Isotropic Square Research Articles

A novel refined shear deformation theory for the buckling analysis of thick isotropic plates

In present study, a novel refined hyperbolic shear deformation theory is proposed for the buckling analysis of thick isotropic plates. The new displacement field is constructed with only two unknowns, as against three or more in other higher order shear deformation theories. However, the hyperbolic sine function is assigned according to the shearing stress distribution across the plate thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using any shear correction factors. The equations of motion associated with the present theory are obtained using the principle of virtual work. The analytical solution of the buckling of simply supported plates subjected to uniaxial and biaxial loading conditions was obtained using the Navier method. The critical buckling load results for thick isotropic square plates are compared with various available results in the literature given by other theories. From the present analysis, it can be concluded that the proposed theory is accurate and efficient in predicting the buckling response of isotropic plates.

Order Reconstruction for Nematics on Squares with Isotropic Inclusions: A Landau--De Gennes Study

We prove the existence of a well order reconstruction solution (WORS)-type Landau--de Gennes critical point on a square domain with an isotropic concentric square inclusion, with tangent boundary c...

Time-Varying Isotropic Vector Random Fields on Compact Two-Point Homogeneous Spaces

A general form of the covariance matrix function is derived in this paper for a vector random field that is isotropic and mean square continuous on a compact connected two-point homogeneous space and stationary on a temporal domain. A series representation is presented for such a vector random field which involves Jacobi polynomials and the distance defined on the compact two-point homogeneous space.

Isotropic random fields with infinitely divisible marginal distributions

ABSTRACTA simple but efficient approach is proposed in this paper to construct the isotropic random field in (d ⩾ 2), whose univariate marginal distributions may be taken as any infinitely divisible distribution with finite variance. The three building blocks in our building tool box are a second-order Lévy process on the real line, a d-variate random vector uniformly distributed on the unit sphere, and a positive random variable that generates a Pólya-type function. The approach extends readily to the multivariate case and results in a vector random field in with isotropic direct covariance functions and with any specified infinitely divisible marginal distributions. A characterization of the turning bands simulation feature is also derived for the covariance matrix function of a Gaussian or elliptically contoured random field that is isotropic and mean square continuous in .

The Study of Damping and Parabolic Temperature on Vibrations of Isotropic Elastic Square Plate

The Study of Damping and Parabolic Temperature on Vibrations of Isotropic Elastic Square Plate

The IMLS-Ritz analysis of laminated CNT-reinforced composite quadrilateral plates subjected to a sudden transverse dynamic load

A first known study on the mechanical behavior of laminated CNT-reinforced quadrilateral composite plates due to a sudden transverse dynamic load is performed. In this study, a moderately thick plate is considered; therefore, the first-order shear deformation theory (FSDT) is employed in the formulation. The numerical analysis of the problem is carried out using the IMLS-Ritz method. The Newmark-β method is employed for the numerical time integration of the dynamic problem. The Mori-Tanaka approach is adopted for predicting the properties of CNT-composites. The numerical stabilities and accuracies of the IMLS-Ritz method are examined. The convergence properties are illustrated through solving an isotropic square plate and a laminated CNT-composite quadrilateral plate by varying their node numbers and support sizes. A comprehensive parametric study has been carried out to examine the dynamic behavior of symmetric and asymmetric CNT-composite plates.

Elastodynamic analysis of regular polygonal CNT-reinforced composite plates via FSDT element-free method

A comprehensive study on elastodynamic behavior of regular polygonal carbon nanotube (CNT) reinforced functionally graded composite plates subjected to a sudden transverse dynamic load is presented in this paper. This analysis uses as its base the first-order shear deformation theory (FSDT) and the element-free IMLS-Ritz method, to conduct a numerical simulation. A numerical time integration for the dynamic problems is performed using the Newmark-β method. Convergence studies are carried out for an isotropic square plate with different support sizes and different numbers of nodes. Parametric studies are further carried out to investigate the effect of four special regular polygons with different CNT volume fractions, CNT distribution types, plate apothem-to-thickness ratios and boundary conditions on the dynamic behaviors of regular polygonal CNT-reinforced composite plates.

Structural Health Monitoring Using Lamb Wave Reflections and Total Focusing Method for Image Reconstruction

This investigation aimed to adapt the total focusing method (TFM) algorithm (originated from the synthetic aperture focusing technique in digital signal processing) to accommodate a circular array of piezoelectric sensors (PZT) and characterise defects using guided wave signals for the development of a structural health monitoring system. This research presents the initial results of a broader study focusing on the development of a structural health monitoring (SHM) guided wave system for advance carbon fibre reinforced plastic (CFRP) composite materials. The current material investigated was an isotropic (aluminium) square plate with 16 transducers operating successively as emitter or sensor in pitch and catch configuration enabling the collection of 240 signals per assessment. The Lamb wave signals collected were tuned on the symmetric fundamental mode with a wavelength of 17 mm, by setting the excitation frequency to 300 kHz. The initial condition for the imaging system, such as wave speed and transducer position, were determined with post processing of the baseline signals through a method involving the identification of the waves reflected from the free edge of the plate. The imaging algorithm was adapted to accommodate multiple transmitting transducers in random positions. A circular defect of 10 mm in diameter was drilled in the plate, which is similar to the delamination size introduced by a low velocity impact event in a composite plate. Images were obtained by applying the TFM to the baseline signals, Test 1 data (corresponding to the signals obtained after introduction of the defect) and to the data derived from the subtraction of the baseline to the Test 1 signals. The result shows that despite the damage diameter being 40 % smaller than the wavelength, the image (of the subtracted baseline data) demonstrated that the system can locate where the waves were reflected from the defect boundary. In other words, the contour of the damaged area was highlighted enabling its size and position to be determined.

Isotropic covariance matrix polynomials on spheres

ABSTRACTThis article characterizes the covariance matrix function of a Gaussian or elliptically contoured vector random field that is stationary, isotropic, and mean square continuous on the sphere. By applying the characterization to examine the validity of a matrix function whose entries are polynomials of degrees up to 4, we obtain a necessary and sufficient condition for the polynomial matrix to be an isotropic covariance matrix function on the sphere.

Time Varying Isotropic Vector Random Fields on Spheres

For a vector random field that is isotropic and mean square continuous on a sphere and stationary on a temporal domain, this paper derives a general form of its covariance matrix function and provides a series representation for the random field, which involve the ultraspherical polynomials. The series representation is somehow an imitator of the covariance matrix function, but differs from the the spectral representation in terms of the ordinary spherical harmonics, and is useful for modeling and simulation. Some semiparametric models are also illustrated.

Stochastic representations of isotropic vector random fields on spheres

ABSTRACTA stochastic representation is derived for a vector random field that is stationary, isotropic, and mean square continuous on a sphere or unit circle. The established stochastic representation is an infinite series involving the sequence of ultraspherical or Gegenbauer's polynomials, looks like a mimic of the series representation of the covariance matrix function of the isotropic vector random field, but differs from the spectral representation in terms of the ordinary spherical harmonics. It is also shown in this paper that some isotropic and continuous covariance matrix functions on the real line or , if they are compactly supported, can be adopted as covariance matrix functions on the unit circle or .

Elastodynamic analysis of quadrilateral CNT-reinforced functionally graded composite plates using FSDT element-free method

An elastodynamic analysis of quadrilateral carbon nanotube (CNT) reinforced functionally graded composite plates subjected to a transverse sudden dynamic load is studied. Based on the first-order shear deformation theory (FSDT), the element-free IMLS-Ritz method is extended to conduct a numerical simulation for this study. A numerical time integration for the dynamic problems is performed using the Newmark-β method. To verify the stability and accuracy of the element-free IMLS-Ritz method, convergence studies are carried out for an isotropic square plate with different support sizes and different numbers of nodes. Detailed numerical simulations are further carried out to investigate the effect of CNT volume fraction, CNT distribution type, side angles, area of quadrilateral plate, plate width-to-thickness ratio and boundary condition on the dynamic behaviors of quadrilateral CNT reinforced composite plates.

A reduced-order integral formulation to account for the finite size effect of isotropic square panels using the transfer matrix method.

The transfer matrix method is a well-established prediction tool for the simulation of sound transmission loss and the sound absorption coefficient of flat multilayer systems. Much research has been dedicated to enhancing the accuracy of the method by introducing a finite size effect of the structure to be simulated. The aim of this paper is to present a reduced-order integral formulation to predict radiation efficiency and radiation impedance for a panel with equal lateral dimensions. The results are presented and discussed for different materials in terms of radiation efficiency, sound transmission loss, and the sound absorption coefficient. Finally, the application of the proposed methodology for rectangular multilayer systems is also investigated and validated against experimental data.

Laser–matter interactions: Inhomogeneous Richtmyer–Meshkov and Rayleigh–Taylor instabilities

AbstractIn this experimental study, the ablative Richtmyer–Meshkov (RM) and the Rayleigh–Taylor (RT) instabilities were generated by the laser pulse of Gaussian-like power profile. The initial multi-modal perturbation, the inhomogeneous momentum transfer and different Atwood numbers generate different shapes of spikes and bubbles in the central region (CR) and the near-central region (NCR) of the spot. A one-dimensional Gaussian-like power profile causes the formation of the wavy-like rows of aperiodic spikes. The periodic spike segments inside the rows appear due to locally coherent flow. In the NCR, the mushroom-shape spikes tend to the organization on the isotropic square and the anisotropic rhombic lattices. The increase of the lattice periods two, three, or four times indicates formation of superstructures. The growth of sharp asymmetric RM/RT spikes in the CR is fast, uncorrelated and linear, while the growth of the symmetric mushroom-shape ones in the NCR is slow, correlated, and nonlinear.

Effects of anisotropy in simple lattice geometries on many-body properties of ultracold fermions in optical lattices

We study the effects of anisotropic hopping amplitudes on quantum phases of ultracold fermions in optical lattices described by the repulsive Fermi-Hubbard model. In particular, using dynamical mean-field theory (DMFT) we investigate the dimensional crossover between the isotropic square and the isotropic cubic lattice. We analyze the phase transition from the antiferromagnetic to the paramagnetic state and observe a significant change in the critical temperature: Depending on the interaction strength, the anisotropy can lead to both a suppression or increase. We also investigate the localization properties of the system, such as the compressibility and double occupancy. Using the local density approximation in combination with DMFT we conclude that density profiles can be used to detect the mentioned anisotropy-driven transitions.

Phases of d-orbital bosons in optical lattices

We explore the properties of bosonic atoms loaded into the d bands of an isotropic square optical lattice. Following the recent experimental success reported in Zhai et al (2013 Phys. Rev. A 87 063638), in which populating d bands with a 99 fidelity was demonstrated, we present a theoretical study of the possible phases that can appear in this system. Using the Gutzwiller ansatz for the three d band orbitals we map the boundaries of the Mott insulating phases. For not too large occupation, two of the orbitals are predominantly occupied, while the third, of a slightly higher energy, remains almost unpopulated. In this regime, in the superfluid phase we find the formation of a vortex lattice, where the vortices come in vortex/anti-vortex pairs with two pairs locked to every site. Due to the orientation of the vortices time-reversal symmetry is spontaneously broken. This state also breaks a discrete -symmetry. We further derive an effective spin-1/2 model that describe the relevant physics of the lowest Mott-phase with unit filling. We argue that the corresponding two dimensional phase diagram should be rich with several different phases. We also explain how to generate anti-symmetric spin interactions that can give rise to novel effects like spin canting.

Covariance Matrix Functions of Isotropic Vector Random Fields

An isotropic scalar or vector random field is a second-order random field in (d ⩾ 2), whose covariance function or direct/cross covariance functions are isotropic. While isotropic scalar random fields have been well developed and widely used in various sciences and industries, the theory of isotropic vector random fields needs to be investigated for applications. The objective of this article is to study properties of covariance matrix functions associated with vector random fields in which are stationary, isotropic, and mean square continuous, and derives the characterizations of the covariance matrix function of the Gaussian or second-order elliptically contoured vector random field in . In particular, integral or spectral representations for isotropic and continuous covariance matrix functions are derived.

Smart sensing of damage in flexible plates through MEMS

In this work, we present a methodology to monitor the state of damage- or crack-containing flexible plates through low-cost, commercial off-the-shelf MEMS accelerometers. Under quasi-static, time-varying loading conditions we track the evolution of the damaged zone (e.g., the length of an inner crack) accounting for the drift in the compliance of the specimens, measured by means of the magnitude of the load-induced rotation at MEMS position. We then validate this health monitoring methodology, showing that it turns out to be sensitive to the damage and provides results in good accordance with theoretical findings. Next, we propose a technique to optimally deploy the MEMS sensors over the plate. Referring to an isotropic square plate containing damaged zones of reduced bending stiffness, we numerically investigate the sensitivity of the load-induced state (in terms of out-of-plane displacement and rotation of the normal to the mid-plane) to the position of the damaged area, and we adopt a constrained topology optimisation tool to determine the best sensor deployment to efficiently sense the damage.

Equation of state of the fermionic two-dimensional Hubbard model

We present results for the equation of state of the two-dimensional Hubbard model on an isotropic square lattice as obtained from a controlled and numerically exact large-cluster dynamical mean field simulation. Our results are obtained for large but finite systems and are extrapolated to infinite system size using a known finite-size scaling relation, and are supplemented by reliable error bars accounting for all sources of errors. We establish the importance of examining the decay of spatial spin correlations to determine whether a sufficiently large cluster has been used and with this in mind we present the energy, entropy, double occupancy, and nearest-neighbor spin correlations extrapolated to the thermodynamic limit. We discuss the implications of these calculations on pseudogap physics of the 2D Hubbard model away from half filling, where we find a strong behavioral shift in energy below a temperature ${T}^{*}$ which becomes more pronounced for larger clusters. Finally, we provide reference calculations and tables for the equation of state for values of doping away from half filling which are of interest to cold-atom experiments.

Characterizing Genuine Multisite Entanglement in Isotropic Spin Lattices

We consider a class of large superposed states, obtained from dimer coverings on spin-1/2 isotropic lattices, whose potential usefulness ranges from organic molecules to quantum computation. We show that they are genuinely multiparty entangled, irrespective of the geometry and dimension of the isotropic lattice. We then present an efficient method to characterize the genuine multisite entanglement in the case of isotropic square spin-1/2 lattices, with short-range dimer coverings. We use this iterative analytical method to calculate the multisite entanglement of finite-sized lattices, which through finite-size scaling, enables us to obtain the estimate of the multisite entanglement of the infinite square lattice. The method can be a useful tool to investigate other single- and multisite properties of such states.