Transient response of structures with uncertain properties to nonlinear shock loading

A method is presented to predict the transient response of a structure at the driving point following an impact or a shock loading. The displacement and the contact force are calculated solving the discrete convolution between the impulse response and the contact force itself, expressed in terms of a nonlinear Hertzian contact stiffness. Application of random point process theory allows the calculation of the impulse response function from knowledge of the modal density and the geometric characteristics of the structure only. The theory is applied to a wide range of structures and results are experimentally verified for the case of a rigid object hitting a beam, a plate, a thin and a thick cylinder and for the impact between two cylinders. The modal density of the flexural modes for a thick slender cylinder is derived analytically. Good agreement is found between experimental, simulated and published results, showing the reliability of the method for a wide range of situations including impacts and pyroshock applications. © 2013 Elsevier Ltd. All rights reserved.

Numerical analysis of shallow foundations under combined horizontal and torsional loading

Foundations of subsea infrastructure in deep water subjected to asymmetric environmental loads have underscored the importance of combined torsional and horizontal loading effects on the bearing capacity of rectangular shallow foundations. The purpose of this study is to investigate the undrained sliding and torsional bearing capacity of rectangular and square shallow foundations together with the interaction response under combined loading using three-dimensional finite element (3D-FE) analysis. Upper bound plastic limit analysis is employed to establish a reference value for horizontal and torsional bearing capacity, and an interaction relationship for the combined loading condition. Satisfactory agreement of plastic limit analysis (PLA) and 3D-FE results for ultimate capacity and interaction curves ensures that simple PLA solution could be used to evaluate the bearing capacity problem of foundation under combined sliding and torsion.

The sensitivity of vibration characteristics of reinforced concrete beams under incremental static and cyclic loading

The use of changes in vibration properties for global damage detection and monitoring of existing concrete structures has received great research attention in the last three decades. To track changes in vibration properties experimentally, structures have been artificially damaged by a variety of scenarios. However, this procedure does not represent realistically the whole design-life degradation of concrete structures. This paper presents experimental work on a set of damaged reinforced concrete beams due to different loading regimes to assess the sensitivity of vibration characteristics. Of the total set, three beams were subject to incremental static loading up to failure to simulate overloading, and two beams subject to 15 million loading cycles with varying amplitudes to produce an accelerated whole-life degradation scenario. To assess the vibration behaviour in both cases, swept sine and harmonic excitations were conducted at every damage level. The results show that resonant frequencies are not sensitive enough to damage due to cyclic loading, whereas cosh spectral and root mean square distances are more sensitive, yet more scattered. In addition, changes in non-linearity follow a softening trend for beams under incremental static loading, whilst they are significantly inconsistent for beams under cyclic loading. Amongst all examined characteristics, changes in modal stiffness are found to be most sensitive to damage and least scattered, but modal stiffness is tedious to compute due mainly to the difficulty of constructing restoring force surfaces from field measurements. © (2013) Trans Tech Publications.

Predicting the response of structures to transient shock loading.

This work concerns the prediction of the response of an uncertain structure to a load of short duration. Assuming an ensemble of structures with small random variations about a nominal form, a mean impulse response can be found using only the modal density of the structure. The mean impulse response turns out to be the same as the response of an infinite structure: the response is calculated by taking into account the direct field only, without reflections. Considering the short duration of an impulsive loading, the approach is reasonable before the effect of the reverberant field becomes important. The convolution between the mean impulse response and the shock loading is solved in discrete time to calculate the response at the driving point and at remote points. Experimental and numerical examples are presented to validate the theory presented for simple structures such as beams, plates, and cylinders.

Isolating shallow foundations from seismic loading

Most modern design codes do not allow for movement between a shallow foundation and the underlying soil during seismic loading. Consequently, the full magnitude of seismic energy is transmitted from the soil to the foundation during an earthquake. This energy either has to be dissipated before reaching the superstructure via engineering solutions such as base isolation systems, or the structure itself must withstand the full impact of the earthquake resulting in high material usage and expensive design. However, the inherent hysteric behaviour of soil can be used to isolate a foundation from the underlying soil. As part of a study into the soil-structure-interaction of shallow foundations, methods to optimise foundation isolation were investigated. In this paper the results from centrifuge tests investigating two of these methods are compared to results when no special foundation layout was implemented and the impact of the proposed isolation methods is discussed. © 2010 Taylor & Francis Group, London.

Centrifuge testing of monopiles subject to cyclic lateral loading

Monopiles supporting offshore wind turbines are subjected to cyclic lateral loading. The properties of the applied cyclic lateral load are known to have an effect on the accumulation of permanent displacement and rotation at the pile head. The results of centrifuge testing on model piles show that certain loading regimes lead to the development of locked in soil stresses around the pile. These locked in soil stresses change the stiffness of the monopile response to cyclic lateral loading and the natural frequency of the pile-soil system. © 2014 Taylor & Francis Group.

Meat and bone meal replacement in diets for juvenile gibel carp (Carassius auratus gibelio): effects on growth performance, phosphorus and nitrogen loading

A 11-week growth trial was conducted in a flow-through system with juvenile gibel carp Carassius auratus gibelio to evaluate the effects of gradual replacement of fish meal (FM) by meat and bone meal (MBM) on growth performance, phosphorus (P) and nitrogen (N) loading. Six isonitrogenous (crude protein: 410 g kg(-1)) and isoenergetic (gross energy: 18 kJ g(-1)) diets were formulated. FM was used as the control protein. In the other five diets, 20, 40, 60, 80 and 100% FM protein was substituted with MBM20, MBM40, MBM60, MBM80, MBM100, respectively. Total P content in the diets ranged from 16.0 to 28.3 g kg(-1) and the available P was 5.0-6.6 g kg(-1). The results showed that the best growth was achieved with fish fed on the control diet and MBM20. Final body weight, weight gain, feed efficiency, protein retention efficiency and energy retention efficiency decreased with increased dietary MBM. No significant differences were found in the feeding rate and hepatosomatic index between the groups. Apparent digestibility coefficient (ADC) of dry matter, protein and P decreased with increase in dietary MBM, while there were no significant differences in the ADC of energy. P and N retention decreased linearly while P and N loading increased linearly with the increased dietary MBM levels. No significant differences were observed in the activity of alkaline phosphatase, aspartate aminotransferase and alanine aminotransferase, as well as pyruvate kinase in liver or in serum. Total superoxide dismutase activity in MBM20 was significantly higher than that of MBM100.

Biological mechanisms driving the seasonal changes in the internal loading of phosphorus in shallow lakes

Because of the obvious importance of P as a nutrient that often accelerates growth of phytoplankton (including toxic cyanobacteria) and therefore worsens water quality, much interest has been devoted to P exchange across the sediment-water interface. Generally, the release mode of P from the sediment differed greatly between shallow and deep lakes, and much of the effort has been focused on iron and oxygen, and also on the relevant environmental factors, for example, turbulence and decomposition, but a large part of the P variation in shallow lakes remains unexplained. This paper reviews experimental and field studies on the mechanisms of P release from the sediment in the shallow temperate (in Europe) and subtropical (in the middle and lower reaches of the Yangtze River in China) lakes, and it is suggested that pH rather than DO might be more important in driving the seasonal dynamics of internal P loading in these shallow lakes, i.e., intense photosynthesis of phytoplankton increases pH of the lake water and thus may increase pH of the surface sediment, leading to enhanced release of P (especially iron-bound P) from the sediment. Based on the selective pump of P (but not N) from the sediment by algal blooms, it is concluded that photosynthesis which is closely related to eutrophication level is the driving force for the seasonal variation of internal P loading in shallow lakes. This is a new finding. Additionally, the selective pump of P from the sediment by algal blooms not only explains satisfactorily why both TP and PO4-P in the hypereutrophic Lake Donghu declined significantly since the mid-1980s when heavy cyanobacterial blooms were eliminated by the nontraditional biomanipulation (massive stocking of the filter-feeding silver and bighead carps), but also explains why TP in European lakes decreased remarkably in the spring clear-water phase with less phytoplankton during the seasonal succession of aquatic communities or when phytoplankton biomass was decreased by traditional biomanipulation. Compared with deep lakes, wax and wane of phytoplankton due to alternations in the ecosystem structure is also able to exert significant influences on the P exchange at the sediment-water interface in shallow lakes. In other words, biological activities are also able to drive P release from sediments, and such a static P release process is especially more prominent in eutrophic shallow lakes with dense phytoplankton.

Spatiotemporal variations of internal P-loading and the related mechanisms in the large shallow Lake Chaohu

Spatiotemporal variations of P species and adsorption behavior in water column, interstitial water, and sediments were investigated in the large shallow eutrophic Lake Chaohu. Orthophosphate (Ortho-P) and total phosphorus (TP) concentrations were significantly higher in the western part than in the eastern part of the lake, due to different nutrient inputs from the surrounding rivers. Moreover, particulate phosphorus (PP) concentration was in a similar spatial pattern to Ortho-P and TIP concentrations, and also showed significantly positive correlation with the biomass of Microcystis, indicating more uptake and store of phosphorus by Microcystis than by other algae. Increase of pH and intensive utilization of P by phytoplankton were the main factors promoting P (especially Fe-P) release from the sediment to interstitial water during the cyanobacterial blooms in Lake Chaohu. Spatial dynamics in TP concentration, P species and adsorption behavior of the sediment, coupled with the statistical analyses, suggested that the spatial heterogeneity of P contents in the sediment was influenced by various factors, e.g. human activities, soil geochemistry and mineral composition. In spite of similar TP contents in the sediments, increase in proportion of Fe-P concentration in the sediment may result in a high risk of P release.

Contributions of phosphatase and microbial activity to internal phosphorus loading and their relation to lake eutrophication

Phosphatase may accelerate the process of lake eutrophication through improving phosphorus bioavailability. This mechanism was studied in three Chinese eutrophic shallow lakes (Lake Taihu, Lake Longyang,and Lake Lianhua). Phosphatase activity was related to the concentration of soluble reactive phosphorus (SRP) and chlorophyll a. Stability of dissolved phosphatase in reverse micelles may be attributed to molecular size, conformation and active residues of the enzyme. At the site with Microcystis bloomed in Lake Taihu, dissolved phosphatase activity was higher and more stable in micelles, SRP concentrations were lower in interstitial water, the contents of different forms of phosphorus and the amounts of aerobic bacteria were lower while respiration efficiency was higher in sediments. Phosphobacteria, both inorganic and organic and other microorganisms were abundant in surface water but rare in sediments. Therefore, internal phosphorus may substantially flux into water column by enzymatic hydrolysis and anaerobic release, together with mobility of bacteria, thereby initiating the bloom. In short, biological mechanism may act in concert with physical and chemical factors to drive the internal phosphorus release and accelerate lake eutrophication.

Dynamic behaviors of mode III interfacial crack under a constant loading rate

In an earlier study on intersonic crack propagation, Gao et al. (J. Mech. Phys. Solids 49: 2113-2132, 2001) described molecular dynamics simulations and continuum analysis of the dynamic behaviors of a mode II dominated crack moving along a weak plane under a constant loading rate. The crack was observed to initiate its motion at a critical time after the onset of loading, at which it is rapidly accelerated to the Rayleigh wave speed and propagates at this speed for a finite time interval until an intersonic daughter crack is nucleated at a peak stress at a finite distance ahead of the original crack tip. The present article aims to analyze this behavior for a mode III crack moving along a bi-material interface subject to a constant loading rate. We begin with a crack in an initially stress-free bi-material subject to a steadily increasing stress. The crack initiates its motion at a critical time governed by the Griffith criterion. After crack initiation, two scenarios of crack propagation are investigated: the first one is that the crack moves at a constant subsonic velocity; the second one is that the crack moves at the lower shear wave speed of the two materials. In the first scenario, the shear stress ahead of the crack tip is singular with exponent -1/2, as expected; in the second scenario, the stress singularity vanishes but a peak stress is found to emerge at a distance ahead of the moving crack tip. In the latter case, a daughter crack supersonic with respect to the softer medium can be expected to emerge ahead of the initial crack once the peak stress reaches the cohesive strength of the interface.

Analytical method of predicating the instabilities of a micro arch-shaped beam under electrostatic loading

An arch-shaped beam with different configurations under electrostatic loading experiences either the direct pull-in instability or the snap-through first and then the pull-in instability. When the pull-in instability occurs, the system collides with the electrode and adheres to it, which usually causes the system failure. When the snap-through instability occurs, the system experiences a discontinuous displacement to flip over without colliding with the electrode. The snap-through instability is an ideal actuation mechanism because of the following reasons: (1) after snap-through the system regains the stability and capability of withstanding further loading; (2) the system flips back when the loading is reduced, i.e. the system can be used repetitively; and (3) when approaching snap-through instability the system effective stiffness reduces toward zero, which leads to a fast flipping-over response. To differentiate these two types of instability responses for an arch-shaped beam is vital for the actuator design. For an arch-shaped beam under electrostatic loading, the nonlinear terms of the mid-plane stretching and the electrostatic loading make the analytical solution extremely difficult if not impossible and the related numerical solution is rather complex. Using the one mode expansion approximation and the truncation of the higher-order terms of the Taylor series, we present an analytical solution here. However, the one mode approximation and the truncation error of the Taylor series can cause serious error in the solution. Therefore, an error-compensating mechanism is also proposed. The analytical results are compared with both the experimental data and the numerical multi-mode analysis. The analytical method presented here offers a simple yet efficient solution approach by retaining good accuracy to analyze the instability of an arch-shaped beam under electrostatic loading.