Mechatronic Model of a Compliant 3PRS Parallel Manipulator

Compliant mechanisms are widely used for instrumentation and measuring devices for their precision and high bandwidth. In this paper, the mechatronic model of a compliant 3PRS parallel manipulator is developed, integrating the inverse and direct kinematics, the inverse dynamic problem of the manipulator and the dynamics of the actuators and the control. The kinematic problem is solved, assuming a pseudo-rigid model for the deflection in the compliant revolute and spherical joints. The inverse dynamic problem is solved, using the Principle of Energy Equivalence. The mechatronic model allows the prediction of the bandwidth of the manipulator motion in the 3 degrees of freedom for a given control and set of actuators, helping in the design of the optimum solution. A prototype is built and validated, comparing experimental signals with the ones from the model.

Space-Time-Energy Equivalence

The equivalence of space–time and energy are the principle that everything that has space and time has an equivalent amount of energy, and vice versa. It is presented here as an axiom that has become widespread in physics and astrophysics.

Unsteady Linearisation of Bed Shear Stress for Idealised Storm Surge Modelling

The modelling of time-varying shallow flows, such as tides and storm surges, is complicated by the nonlinear dependency of bed shear stress on flow speed. For tidal flows, Lorentz’s linearisation circumvents nonlinearity by specifying a (steady) friction coefficient r based on a tide-averaged criterion of energy equivalence. However, this approach is not suitable for phenomena with episodic and irregular forcings such as storm surges. Here, we studied the implications of applying Lorentz’s energy criterion in an instantaneous sense, so that an unsteady friction coefficient r(t) adjusts to the temporal development of natural wind-driven flows. This new bed-stress parametrisation was implemented in an idealised model of a single channel, forced by time-varying signals of wind stress (acting over the entire domain) and surface elevation (at the channel mouth). The solution method combines analytical solutions of the cross-sectionally averaged linearised shallow-water equations, obtained in the frequency domain, with an iterative procedure to determine r(t). Model results, compared with a reference finite-difference solution retaining the quadratic bed shear stress, show that this new approach accurately captures the qualitative and quantitative aspects of the surge dynamics (height and timing of surge peaks, sloshing, friction-induced tide-surge interaction) for both synthetic and realistic wind forcings.

Long-term experimental evolution decouples size and production costs in Escherichia coli

Body size covaries with population dynamics across lifes domains. Theory holds that metabolism imposes fundamental constraints on the coevolution of size and demography. However, studies of interspecific patterns are confounded by other factors that covary with size and demography, and experimental tests of the causal links remain elusive. Here we leverage a 60,000-generation experiment in which Escherichia coli populations evolved larger cells to examine intraspecific metabolic scaling and correlations with demographic parameters. Metabolic theory successfully predicted the relations among size, metabolism, and maximum population density, with strong support for Damuths law of energy equivalence in this experiment. In contrast, populations of larger cells grew faster than those of smaller cells, contradicting the fundamental assumption that costs of production should increase proportionately with size. The finding that the costs of production are substantially decoupled from size requires re-examining the evolutionary drivers and ecological consequences of biological size more generally.

Validation of notch stress estimation schemes for different constraints, strain gradients and loading conditions on low C-Mn steel

The present study is aimed at validation of notch stress/ strain estimation schemes such as classical Neuber, Hoffmann-Seeger and recently developed Ince-Glinka method for Nuclear piping material (low C-Mn steel). The study has considered different constraints, loading conditions, various hole sizes to accommodate strain gradient variations and equivalent peak strains. The notch stress field evaluated using these schemes is compared with corresponding stress using elastic-plastic Finite Element (FE) analyses. The comparisons have brought out that the Hoffmann-Seeger scheme results in reasonably accurate assessment of stress localization nearly for all constraint geometries, loadings and strain gradients. However, the classical Neuber scheme is more suitable for low constraint geometries and intermediate constraint geometries whereas it results in under-estimation of maximum principal stress for high constraint geometries, thereby leading to over-prediction of fatigue life. Further, the suitability of energy equivalence equations of Ince-Glinka model for individual stress components, has been reviewed.

Metabolism drives demography in an experimental field test

Metabolism should drive demography by determining the rates of both biological work and resource demand. Long-standing “rules” for how metabolism should covary with demography permeate biology, from predicting the impacts of climate change to managing fisheries. Evidence for these rules is almost exclusively indirect and in the form of among-species comparisons, while direct evidence is exceptionally rare. In a manipulative field experiment on a sessile marine invertebrate, we created experimental populations that varied in population size (density) and metabolic rate, but not body size. We then tested key theoretical predictions regarding relationships between metabolism and demography by parameterizing population models with lifetime performance data from our field experiment. We found that populations with higher metabolisms had greater intrinsic rates of increase and lower carrying capacities, in qualitative accordance with classic theory. We also found important departures from theory—in particular, carrying capacity declined less steeply than predicted, such that energy use at equilibrium increased with metabolic rate, violating the long-standing axiom of energy equivalence. Theory holds that energy equivalence emerges because resource supply is assumed to be independent of metabolic rate. We find this assumption to be violated under real-world conditions, with potentially far-reaching consequences for the management of biological systems.

Analytical examination of mesh-dependency issue for uniaxial RC elements and new fracture energy-based regularization technique

This paper presents a comprehensive analysis of the mesh-dependency issue for both plain concrete and reinforced concrete (RC) members under uniaxial loading. The detailed mechanisms for each case are firstly derived, and the analytical and numerical strain energies for concrete in different cases are compared to explain the phenomena of mesh-dependency. It is found that the mesh-dependency will be relieved or even eliminated with the increasing of the reinforcing ratio. Meanwhile, a concept of the critical reinforcing ratio is proposed to identify the corresponding boundary of mesh-dependency of RC members. In order to verify the above findings, several illustrative examples are performed and discussed. Finally, to overcome the mesh-dependency issue for RC members with lower reinforcing ratios, we propose a unified regularization method that modifies both stress-strain relations of steel and concrete based on the strain energy equivalence. The method is also applied to the illustrative examples for validation, and the numerical results indicate that the developed method can obtain objective results for cases with different meshes and reinforcing ratios.

Solid Truss to Shell Numerical Homogenization of Prefabricated Composite Slabs

The need for quick and easy deflection calculations of various prefabricated slabs causes simplified procedures and numerical tools to be used more often. Modelling of full 3D finite element (FE) geometry of such plates is not only uneconomical but often requires the use of complex software and advanced numerical knowledge. Therefore, numerical homogenization is an excellent tool, which can be easily employed to simplify a model, especially when accurate modelling is not necessary. Homogenization allows for simplifying a computational model and replacing a complicated composite structure with a homogeneous plate. Here, a numerical homogenization method based on strain energy equivalence is derived. Based on the method proposed, the structure of the prefabricated concrete slabs reinforced with steel spatial trusses is homogenized to a single plate element with an effective stiffness. There is a complete equivalence between the full 3D FE model built with solid elements combined with truss structural elements and the simplified homogenized plate FE model. The method allows for the correct homogenization of any complex composite structures made of both solid and structural elements, without the need to perform advanced numerical analyses. The only requirement is a correctly formulated stiffness matrix of a representative volume element (RVE) and appropriate formulation of the transformation between kinematic constrains on the RVE boundary and generalized strains.

Absolute mass of photons based upon the Hamiltonian of energy content

In this article, the mass-energy equivalence is analyzed based on the total energy content & inertia of a body. The analysis included quantum energy formalization with relativity. The finding suggests that photons have absolute mass to justify their momentum.