Constrained Boundary Research Articles

Fractional modeling of Pasternak-type viscoelastic foundation

In this paper, we propose a fractional Pasternak-type foundation model to characterize the time-dependent properties of the viscoelastic foundation. With varying fractional orders, the proposed model can govern the traditional Winkler model, Pasternak model, and viscoelastic model. We take the four-edge simply supported rectangular thin plate as an example to analyze the viscoelastic foundation reaction, and obtain the solution of the new governing equation. Theoretical results show that the fractional order has a dramatic influence on the deflection and bending moment. It can be further concluded that the softer foundation will become more time-dependent. Subsequently, the difference between fractional Pasternak-type and Winkler foundation model is presented in this work. The existence of constrained boundary is found to definitely affect deflection and bending moment. Such phenomenon, known as the wall effect, is deeply discussed.

Dynamic Characteristics of the Herringbone Groove Gas Journal Bearings: Numerical Simulations

Dynamic characteristics of the herringbone grooved gas journal bearings (HGGJB) under fluid-structure interactions are systematically investigated using the finite element method. Stability and bearing capacity of the HGGJB are estimated and compared with those of the plain gas journal bearings (PGJB). Influences of the structural parameters, including the spiral angle, the groove number, the groove depth, the pressure relief hole diameter, the bearing radial clearance, the length to diameter ratio, and the rotating speed, on dynamic characteristics of HGGJB are analyzed. To verify the numerical simulation results, pressure nephograms and cross-section pressure curves of the same rotor model, calculated by the numerical simulation and the theoretical method, respectively, are compared. Similar results are obtained. Compared to the common constrained boundary conditions in the previous numerical simulations, boundary conditions adopted in this paper are complete self-absorption and the change of the gas inlet and outlet depends on the rotating state of the rotor, which are more accordant with the real dynamic characteristics of the HGGJB. In all, the results presented in this paper provide a deeper and better understanding of the dynamic characteristics of the HGGJB under fluid-structure interactions.

Coupled instabilities of surface crease and bulk bending during fast free swelling of hydrogels.

Most studies on hydrogel swelling instability have been focused on a constrained boundary condition. In this paper, we studied the mechanical instability of a piece of disc-shaped hydrogel during free swelling. The fast swelling of the gel induces two swelling mismatches; a surface-inner layer mismatch and an annulus-disc mismatch, which lead to the formation of a surface crease pattern and a saddle-like bulk bending, respectively. For the first time, a stripe-like surface crease that is at a right angle on the two surfaces of the gel was observed. This stripe pattern is related to the mechanical coupling of surface instability and bulk bending, which is justified by investigating the swelling-induced surface pattern on thin hydrogel sheets fixed onto a saddle-shaped substrate prior to swelling. A theoretical mechanism based on an energy model was developed to show an anisotropic stripe-like surface crease pattern on a saddle-shaped surface. These results might be helpful to develop novel strategies for controlling crease patterns on soft and wet materials by changing their three-dimensional shape.

Boundary effects on ground surface rupture induced by normal faulting

Although centrifuge modelling has been used for studying soil–bedrock interaction, the limited space available in a model container to simulate prototype situations imposes challenges. This article introduces and discusses boundary effects on surface fault ruptures induced by normal faulting in clay and nine-layered soil strata in a geotechnical centrifuge. Both a horizontal kinematically constrained boundary and an unconstrained boundary, representing two extreme cases in the field, were applied. Their effects on soil deformation and the location of surface fault rupture are thoroughly compared and discussed. For both the clay and the nine-layered soil strata, the unconstrained boundary shifted the induced settlement profile towards the footwall, extended the range of soil subjected to tension, increased the horizontal displacement of the soil at the hanging wall and extended the influence zone of the surface fault rupture when compared with the constrained boundary cases. Compared with the clay stratum, the influence zone of surface fault rupture in the nine-layered soil was significantly reduced under the constrained boundary. However, the main rupture in both the clay and nine-layered soil strata was located at the intersection of the bedrock fault plane and the ground surface, independent of the boundary condition.

Modeling and Vibration Control for a Nonlinear Moving String With Output Constraint

In this paper, boundary control laws are developed to stabilize the transverse vibration for a nonlinear vertically moving string system. The control system is considered with varying length, varying speed, and the constrained boundary output. Based on the integral-barrier Lyapunov function, the exponential stability is proved with the proposed control without consideration of the disturbance. When the external boundary disturbance is taken into account, the disturbance observer is designed to eliminate its effect. The vibration is regulated and the boundary output always remains in the constrained space by appropriately choosing the control parameters. The control design and the stability analysis are based on the original infinite-dimensional dynamic equations. Extensive numerical examples illustrate the performance of the control system.

Healing-on-demand composites based on polymer artificial muscle

In this study, a new polymer artificial muscle based healing-on-demand composite was prepared and characterized. The composite consists of polymer artificial muscle made of commercial fishing line, thermoset host, and thermoplastic particle. Three-point bending damage to the beam sample can be healed even at a constrained boundary condition upon local heating, undergoing a close-then-heal procedure. The fractured beams were heated locally by a heat gun for 10 min. The healing efficiency was investigated at both free boundary condition and fixed boundary condition. The fast contraction of artificial muscle brings the fractured surfaces in spatial proximity; simultaneously, the melting thermoplastic agent fills the crack via capillary action and bonds the two fracture surfaces. With 60% prestrain of the reinforcing polymer artificial muscles (8% volume fraction), over 60% of healing efficiency was achieved at free boundary condition and 54% at fixed boundary condition after repeated damage-healing events. Due to its low cost, high healing efficiency, good compatibility, and excellent flexibility, we envision that the polymer artificial muscle will be a new device in designing next generation healing-on-demand polymer composite.

Minimum Energy Input Control Problem on a Constrained Boundary Subregion

In this paper we focus on solving the problem of minimum energy control using the subdifferential approach. We show how one can steers a hyperbolic system from an initial state to a final one between two prescribed profiles, only on a boundary subregion Γ of the system evolution domain Ω. First we give some definitions and properties of this new concept, and then we concentrate on the determination of the control which would realize a given final state with minimum energy.

The constrained buckling problem of geometrically imperfect beams: a mathematical approach for the determination of the critical instability points

The constrained buckling problem of geometrically imperfect beams with intermediate unilateral supports is studied in the present paper. The proposed methodology offers the ability to calculate analytically the critical loads and the buckling shape of beams with arbitrary initial geometric imperfections, for a variety of different initial contact conditions in the framework of elastic stability theory. The proposed mathematical approach is based on the formulation of the equilibrium equations in the deformed position, in which the function of the unilateral constraints is appropriately taken into account. The analytical solution is obtained after the splitting of the initial constrained non-homogeneous boundary value problem (BVP) into constrained subproblems and the utilization of a classical mathematical theorem from the field of ordinary non-homogeneous BVPs. The implementation of the presented technique is demonstrated through characteristic examples. In order to validate the proposed mathematical method, the obtained results are compared with the respective numerical ones. The latter are obtained through the utilization of geometric nonlinear finite element analysis. The paper ends with the presentation of an investigation on the variation of the critical load with respect to different positions of the unilateral constraints.

Effect of stress state on deformation and fracture of nanocrystalline copper: Molecular dynamics simulation

Deformation in a microcomponent is often constrained by surrounding joined material making the component under mixed loading and multiple stress states. In this study, molecular dynamics (MD) simulation are conducted to probe the effect of stress states on the deformation and fracture of nanocrystalline Cu. Tensile strain is applied on a Cu single crystal, bicrystal and polycrystal respectively, under two different tension boundary conditions. Simulations are first conducted on the bicrystal and polycrystal models without lattice imperfection. The results reveal that, compared with the performance of simulation models under free boundary condition, the transverse stress caused by the constrained boundary condition leads to a much higher tensile stress and can severely limit the plastic deformation, which in return promotes cleavage fracture in the model. Simulations are then performed on Cu single crystal and polycrystal with an initial crack. Under constrained boundary condition, the crack tip propagates rapidly in the single crystal in a cleavage manner while the crack becomes blunting and extends along the grain boundaries in the polycrystal. Under free boundary condition, massive dislocation activities dominate the deformation mechanisms and the crack plays a little role in both single crystals and polycrystals.

Micromechanical model of a surrogate for collagenous soft tissues: development, validation and analysis of mesoscale size effects

Aligned, collagenous tissues such as tendons and ligaments are composed primarily of water and type I collagen, organized hierarchically into nanoscale fibrils, microscale fibers and mesoscale fascicles. Force transfer across scales is complex and poorly understood. Since innervation, the vasculature, damage mechanisms and mechanotransduction occur at the microscale and mesoscale, understanding multiscale interactions is of high importance. This study used a physical model in combination with a computational model to isolate and examine the mechanisms of force transfer between scales. A collagen-based surrogate served as the physical model. The surrogate consisted of extruded collagen fibers embedded within a collagen gel matrix. A micromechanical finite element model of the surrogate was validated using tensile test data that were recorded using a custom tensile testing device mounted on a confocal microscope. Results demonstrated that the experimentally measured macroscale strain was not representative of the microscale strain, which was highly inhomogeneous. The micromechanical model, in combination with a macroscopic continuum model, revealed that the microscale inhomogeneity resulted from size effects in the presence of a constrained boundary. A sensitivity study indicated that significant scale effects would be present over a range of physiologically relevant inter-fiber spacing values and matrix material properties. The results indicate that the traditional continuum assumption is not valid for describing the macroscale behavior of the surrogate and that boundary-induced size effects are present.

Shear viscosity measurements on Polyamide‐12 polymers for laser sintering

PurposeLaser sintering kinetics and part reliability are critically dependent on the melt viscosity of materials, including polyamide 12 (PA‐12). The purpose of this paper is to characterise the viscosity of PA‐12 powders using alternative scientific methods: constrained boundary flows (capillary rheometry) and rotational rheometry.Design/methodology/approachVarious PA‐12 powders were selected and characterised by both techniques. Measurement of molecular weight was also carried out to interpret the viscosity data.FindingsResults demonstrate conventional pseudoplastic flow in all PA‐12 materials. Zero‐shear viscosity has been quantified by rotational rheometry; a notable observation is the striking difference between virgin/used PA‐12. This is interpreted in terms of molecular weight and chain structure modifications, arising from polycondensation of PA‐12 held at the bed temperature during laser sintering.Research limitations/implicationsAccurate zero‐shear viscosity data provide scope for use in predictive computational models for laser sintering processes. Careful sample preparation and equipment operation are critical prerequisites for accurate rheological characterisation of PA‐12 powders.Practical implicationsDifferences in flow behaviour and molecular structure allow prediction and deeper understanding of process‐property relationships in laser sintering, giving potential for further optimisation of material specification and in‐process machine parameter control.Originality/valueThis is believed to be the first time that techniques other than melt flow rate (MFR) have been reported to measure the viscosity of PA‐12 in a laser sintering context, noting the effects of pre‐drying and molecular weight, then predicting differences between virgin/used powders in practical sintering behaviour.

Bidirectional Dynamic Diversity Evolutionary Algorithm for Constrained Optimization

Evolutionary algorithms (EAs) were shown to be effective for complex constrained optimization problems. However, inflexible exploration-exploitation and improper penalty in EAs with penalty function would lead to losing the global optimum nearby or on the constrained boundary. To determine an appropriate penalty coefficient is also difficult in most studies. In this paper, we propose a bidirectional dynamic diversity evolutionary algorithm (Bi-DDEA) with multiagents guiding exploration-exploitation through local extrema to the global optimum in suitable steps. In Bi-DDEA potential advantage is detected by three kinds of agents. The scale and the density of agents will change dynamically according to the emerging of potential optimal area, which play an important role of flexible exploration-exploitation. Meanwhile, a novel double optimum estimation strategy with objective fitness and penalty fitness is suggested to compute, respectively, the dominance trend of agents in feasible region and forbidden region. This bidirectional evolving with multiagents can not only effectively avoid the problem of determining penalty coefficient but also quickly converge to the global optimum nearby or on the constrained boundary. By examining the rapidity and veracity of Bi-DDEA across benchmark functions, the proposed method is shown to be effective.

Continuous dependence on elastic moduli in the motion of a semi-infinite elastic cylinder

Continuous dependence upon the elastic moduli of the total energy, and consequently in appropriate measure of the stress, strain and displacement, is established in the initial boundary value problem defined on a semi-infinite cylinder occupied by a linear anisotropic compressible elastic material. Free, constrained and mixed boundary conditions on the lateral surface of the cylinder are discussed. The conclusions are obtained using differential inequalities and partly depend upon previously published results.

Stability and Ergonomic Design Features of Tractor Mounted Hydraulic Elevator for Coconut Harvesting

Problem statement: The most important design criterion of mechanized device was safety; safety comprises both the safety of operator and safety of maintenance personnel. Failures and safety of harvesting platform of Tractor Mounted Hydraulic Elevator (TMHE) powered by tractor PTO was tested by finite element method for the mechanical harvesting of coconut orchards using digital ergonomic hart rate meter. The objective of this study was to study the stability of the THME by finite element method, operational safety and power requirement for the use of this elevator for coconut harvesting. Provide sufficient adjustment and space to account for variation in body sizes, ensure controls were situated within suitable reach and were properly marked. Approach: The modal analysis was carried out for the whole assembly of tractor mounted hydraulic elevator by using Ansis software. The digital polar hart rate meter RS400TM having infrared connectivity sensor was used for recording the hart rates. The research stusy was conducted at, Dr. Balasaheb Sawant Kokan Krishi Vidyapeeth Dapoli. The harvesting of coconuts was performed by manual climbing labor and by tractor mounted hydraulic elevator. The technical assessments included the use of biomechanical models, vibration testing equipment, ODR, BPDS. The ergonomical evaluation results of the above study were correlates to decide the feasibility, safety and efficiency of Tractor mounted hydraulic elevator for coconut harvesting. The PTO rpm influence for the lifting and lowering of the harvesting platform was studied experimentally by using digital tachometer. Results: The better stability results with the controlled vibrations and frequency of the lifting platform and welded joints were recorded by keeping constrained boundary conditions. Ergonomically operational safe and controlled heart rates were recorded. Hence the labors can continuously do the coconut harvesting work by using the tractor mounted hydraulic elevator. The minimum PTO power was required for the coconut harvesting by using tractor mounted hydraulic elevator. Conclusion/Recommendation: The tractor mounted hydraulic elevator is suitable, safe, less hazardous and economical as compared to manual climbing for coconut harvesting. Hence it is recommended to use tractor mounted hydraulic elevator for harvesting, cleaning and breeding of coconut orchards upto 14 m height.

Three-dimensional constrained boundary recovery with an enhanced Steiner point suppression procedure

Boundary recovery is one of the primary obstacles in applying the Delaunay criterion to mesh generation. Minimization of the number of Steiner points is a common goal for three-dimensional boundary recovery. In this paper, this goal is achieved by using an enhanced Steiner point suppression procedure and introducing a small polyhedron reconnection operation. Combining the suppression procedure with Steiner point insertion and splitting, a complete three-dimensional constrained boundary recovery algorithm is presented, and its effectiveness is demonstrated in various numerical examples.

The bonding of nickel foam to Ti–6Al–4V using Ti–Cu–Ni braze alloy

A titanium-copper-nickel braze powder is combined with various carrier polymers at a range of loadings and used to braze open cell nickel foams to Ti–6Al–4V plate. The microstructure of the interfaces and the chemical composition are examined, and these are correlated with the mechanical behaviour of the joints, as determined by shear and tensile tests, with the aim being to determine the influence the polymer binder and application method have on the final bond microstructure and properties. The investigations show that, as expected, the binder system used can have an important effect on the amount of oxygen, carbon and nitrogen contained in the braze material, and the mechanical properties obtained. However, the effect is complex, better properties in shear being obtained with an apparently lower quality bond, an observation that is explained by considering the constrained boundary layer formed by the bond. Further Weibull tests show that, although the density variations in the commercially available nickel based foam affect the properties, there is additional variation due to the high degree of process control required to achieve a good bond.

The energy and spanning trees of the Aztec diamonds

The Aztec diamond was extensively studied in both graph theory and statistical physics. Knuth obtained a formula of the number of spanning trees of the Aztec diamond with the constrained boundary condition, which solved a conjecture posed by Stanley in 1994. In this paper, We give the formulae of the energy and the number of spanning trees of the Aztec diamond with the toroidal boundary condition.

An Inter-Landmark Approach to 4-D Shape Extraction and Interpretation: Application to Myocardial Motion Assessment in MRI

This paper presents a novel approach to shape extraction and interpretation in 4-D cardiac magnetic resonance imaging data. Statistical modeling of spatiotemporal interlandmark relationships is performed to enable the decomposition of global shape constraints and subsequently of the image analysis tasks. The introduced descriptors furthermore provide invariance to similarity transformations and thus eliminate pose estimation errors in the presence of image artifacts or geometrical inconsistencies. A set of algorithms are derived to address key technical issues related to constrained boundary tracking, dynamic model relaxation, automatic initialization, and dysfunction localization. The proposed framework is validated with a relatively large dataset of 50 subjects and compared to existing statistical shape modeling methods. The results indicate increased adaptation to spatiotemporal variations and imaging conditions.

Porosity Evolution of Free and Confined Bentonites during Interlayer Hydration

AbstractMethods for predicting the volume change and swelling-pressure behavior of expansive clays require detailed understanding of coupled interactions between clay microstructure and macrostructure under hydraulic, thermal, and mechanical loads. In this study a suite of water-vapor sorption experiments was conducted using compacted bentonites hydrated in controlled relative humidity (RH) environments maintained under free and constrained volume-change boundary conditions. Emphasis was placed on examining the influences of compaction and predominant exchange cation on the water uptake, volume change, and swelling pressure response. Densely compacted specimens exhibited greater volume changes under free swelling conditions and greater swelling pressures under fully confined conditions. Water uptake, volume change, and swelling pressure were all more significant for Colorado (Ca2+/Mg2+) bentonite than forWyoming (Na+) bentonite. Plastic yielding, evident as a peak in the relationship between swelling pressure and RH, was more evident and occurred at lower RH for the Colorado bentonite. This observation was interpreted to reflect the limited capacity for interlayer swelling in Ca2+/Mg2+ bentonites and corresponding structural collapse induced by the onset of water uptake in larger intra-aggregate and inter-aggregate pores. A semi-quantitative model for the evolution of clay microstructure resulting from interlayer hydration was considered to attribute the experimental observations to differences in the efficiency with which transitions in basal spacing translate to bulk volume changes and swelling pressure. Results provide additional insight and experimental evidence to more effectively model the mechanical behavior of compacted bentonites used as buffer or barrier materials in waste repository applications.

Variational formulations of nonlinear constrained boundary value problems

Variational formulations of nonlinear constrained boundary value problems in reflexive Banach spaces are discussed from a compositional duality approach. The mixed variational compatibility conditions of the theory correspond to the surjectivity of the primal coupling boundary and interior operators.