction of annual photosynthesis used below-ground and for wood production. High resources (nutrition or water) decrease the partitioning below-ground and increase partitioning to wood production. Annual foliage and wood respiration and foliage production as a fraction of annual photosynthesis was remarkably constant across a wide range of fertility treatments and forest age. In the Brazil Eucalyptus Productivity Project, stand structure was manipulated by planting clonal Eucalyptus all at once or in three groups at three-monthly intervals, producing a stand where trees did not segregate into dominants and one that had strong dominance. The uneven stand structure reduced production 10-15% throughout the rotation.

Production and carbon allocation in a clonal Eucalyptus plantation with water and nutrient manipulations

We examined resource limitations on growth and carbon allocation in a fast-growing, clonal plantation of Eucalyptus grandis x urophylla in Brazil by characterizing responses to annual rainfall, and response to irrigation and fertililization for 2 years. Productivity measures included gross primary production (GPP), total belowground carbon allocation (TBCA), bole growth, and net ecosystem production (NEP). Replicate plots within a single plantation were established at the midpoint of the rotation (end of year 3), with treatments of no additional fertilization or irrigation, heavy fertilization (to remove any nutrient limitation), irrigation (to remove any water limitation), and irrigation plus fertilization. Rainfall was unusually high in the first year (1769mm) of the experiment, and control plots had high rates of GPP (6.64 kg C m(-2) year(-1)), TBCA (2.14 kg C m(-2) year(-1)), and bole growth (1.81 kg C m(-2) year). Irrigation increased each of these rates by 15-17%. The second year of the experiment had average rainfall (1210 mm), and lower rainfall decreased production in control plots by 46% (GPP), 52% (TBCA), and 40% (bole growth). Fertilization treatments had neglible effects. The response to irrigation was much greater in the drier year, with irrigated plots exceeding the production in control plots by 83% (GPP), 239% (TBCA), and 24% (bole growth). Even though the rate of irrigation ensured no water limitation to tree growth, the high rainfall year showed higher production in irrigated plots for both GPP (38% greater than in drier year) and bole growth (23% greater). Varying humidity and supplies of water led to a range in NEP of 0.8-2.7 kg C m(-2) year. This difference between control and irrigated treatments, combined with differences between drier and wetter years, indicated a strong response of these Eucalyptus trees to both water supply and atmospheric humidity during the dry season. The efficiency of converting light energy into fixed carbon ranged from a low of 0.027 mol C to a high of 0.060 mol C per mol of absorbed photosynthetically active radiation (APAR), and the efficiency of bolewood production ranged from 0.78 to 1.98 g wood per MJ of APAR. Irrigation increased the efficiency of wood production per unit of water used from 2.55 kg wood m(-3) in the rainfed plot to 3.51 kg m(-3) in irrigated plots. Detailed information on the response of C budgets to environmental conditions and resource supplies will be necessary for accurate predictions of plantation yields across years and landscapes. (V) 2007 Elsevier B.V. All rights reserved.

Annual and polyetic progression of citrus canker on trees protected with copper sprays

The effects of copper sprays on annual and polyetic progress of citrus canker, caused by Xanthomonas citri subsp. citri, in the presence of the Asian citrus leafminer (Phyllocnistis citrella), were evaluated in a study conducted in a commercial orchard in northwest Parana state, Brazil, where citrus canker is endemic. Nonlinear monomolecular, logistic and Gompertz models were fitted to monthly disease incidence data (proportion of leaves with symptoms) for each treatment for three seasons. The logistic model provided the best estimate of disease progress for all years and treatments evaluated and logistic parameter estimates were used to describe polyetic disease dynamics. Although citrus canker incidence increased during each of the seasons studied, it decreased over the whole study period, more so in copper-treated trees than in water-sprayed controls. Copper treatment reduced disease incidence compared with controls in every year, especially 2004-2005, when incidence was ca. 10-fold higher in controls than in treated plots (estimated asymptote values 0 center dot 82 and 0 center dot 07, respectively). Copper treatment also reduced estimated initial disease incidence and epidemic growth rates every year.