Representation Of Displacements Research Articles

A Closed-Form Solution to the Mechanism of Interface Crack Formation with One Contact Area in Decagonal Quasicrystal Bi-Materials

Cracks and crack-like defects in engineering structures have greatly reduced the structural strength. An interface crack with one contact area in a combined tension–shear field of decagonal quasicrystal bi-material is investigated. Based on the deformation compatibility equation and displacement potential function, the complex representation of stress and displacement is given. Using the mixed boundary conditions, the closed-form expressions for the stresses and the displacement jumps in the phonon field and phason field on the material interface are obtained. The results show that the stress intensity factor at the crack tip is zero for the phason field. The variation in the stress intensity factor and the length of the contact zone in the phonon field is given, and the result is consistent with the properties of the crystal. The design of safe engineering structures and the formulation of reasonable quality acceptance standards may benefit from the theoretical research carried out here.

Mechanical Analysis of Functionally Graded Multilayered Two-Dimensional Decagonal Piezoelectric Quasicrystal Laminates with Imperfect Interfaces

Quasicrystals have a wide range of applications due to their unique multi-field coupling effects and distinctive physical and mechanical characteristics. In this paper, the static and dynamic problems of imperfectly bonded, multilayered, functionally graded, two-dimensional decagonal piezoelectric quasicrystal laminates under mixed boundary conditions are investigated. The state equations in a concise and compact matrix form can be expressed by using differential quadrature regional discrete point expansions in any layer of the laminate. This allows for the representation of displacement, stress, electric potential, and electric displacement components. Then, different imperfect interface conditions are introduced to characterize specific structural and electric contact properties at the bounding interfaces, which are further converted to the interface propagator matrix. Numerical examples are carried out to investigate the impact of varying interface compliances, load types, and functional gradient factors on the static bending and vibration phenomena of QC laminates. These results can be used as references to validate existing or future numerical work on QC laminates and could further guide the design of related QC laminate structures.

On the Construction of Confidence Regions for Uncertain Planar Displacements.

This paper studies the statistical concept of confidence region for a set of uncertain planar displacements with a certain level of confidence or probabilities. Three different representations of planar displacements are compared in this context and it is shown that the most commonly used representation based on the coordinates of the moving frame is the least effective. The other two methods, namely the exponential coordinates and planar quaternions, are equally effective in capturing the group structure of SE(2). However, the former relies on the exponential map to parameterize an element of SE(2), while the latter uses a quadratic map, which is often more advantageous computationally. This paper focus on the use of planar quaternions to develop a method for computing the confidence region for a given set of uncertain planar displacements. Principal component analysis (PCA) is another tool used in our study to capture the dominant direction of movements. To demonstrate the effectiveness of our approach, we compare it to an existing method called rotational and translational confidence limit (RTCL). Our examples show that the planar quaternion formulation leads to a swept volume that is more compact and more effective than the RTCL method, especially in cases when off-axis rotation is present.

SOLUTION OF PHYSICALLY NONLINEAR PROBLEMS OF DEFORMATION OF MASSIVE AND THIN-WALLED PRISMATIC BODIES

The results of a numerical study on test examples of the convergence of the developed version of the semi-analytical method of finite elementsare presented. A comparison of machine time and accuracy of solving elastic and plastic problems obtained on the basis of finite elements with variableand averaged mechanical parameters was performed.The convergence of the finite element method and the semianalytical finite element method in the calculation of prismatic bodies loaded with localized and distributed external influences was studied. An effective numerical approach to the study of arbitrarily loaded massive and thin-walled prismatic bodies of complex shape, the deformation of which can pass beyond theelastic limit of the material, is being developed based on the finite element moment scheme and the semianalytical variant of the finite element method. Due to the representation of displacements by polynomials and the use of iterative methods of solving systems of equations, this approach is developed in relation to the calculation of objects with arbitrary boundary conditions on the ends, which made it possible to expand the area of effective application of the semi-analytical method of finite elements to a new class ofproblems.A number of new complex problems of elastic and elastic-plastic deformation of massive and thinwalled prismatic bodies, which have an independentapplied value, have been solved.

Modeling the matching stage of HDPE hot plate welding: A study using regression and support vector machine models

AbstractThis research studies the material displacement of high‐density polyethylene (HDPE) during the initial stage of the hot plate welding (HPW) process, called the Matching stage. Newly developed mathematical models simulate the relationship between the main process parameters (force, temperature, and time) and the size of the surface area. The collected data was used to develop four mathematical models for material displacement and time. Two models are machine learning based models (support vector machines). The other two models are regression models in the form of functions. In addition, this study provides a visual representation of HDPE melt displacement with the changes in temperature and pressure. The obtained results indicate that these models can be used for developing a parameter adjustment process or determining specifications for new production equipment. The potential applications of the developed models can be extended to industries that use HPW of HDPE, such as automotive or aerospace. This could result in significant savings in the amount of scrap and waste due to inaccurate and ad hoc settings that currently take place in the industry.Highlights Study of HDPE material displacement in the hot plate welding Matching stage. Visualization of HDPE melt displacement with temperature and pressure changes. Development of SVM and mathematical regression models. Applications in parameter adjustment and equipment specification. Savings in scrap and waste by reducing inaccurate settings.

Investigation of the Fracture and Fragmentation of Implosively Driven Thin-Walled Cylindrical Shell: From Thermodynamic Analysis to CDEM Simulation.

The scattering of fragments is a notable characteristic of the explosive detonation of a shelled charge. This study examines the fracture and fragmentation of the shell and the process by which natural fragments form under the strains of implosion. The analysis takes into account both the explosive's energy output and the casing's dynamic response. For this purpose, utilizing a thermochemical code as an alternative to the conventionally employed cylinder test, the Jones-Wilkins-Lee equation of state (JWL EOS) was calibrated within a range of relative specific volume up to 13. The detonation of the shelled charge was subsequently analyzed using the continuum-discontinuum element method (CDEM). Following this, the formation mechanisms and scattering characteristics of natural fragments were scrutinized. The analysis found that the shell predominantly experiences shear failure with uniform evolution, displaying a "hysteresis effect" and two mutation stages in the evolution of tensile failure. Within the JWL EOS's calibrated range, the representation of fragment displacement and velocity improved by 47.97% and 5.30%, respectively. This study provides valuable guidance for designing the power field of warheads and assessing their destructive power.

A problem for a material surface attached to the boundary of an elastic semi-plane

A problem for a nano-sized material surface attached to the boundary of an elastic isotropic semi-plane is considered. The semi-plane and the material surface are assumed to be in a plane strain state under the action of a normal external tractions applied to the material surface. The material surface is modeled using the Steigmann–Ogden form of surface energy. The problem is solved using integral representations of stresses and displacements. With the help of these representations, the problem can be reduced to either a system of two singular integral equations or a single singular integral equation. Two types of material surface tip conditions are considered: tip conditions with an uncompensated surface prestress (free tip conditions) and tip conditions with a compensated surface prestress term. The numerical solution of the system of singular integral equations is obtained by expanding each unknown function into a series based on the Chebyshev polynomials. Then, the approximations of the unknown functions can be obtained from a system of linear algebraic equations. Accuracy of the numerical procedure is studied. Various numerical examples for different values of the surface energy parameters are considered. It is shown that both the surface parameters and the type of tip conditions have significant influence on the behavior of the material system.

Intensity of Dynamic Stresses of Longitudinal Shear in a Periodically Layered Composite with Penny-Shaped Cracks

We consider the problem of harmonic torsional loading of an infinite elastic composite formed by alternating plane layers made of two different materials in the presence of a penny-shaped crack in one of the components of periodic structure. By using the integral representations for displacements and stresses in the frequency domain and satisfying the conditions of periodicity and perfect contact on the interfaces, we deduce a system of uncoupled boundary integral equations for the functions of tangential dynamic crack-opening displacement in a two-layered representative element of the composite. We perform the numerical analysis of the mode-III dynamic stress intensity factors in the vicinity of the analyzed crack depending on the wave number, the thicknesses of constituent layers, and the properties of their materials.

Art and/as open education: A collaborative action with refugee artists

The article illustrates the potential of engaged arts-based pedagogies in higher education with respect to integration interventions for young refugees in Europe. It discusses the conception and implementation of the collaborative initiative “Find Refuge in Art”, which was part of the research Project PRESS at the Hellenic Open University. This example shows how artistic synergy may become an integral part of research design, framing both awareness raising and open education in the backdrop of intercultural exchange. The initiative encouraged the co-production of artistic work from pairs of artists with refugee and non-refugee background and culminated in an exhibition with over 75 participating artists. Challenging the victimizing conceptualizations of refugee art as a primarily trauma-centered representation of displacement, the article invites us to consider questions of agency and inclusion in terms of mutual recognition and to widen participation as a means of fostering transformative intercultural learning and epistemic justice in universities.

Grounding Mental Representations in a Virtual Multi-Level Functional Framework.

According to the associative theory of learning, reactive behaviors described by stimulus-response pairs result in the progressive wiring of a plastic brain. In contrast, flexible behaviors are supposedly driven by neurologically grounded mental states that involve computations on informational contents. These theories appear complementary, but are generally opposed to each other. The former is favored by neuro-scientists who explore the low-level biological processes supporting cognition, and the later by cognitive psychologists who look for higher-level structures. This situation can be clarified through an analysis that independently defines abstract neurological and informational functionalities, and then relate them through a virtual interface. This framework is validated through a modeling of the first stage of Piaget's cognitive development theory, whose reported end experiments demonstrate the emergence of mental representations of object displacements. The neural correlates grounding this emergence are given in the isomorphic format of an associative memory. As a child's exploration of the world progresses, his mental models will eventually include representations of space, time and causality. Only then epistemological concepts, such as beliefs, will give rise to higher level mental representations in a possibly richer propositional format. This raises the question of which additional neurological functionalities, if any, would be required in order to include these extensions into a comprehensive grounded model. We relay previously expressed views, which in summary hypothesize that the ability to learn has evolved from associative reflexes and memories, to suggest that the functionality of associative memories could well provide the sufficient means for grounding cognitive capacities.

Extreme springing response statistics of a tethered platform by deconvolution

The research examines the motion response and hydrodynamic wave loads of a deep-water Tension Leg Platform (TLP), emphasising the impacts of the wave sum frequency on the restrained modes of heave, roll, and pitch. The stochastic TLP structural reaction in a random sea state was precisely computed using a Volterra series representation of the TLP corner vertical displacement, which was selected as a response process. The wave loading was evaluated using the second-order diffraction code WAMIT and applied to a linear damped mass-spring model representing the dynamic system. Then, platform displacement response at the design low probability level has been determined using a novel deconvolution approach. Since the Volterra series represented the analytical solution, the exact Volterra and the approximated predictions have been compared in this study. The latter provided an accurate way to validate the effectiveness and precision of the proposed novel deconvolution method. Compared to existing engineering techniques, the most attractive advantage of the proposed deconvolution method is that it does not rely on any pre-assumed asymptotic probability distribution class. The latter may be an attractive point for practical engineering design. Thus the primary objective of this work was to validate a novel deconvolution approach using exact quasi-analytical solutions. This work also highlights the limitations of mean up-crossing rate-based extrapolation methodologies for the situation of narrowband effects, including clustering, which are often included in the springing type of response.

Elasticity-based locally-exact homogenization theory for three-phase composites considering the morphological effect of carbon fibers

Elasticity-based locally-exact homogenization theory (LEHT) is further extended in this paper to investigate the mechanical behaviors of three-phase composites with orthotropic interlayer as well as circumferentially orthotropic (CO) and radially orthotropic (RO) carbon fibers that are determined by their morphological basal plane. Taking advantage of the Fourier series representations for displacements of each phase, in-plane and out-of-plane exact solutions are obtained for orthotropic media through rigorous mathematical derivations and the internal eigenvalue functions are directly solved within rectangular and hexagonal representative unit cells (RUCs) subjected to axial normal, transverse loading and axial shear loading, respectively. The balanced variational principle is applied to enforce periodical boundary conditions which ensures rapid convergence of displacement fields. The solutions of LEHT are verified with far-field Eshelby problems with good agreement and the morphological effects of fiber are investigated by comparing CO/RO properties and equivalent transversely isotropic (TI) parameters obtained from replacement scheme. Homogenized elastic moduli of RUCs with orthotropic interlayer are predicted through homogenization constitutive relations and compared to special extension of the composite cylinders approach and numerical results based on the asymptotic expansion homogenization method to demonstrate excellent correlation. Finally, the effects of orthotropic interlayer have been demonstrated and local stress distributions are obtained from a “top-to-down” procedure, illustrating constituents’ interactions from microscope perspective and identifying the possible crack initiations/propagations within microstructures.

Offshore tethered platform springing response statistics

This paper demonstrates the validity of the Naess–Gadai method for extrapolating extreme value statistics of second-order Volterra series processes through application on a representative model of a deep water small size tension leg platform (TLP), with specific focus on wave sum frequency effects affecting restrained modes: heave, roll and pitch. The wave loading was estimated from a second order diffraction code WAMIT, and the stochastic TLP structural response in a random sea state was calculated exactly using Volterra series representation of the TLP corner vertical displacement, chosen as a response process. Although the wave loading was assumed to be a second order (non-linear) process, the dynamic system was modelled as a linear damped mass-spring system. Next, the mean up-crossing rate based extrapolation method (Naess–Gaidai method) was applied to calculate response levels at low probability levels. Since exact solution was available via Volterra series representation, both predictions were compared in this study, namely the exact Volterra and the approximate one. The latter gave a consistent way to estimate efficiency and accuracy of Naess–Gaidai extrapolation method. Therefore the main goal of this study was to validate Naess–Gaidai extrapolation method by available analytical-based exact solution. Moreover, this paper highlights limitations of mean up-crossing rate based extrapolation methods for the case of narrow band effects, such as clustering, typically included in the springing type of response.

Learning V1 Simple Cells with Vector Representation of Local Content and Matrix Representation of Local Motion

This paper proposes a representational model for image pairs such as consecutive video frames that are related by local pixel displacements, in the hope that the model may shed light on motion perception in primary visual cortex (V1). The model couples the following two components: (1) the vector representations of local contents of images and (2) the matrix representations of local pixel displacements caused by the relative motions between the agent and the objects in the 3D scene. When the image frame undergoes changes due to local pixel displacements, the vectors are multiplied by the matrices that represent the local displacements. Thus the vector representation is equivariant as it varies according to the local displacements. Our experiments show that our model can learn Gabor-like filter pairs of quadrature phases. The profiles of the learned filters match those of simple cells in Macaque V1. Moreover, we demonstrate that the model can learn to infer local motions in either a supervised or unsupervised manner. With such a simple model, we achieve competitive results on optical flow estimation.

Deformation induced by distributions of single forces in a layered half-space: [formula omitted

In the present paper we introduce a numerical model for the representation of displacement, strain and stress due to single forces embedded in a layered elastic half-space. The code EFGRN/EFCMP (Elastic Forces GReeN functions/Elastic Forces CoMPutation) is able to represent the mechanical effects due to pre-assigned distributions of single forces. Even if internal deformation sources can be described by distributions of equivalent body forces with vanishing resultant and moment, single forces are employed in geophysics to represent hydraulic and/or lithostatic loads, effects of internal density anomalies, and even some kind of seismic events. A distribution of single forces is also used to describe the effects of an inelastic inclusion located inside an elastic medium. In fact, the recent literature shows that poro-elastic and thermo-elastic inclusions can be represented using single forces distributed on their boundaries. EFGRN/EFCMP shares the benefits of rapid and semi-analytical calculation offered by the parent code, EDGRN/EDCMP, which is instead suitable for the representation of extended dislocation sources, as seismic faults. The present code also provides an option for computing the effects of a distribution of single forces embedded in a homogeneous half-space, by using the analytical solutions of Mindlin. Accordingly, EFGRN/EFCMP can be a valid support both for the representation of forward models of deformation sources and for the procedures of inversion of geodetic data in a layered medium. We show some applications of the code and we provide several scripts in MATLAB language which help the user to quickly start using EFGRN/EFCMP.

NODAL REACTIONS AND COEFFICIENTS OF THE STIFFNESS MATRIX OF A FINITE ELEMENT BASED ON THE REPRESENTATION OF DISPLACEMENTS BY POLYNOMIALS

The study of prismatic bodies with constants along one of the coordinates of mechanical and geometric parameters is most appropriate to conduct on the basis of the semianalytical finite element method (NMSE). Its essence is a combination of finite element sampling and decomposition of displacements in the characteristic direction by a system of trigonometric coordinate functions.In [8, 15], a variant of the semivanalytic finite element method for the calculation of prismatic bodies when used as a system of coordinate functions of Fourier series was developed. The use of trigonometric series provides maximum efficiency of the semi-analytical finite element method, however, only the boundary conditions corresponding to the object's support on an absolutely rigid in its plane and flexible diaphragm can be satisfied at the ends of the body.As a result of the performed researches, the basis of the representation of displacements by polynomials is obtained, which allows to significantly expand the range of boundary conditions at the ends of the body. In this case, it isnot possible to reduce the solution of the initial spatial boundary value problem to a sequence of two-dimensional problems, so a reasonable choice of appropriate polynomials becomes especially important.Both the conditionality of the matrix of the system of separate equations and, consequently, the convergence of integration algorithms for its solution, and the universality of the approach to the possibility of satisfying different variants of boundary conditions at the ends of the body depend on their correct choice.In addition, the question of methods of integration in the calculation of the coefficients of the stiffness matrix of a finite element (CE), which is quite common, due to the significant complexity of this procedure.

Circular inclusion problem of two‐dimensional decagonal quasicrystals with interfacial rigid lines under concentrated force

AbstractThe plane problem of two‐dimensional decagonal quasicrystals with a rigid circular arc inclusion was investigated under infinite tension and concentrated force. Based on complex representations of stresses and displacements of two‐dimensional decagonal quasicrystals, the above problem is transformed into Riemann boundary problem by using the analytic continuation principle of complex functions. The general solutions of two‐dimensional decagonal quasicrystals under the action of plane concentrated force and infinite uniform tension are derived. The closed solutions of complex potential functions in several typical cases are obtained, and the formula of singular stress field at the tip of rigid line inclusions is given. The results show that the stress field at the tip of circular arc rigid line inclusions has singularity of oscillation under plane load. Numerical examples are given to analyze the effects of inclusion radius, different inclusions, the coupling coefficient and phason field parameter on stress singularity coefficients.

Discussion on “A non-intrusive model-order reduction of geometrically nonlinear structural dynamics using modal derivatives”

This note is a short discussion of the paper “A Non-Intrusive Model-Order Reduction of Geometrically Nonlinear Structural Dynamics Using Modal Derivatives” in which reduced order models (ROMs) of the dynamic response of structures in the nonlinear geometric regime are constructed. The paper proposes modal derivatives to complement the linear modes for the representation of the structural displacements and compares the corresponding predictions obtained for 3 simple structures to those obtained with the linear modes + dual modes basis initially published about a decade ago. The predictions obtained with the latter bases are shown in the paper to be rather poor in contradiction with the many successful applications of this methodology in the literature. It is shown here that the issue stems in the paper from truncating too early the proper orthogonal decomposition (POD), i.e., taking too few eigenvectors in the dual mode construction. When the POD approximation is conducted normally to convergence, it is found that the ROMs with linear modes + dual modes bases lead to very good predictions of the dynamic response. In fact, this good accuracy is seen to be maintained even when the response level is much larger than the examples shown in the paper.

Atrioventricular plane displacement versus mitral and tricuspid annular plane systolic excursion: A comparison between cardiac magnetic resonance and M-mode echocardiography.

Both echocardiography and CMR imaging are used to quantify longitudinal function. Inter-method variability for mitral (MAPSE) and tricuspid (TAPSE) annular plane systolic excursion, and variability between directly measured MAPSE and TAPSE and as based on atrioventricular plane displacement (AVPD) analysis by CMR, are, however, not known. This study, therefore, assessed inter-method variability and variability between annular plane systolic excursion and AVPD-based values in a healthy adult population. Echocardiography and CMR were performed in 111 adults (35 [32-38] years). Method comparisons were assessed with Deming regression, Bland-Altman analysis and coefficient of variation. Observer reproducibility was assessed by the concordance correlation coefficient. Echocardiography and semi-automatic CMR agreed on MAPSE (17±2mm vs. 17±2mm, p=0.1) and TAPSE (25±3mm vs. 25±3mm, p=0.5), correlated highly between methods (fitted-slope 1.22 [95% CI 1.07-1.38] and 1.12 [95% CI 0.95-1.29]) and showed low bias (0.42 [95% CI-2.05 to 2.88] and-0.18 [95% CI-4.78 to 4.43]). Intra-/inter-observer reproducibility was high for both methods for both MAPSE (echocardiography 0.96/0.86; CMR 0.87/0.85) and TAPSE (echocardiography 0.96/0.95; CMR 0.97/0.96). MAPSE (16±2mm vs. 17±2mm; p<0.001) and TAPSE (24±3 vs. 25±3mm; p<0.001) based on AVPD were similar but statistically different compared with semi-automatic CMR. Echocardiography and semi-automatic CMR have low variability and provide similar values for MAPSE and TAPSE and are thus interchangeable for follow-up studies. Lateral values based on tracked data from AVPD analysis are not clinically significantly different and could be used as a representation of annular displacement.

Gyroscope Sensor Based In Vivo Finger Axes of Rotation Identification Using Screw Displacement.

This paper presents a low-cost, efficient, and portable in vivo method for identifying axes of rotation of the proximal interphalangeal and distal interphalangeal joints in an index finger. The approach is associated with the screw displacement representation of rigid body motion. Using the matrix exponential method, a detailed derivation of general spatial displacement of a rigid body in the form of screw displacement including the Rodrigues' formulae for rotation is presented. Then, based on a gyroscope sensor, a test framework for determining axes of rotation of finger joints is established, and experiments on finding the directions of joint axes of the PIP and DIP joints are conducted. The results obtained highly agree with those presented in literature through traditional but complex methods.