Showing papers on "Antisymmetric relation published in 2019"
TL;DR: In this article, the authors derive relativistic hydrodynamic equations with a dynamical spin degree of freedom on the basis of an entropy-current analysis, showing that spin density is damped out after a characteristic time scale controlled by transport coefficients introduced in the antisymmetric part of the energy-momentum tensor in the entropy current analysis.
152 citations
TL;DR: In this paper, the authors derived a thermodynamic uncertainty relation from the fluctuation theorem, which is the fundamental equality in nonequilibrium thermodynamics that is used to derive many important thermodynamic relations.
Abstract: The fluctuation theorem is the fundamental equality in nonequilibrium thermodynamics that is used to derive many important thermodynamic relations, such as the second law of thermodynamics and the Jarzynski equality. Recently, the thermodynamic uncertainty relation was discovered, which states that the fluctuation of observables is lower bounded by the entropy production. In the present Letter, we derive a thermodynamic uncertainty relation from the fluctuation theorem. We refer to the obtained relation as the fluctuation theorem uncertainty relation, and it is valid for arbitrary dynamics, stochastic as well as deterministic, and for arbitrary antisymmetric observables for which a fluctuation theorem holds. We apply the fluctuation theorem uncertainty relation to an overdamped Langevin dynamics for an antisymmetric observable. We demonstrate that the antisymmetric observable satisfies the fluctuation theorem uncertainty relation but does not satisfy the relation reported for current-type observables in continuous-time Markov chains. Moreover, we show that the fluctuation theorem uncertainty relation can handle systems controlled by time-symmetric external protocols, in which the lower bound is given by the work exerted on the systems.
138 citations
TL;DR: In this paper, the authors examined the bending behavior of the antisymmetric cross-ply laminates using a new simple four variable trigonometric plate theory, which utilizes a novel displacement field which introduces undetermined integral terms and needs only four variables.
Abstract: The thermo-mechanical bending behavior of the antisymmetric cross-ply laminates is examined using a new simple four variable trigonometric plate theory The proposed theory utilizes a novel displacement field which introduces undetermined integral terms and needs only four variables The validity of the present model is proved by comparison with solutions available in the literature
109 citations
TL;DR: In this paper, an analytical model to predict the static analysis of laminated reinforced composite plates subjected to sinusoidal and uniform loads by using a simple first-order shear deformation theory (SFSDT) is presented.
Abstract: This paper aims to present an analytical model to predict the static analysis of laminated reinforced composite plates subjected to sinusoidal and uniform loads by using a simple first-order shear deformation theory (SFSDT). The most important aspect of the present theory is that unlike the conventional FSDT, the proposed model contains only four unknown variables. This is due to the fact that the inplane displacement field is selected according to an undetermined integral component in order to reduce the number of unknowns. The governing differential equations are derived by employing the static version of principle of virtual work and solved by applying Navier\'s solution procedure. The non-dimensional displacements and stresses of simply supported antisymmetric cross-ply and angle-ply laminated plates are presented and compared with the exact 3D solutions and those computed using other plate theories to demonstrate the accuracy and efficiency of the present theory. It is found from these comparisons that the numerical results provided by the present model are in close agreement with those obtained by using the conventional FSDT.
87 citations
TL;DR: In this article, the authors show that the amplitude of the Kalb-Ramond field may be actually large and play a significant role during the early universe, while the presence of higher-order gravity suppresses this field during the cosmological evolution, so that it eventually becomes negligible in the current universe.
Abstract: The intriguing question, why the present scale of the universe is free from any perceptible footprints of rank-2 antisymmetric tensor fields (generally known as Kalb-Ramond fields), is addressed. A quite natural explanation of this issue is given from the angle of higher-curvature gravity, both in four- and in five-dimensional spacetime. The results here obtained reveal that the amplitude of the Kalb-Ramond field may be actually large and play a significant role during the early universe, while the presence of higher-order gravity suppresses this field during the cosmological evolution, so that it eventually becomes negligible in the current universe. Besides the suppression of the Kalb-Ramond field, the extra degree of freedom in $F(R)$ gravity, usually known as scalaron, also turns out to be responsible for inflation. Such $F(R)$ gravity with Kalb-Ramond fields may govern the early universe to undergo an inflationary stage at early times (with the subsequent graceful exit) for a wider range of $F(R)$ gravity than without antisymmetric fields. Furthermore, the models---in four- and five-dimensional spacetimes---are linked to observational constraints, with the conclusion that the corresponding values of the spectral index and tensor-to-scalar ratio closely match the values provided by the Planck survey 2018 data.
66 citations
TL;DR: In this article, the authors proposed 5-brane web diagrams for the theories of SU(6) and Sp(3) gauge groups with rank-3 antisymmetric matter and applied the topological vertex method to compute the partition function for one of these theories.
Abstract: We discuss Type IIB 5-brane configurations for 5d $$ \mathcal{N}=1 $$
gauge theories with hypermultiplets in the rank-3 antisymmetric representation and with various other hypermultiplets, which flow from a UV fixed point at the infinite coupling. We propose 5-brane web diagrams for the theories of SU(6) and Sp(3) gauge groups with rank-3 antisymmetric matter and check our proposed 5-brane webs against several consistency conditions implied from the one-loop corrected prepotential. Using the obtained 5-brane webs for rank-3 antisymmetric matter, we apply the topological vertex method to compute the partition function for one of these SU(6) gauge theories.
60 citations
TL;DR: The discovery of a long-range chiral interaction provides an additional handle to engineer magnetic structures and could enable three-dimensional topological structures, with implications for spintronics and chiral magnetic devices.
Abstract: The exchange interaction governs static and dynamic magnetism. This fundamental interaction comes in two flavours-symmetric and antisymmetric. The symmetric interaction leads to ferro- and antiferromagnetism, and the antisymmetric interaction has attracted significant interest owing to its major role in promoting topologically non-trivial spin textures that promise fast, energy-efficient devices. So far, the antisymmetric exchange interaction has been found to be rather short ranged and limited to a single magnetic layer. Here we report a long-range antisymmetric interlayer exchange interaction in perpendicularly magnetized synthetic antiferromagnets with parallel and antiparallel magnetization alignments. Asymmetric hysteresis loops under an in-plane field reveal a unidirectional and chiral nature of this interaction, which results in canted magnetic structures. We explain our results by considering spin-orbit coupling combined with reduced symmetry in multilayers. Our discovery of a long-range chiral interaction provides an additional handle to engineer magnetic structures and could enable three-dimensional topological structures.
60 citations
TL;DR: In this paper, the effects of the Kalb-Ramond field on the inflationary phenomenology of F(R) gravity theory were investigated and the spectral index and tensor-to-scalar ratio for the model at hand were derived.
Abstract: In this paper we shall study the inflationary aspects of a logarithmic corrected R2 Starobinsky inflation model, in the presence of a Kalb-Ramond field in the gravitational action of F(R) gravity. Our main interest is to pin down the effect of this rank two antisymmetric tensor field on the inflationary phenomenology of the F(R) gravity theory at hand. The effects of the Kalb-Ramond field are expected to be strong during the inflationary era, however as the Universe expands, the energy density of the Kalb-Ramond field scales as ~ a−6 so dark matter and radiation dominate over the Kalb-Ramond field effects. In general, antisymmetric fields constitute the field content of superstring theories, and thus their effect at the low-energy limit of the theory is expected to be significant. As we will show, for a flat Friedmann-Robertson-Walker metric, the Kalb-Ramond field actually reduces to a scalar field, so it is feasible to calculate the observational indices of inflation. We shall calculate the spectral index and the tensor-to-scalar ratio for the model at hand, by assuming two conditions for the resulting Kalb-Ramond scalar field, the slow-roll and the constant-roll condition. As we shall demonstrate, in both the slow-roll and constant-roll cases, compatibility with the latest observational data can be achieved. Also the effect of the Kalb-Ramond field on the inflationary phenomenology is to increase the amount of the predicted primordial gravitational radiation, in comparison to the corresponding f(R) gravities, however the results are still compatible with the observational data.
51 citations
TL;DR: In this paper, various aspects of the 4d/3d reduction of $$ \mathcal{N} = 1 dualities involving USp(2Nc) gauge theories with 2Nf fundamentals and one antisymmetric.
Abstract: We study various aspects of the 4d/3d reduction of $$ \mathcal{N} $$
= 1 dualities involving USp(2Nc) gauge theories with 2Nf fundamentals and one antisymmetric. We discuss the non-trivial role played by the monopole superpotentials in the reduction and obtain new 3d dualities for models with both symplectic and unitary gauge groups. For Nf = 4 we observe interesting webs of dualities and symmetry enhancements, recovering and extending some results already appeared in the literature.
49 citations
TL;DR: In this article, the synchronization problem of N-coupled fractional-order chaotic systems with ring connection via bidirectional coupling is discussed. But the authors focus on the problem of finding the appropriate controllers to transform the fractionalorder error dynamical system into a nonlinear system with antisymmetric structure.
Abstract: This paper discusses the synchronization problem of N-coupled fractional-order chaotic systems with ring connection via bidirectional coupling. On the basis of the direct design method, we design the appropriate controllers to transform the fractional-order error dynamical system into a nonlinear system with antisymmetric structure. By choosing appropriate fractional-order Lyapunov functions and employing the fractional-order Lyapunov-based stability theory, several sufficient conditions are obtained to ensure the asymptotical stabilization of the fractional-order error system at the origin. The proposed method is universal, simple, and theoretically rigorous. Finally, some numerical examples are presented to illustrate the validity of theoretical results.
47 citations
TL;DR: In this article, the authors presented the first calculation of the relevant matrix element in a lattice model which is very close to a candidate theory containing a composite Higgs boson and a partially composite top quark.
Abstract: Partial compositeness is a mechanism for the generation of fermion masses which replaces a direct Higgs coupling to the fermions by a linear mixing with heavy composite partners. We present the first calculation of the relevant matrix element in a lattice model which is very close to a candidate theory containing a composite Higgs boson and a partially composite top quark. Specifically, our model is an $\mathrm{SU}(4)$ gauge theory coupled to dynamical fermions in the fundamental and two-index antisymmetric (sextet) representations. The matrix element we obtain is small and hence our result disfavors the scenario of obtaining a realistic top mass in this model.
TL;DR: In this article, an expression for the vacuum expectation value (vev) of the 1/2 BPS circular Wilson loop of the super Yang Mills in terms of color invariants, valid for any representation R of any gauge group G, was derived.
Abstract: We derive an expression for the vacuum expectation value (vev) of the 1/2 BPS circular Wilson loop of $$ \mathcal{N}=4 $$
super Yang Mills in terms of color invariants, valid for any representation R of any gauge group G. This expression allows us to discuss various exact relations among vevs in different representations. We also display the reduction of these color invariants to simpler ones, up to seventh order in perturbation theory, and verify that the resulting expression is considerably simpler for the logarithm of 〈W〉R than for 〈W〉R itself. We find that in the particular case of the symmetric and antisymmetric representations of SU(N), the logarithm of 〈W〉R satisfies a quadratic Casimir factorization up to seventh order, and argue that this property holds to all orders. Finally, we derive the large N expansion of 〈W〉R for an arbitrary, but fixed, representation of SU(N), up to order 1/N2.
TL;DR: In this paper, a non-perturbative lattice study of lattice theory with two flavors of fermions in the fundamental representation and two in the two-index antisymmetric representation is presented, which is closely related to a minimal partial-compositeness model for physics beyond the Standard Model.
Abstract: We present a non-perturbative lattice study of $$\mathrm {SU}(4)$$
gauge theory with two flavors of fermions in the fundamental representation and two in the two-index antisymmetric representation: a theory closely related to a minimal partial-compositeness model for physics beyond the Standard Model, that was proposed by Ferretti. We discuss the phase structure of the lattice theory and report results for various observables of interest, including the masses of states obtained from different combinations of valence fermions and the spectrum of the Dirac operator. Finally, we comment on the extension of this type of studies to other partial-compositeness models (including, in particular, one that was recently suggested by Gertov et al.), which could admit lighter top-quark partners, highlighting some key features of our lattice simulation algorithm, that make it suitable for such generalizations.
TL;DR: In this article, the interface-dependent spin Hall or valley Hall-like transport in a Kekul\'e lattice was used to generate directed beams: one, two in symmetric or antisymmetric fashion, or multiple beams.
Abstract: Acoustic topological insulators can yield directional antennas for sound, enabling energy-efficient communication. This study explores using the interface-dependent spin Hall or valley Hall -like transport in a Kekul\'e lattice to generate directed beams: one, two in symmetric or antisymmetric fashion, or multiple beams. This topological refractive system could serve as an acoustic beam splitter, offering the advantages of stability, efficiency, and parity control.
TL;DR: It is proved that the fluctuation of arbitrary dynamical observables is constrained by the Kullback-Leibler divergence between the distributions of the forward path and its reversed counterpart, and provides a lower bound for arbitrary observables that are odd under position reversal.
Abstract: The thermodynamic uncertainty relation, which establishes a universal trade-off between nonequilibrium current fluctuations and dissipation, has been found for various Markovian systems. However, this relation has not been revealed for non-Markovian systems; therefore, we investigate the thermodynamic uncertainty relation for time-delayed Langevin systems. We prove that the fluctuation of arbitrary dynamical observables is constrained by the Kullback-Leibler divergence between the distributions of the forward path and its reversed counterpart. Specifically, for observables that are antisymmetric under time reversal, the fluctuation is bounded from below by a function of a quantity that can be identified as a generalization of the total entropy production in Markovian systems. We also provide a lower bound for arbitrary observables that are odd under position reversal. The term in this bound reflects the extent to which the position symmetry has been broken in the system and can be positive even in equilibrium. Our results hold for finite observation times and a large class of time-delayed systems because detailed underlying dynamics are not required for the derivation. We numerically verify the derived uncertainty relations using two single time-delay systems and one distributed time-delay system.
TL;DR: In this paper, it was shown that the free super-Yang-Mills Feynman diagrams are described by the BRST-trivial term where the thickened propagators are the regions of the string worldsheet near the AdS boundary and the holes are the areas near the adS horizon.
Abstract: At small AdS radius, the superstring on AdS5 × S5 was conjectured by Maldacena to be equivalent to $$ \mathcal{N} $$
= 4 super-Yang-Mills at small ‘t Hooft coupling where thickened Feynman diagrams can be used to compute scattering amplitudes. It was previously shown that the pure spinor worldsheet action of the AdS5 × S5 superstring can be expressed as the sum of a BRST-trivial term and a “B-term” which is antisymmetric in worldsheet derivatives. Using the explicit form of the pure spinor vertex operators, it will be argued here that the free super-Yang-Mills Feynman diagrams are described by the BRST-trivial term where the thickened propagators are the regions of the string worldsheet near the AdS boundary and the holes are the regions near the AdS horizon. Evidence will then be presented that the antisymmetric B-term generates the super-Yang-Mills vertex so that, at small radius and arbitrary genus, the superstring amplitudes correctly reproduce the super-Yang-Mills Feynman diagram expansion.
[...]
TL;DR: In this article, the SU(6) Yang-Mills theory with fermions in the adjoint and 3-index antisymmetric mixed representation was studied on a small circle.
Abstract: We carry out a systematic study of SU(6) Yang-Mills theory endowed with fermions in the adjoint and 3-index antisymmetric mixed-representation. The fermion bilinear in the 3-index antisymmetric representation vanishes identically, which leads to interesting new phenomena. We first study the theory on a small circle, i.e., on $$ {\mathrm{\mathbb{R}}}^3\times {\mathbbm{S}}_L^1 $$
, employing symmetry-twisted boundary conditions and semi-classical techniques. We find that the ground state is 3-fold degenerate, which can be explained as a consequence of a 1-form/0-form mixed ’t Hooft anomaly. In addition, the theory may admit massless bosonic and fermionic degrees of freedom, depending on the number of flavors, and confines the electric probes in the infrared. Empowered by ’t Hooft anomaly matching conditions along with the 2-loop β-function, we further examine the possible infrared symmetry realizations on ℝ4 for various number of adjoint and 3-index antisymmetric fermions. The infrared theory is either a conformal field theory, which is expected for a large number of flavors, or it is confining with or without chiral symmetry breaking. In a few cases, we are able to give enough evidence for adiabatic continuity between the small- and large-circle limits.
TL;DR: This paper provides a comprehensive assessment of the current status of the nucleon form factors of the quark tensor using lattice QCD results in the meson sector and, in combination with pole dominance, extends this method to the nucleons case.
Abstract: If physics beyond the standard model enters well above the electroweak scale, its low-energy effects are described by standard model effective field theory. Already, at dimension 6, many operators involve the antisymmetric quark tensor q[over ¯]σ^{μν}q, whose matrix elements are difficult to constrain from experiment, Ward identities, or low-energy theorems, in contrast to the corresponding vector and axial-vector or even scalar and pseudoscalar currents. However, with normalizations determined from lattice QCD, analyticity and unitarity often allow one to predict the momentum dependence in a large kinematic range. Starting from recent results in the meson sector, we extend this method to the nucleon case and, in combination with pole dominance, provide a comprehensive assessment of the current status of the nucleon form factors of the quark tensor.
TL;DR: In this paper, the authors solved the antisymmetric vacuum field equations for a generic rotating tetrad ansatz in Weyl canonical coordinates, and found the corresponding spin connection coefficients.
Abstract: Teleparallel geometry utilizes Weitzenbock connection which has nontrivial torsion but no curvature and does not directly follow from the metric like Levi–Civita connection. In extended teleparallel theories, for instance in f ( T ) or scalar-torsion gravity, the connection must obey its antisymmetric field equations. Thus far, only a few analytic solutions were known. In this note, we solve the f ( T , ϕ ) gravity antisymmetric vacuum field equations for a generic rotating tetrad ansatz in Weyl canonical coordinates, and find the corresponding spin connection coefficients. By a coordinate transformation, we present the solution also in Boyer–Lindquist coordinates, often used to study rotating solutions in general relativity. The result hints for the existence of another branch of rotating solutions besides the Kerr family in extended teleparallel gravities.
TL;DR: In this paper, the second-rank antisymmetric (pseudo) tensor field minimally coupled to a spinor is shown to possess a continuous set of minima, both for tensor and pseudotensor cases.
Abstract: In this paper, we formulate a theory of the second-rank antisymmetric (pseudo)tensor field minimally coupled to a spinor; calculate the one-loop effective potential of the (pseudo)tensor field; and, explicitly, demonstrate that it is positively defined and possesses a continuous set of minima, both for tensor and pseudotensor cases. Therefore, our model turns out to display the dynamical Lorentz symmetry breaking. We also argue that, contrary to the derivative coupling we use here, derivative-free couplings of the antisymmetric tensor field to a spinor do not generate the positively defined potential and thus do not allow for the dynamical Lorentz symmetry breaking.
TL;DR: In this paper, the decay rate for a contraction of a semigroup on a separable Hilbert space is derived by using weak Poincare inequalities for the symmetric and antisymmetric part of the generator.
Abstract: For a contraction $C_{0}$-semigroup on a separable Hilbert space, the decay rate is estimated by using the weak Poincare inequalities for the symmetric and antisymmetric part of the generator. As applications, nonexponential convergence rate is characterized for a class of degenerate diffusion processes, so that the study of hypocoercivity is extended. Concrete examples are presented.
TL;DR: The pseudospins edge states of fundamental antisymmetric Lamb waves in a snowflakelike phononic slab are investigated and the topologically protected edge states and its unidirectional robust propagation are further demonstrated.
Abstract: The topological transport of Lamb wave in phononic crystal slabs provides a great potential in reinforcing nondestructive testing, high sensitivity sensing, and information processing. In this paper, the authors investigate the pseudospins edge states of fundamental antisymmetric Lamb waves in a snowflakelike phononic slab. Significantly, the fourfold Dirac degeneracy for antisymmetric Lamb mode is accidentally formed at the Γ point with the critical angle of the snowflakelike holes, which does not require the folding of the lattices. Meanwhile, based on the rotating-scatterer mechanism, the mirror symmetry is broken and the topological multipole phase transitions are well induced during the gradual change of the scattering strength among the scatterers with the rotation angle. The topologically protected edge states and its unidirectional robust propagation are further demonstrated. The proposed topological phononic slabs will be a more hopeful option to apply in engineering practices.
Posted Content•
TL;DR: In this paper, the authors deform two-dimensional quantum field theories by antisymmetric combinations of their conserved currents that generalize Smirnov and Zamolodchikov's $T\bar{T}$ deformation.
Abstract: We deform two-dimensional quantum field theories by antisymmetric combinations of their conserved currents that generalize Smirnov and Zamolodchikov's $T\bar{T}$ deformation. We obtain that energy levels on a circle obey a transport equation analogous to the Burgers equation found in the $T\bar{T}$ case. This equation relates charges at any value of the deformation parameter to charges in the presence of a (generalized) Wilson line. We determine the initial data and solve the transport equations for antisymmetric combinations of flavor symmetry currents and the stress tensor starting from conformal field theories. Among the theories we solve is a conformal field theory deformed by $J\bar{T}$ and $T\bar{T}$ simultaneously. We check our answer against results from AdS/CFT.
TL;DR: The role of the DMI is still under debate, because largely distinct strengths of DMI have been measured for different magnetic objects, particularly chiral magnetic domain walls (DWs) and non-reciprocal spin waves (SWs).
Abstract: The magnetic exchange interaction is one of the key factors governing the basic characteristics of magnetic systems. In contrast to the symmetric nature of the Heisenberg exchange interaction, the interfacial Dzyaloshinskii-Moriya interaction (DMI) generates an antisymmetric exchange interaction, which offers challenging opportunities in spintronics with intriguing antisymmetric phenomena. The role of the DMI, however, is still under debate, because largely distinct strengths of the DMI have been measured for different magnetic objects, particularly chiral magnetic domain walls (DWs) and nonreciprocal spin waves (SWs). In this paper, by carefully examining the measurement principles, we demonstrate that both the DWs and SWs experience the same strength of the DMI. The key factor in this demonstration is to identify the appropriate experimental conditions by excluding all possible artifacts that causes additional undesired symmetric and antisymmetric contributions in chiral DW dynamics. The present demonstration, therefore, verifies the universality of the DMI between different magnetic dynamics as an intrinsic exchange interaction and also, guarantees the compatibility of several DMI-measurement schemes recently proposed.
TL;DR: In this article, the spontaneous Lorentz symmetry breaking due to an antisymmetric 2-tensor field in Minkowski spacetime was studied, and it was shown that the equations of motion for the free field obey some constraints which lead to the massive mode be non-propagating at leading order.
Abstract: In this work, we study the spontaneous Lorentz symmetry breaking due to an antisymmetric 2-tensor field in Minkowski spacetime. For a smooth quadratic potential, the spectrum of the theory exhibits massless and massive excitations. We show that the equations of motion for the free field obey some constraints which lead to the massive mode be non-propagating at leading order. Besides, there exists a massless mode in the theory which can be identified with the usual Kalb-Ramond field, carrying only one on-shell degree of freedom. The same conclusion holds when one analyses the pole structure of its Feynman propagator. A new complete set of spin-type operators is found, which was the requirement to evaluate the propagator of the Kalb-Ramond field modified by the presence of a nonzero vacuum expectation value responsible for the Lorentz violation.
TL;DR: In this paper, the authors demonstrate a metasurface design of a multi-branch dispersion that can converge plane wave into a focal region at sub-wavelength scale.
TL;DR: The particle swarm-optimized self-tuning fuzzy logic controller (FLC) adapted for the multiple-input multiple-output (MIMO) control is implemented for active vibration suppression of the plates.
TL;DR: In this paper, a non-perturbative lattice study of SU(4) gauge theory with two flavors of fermions in the fundamental representation and two in the two-index antisymmetric representation is presented.
Abstract: We present a non-perturbative lattice study of SU(4) gauge theory with two flavors of fermions in the fundamental representation and two in the two-index antisymmetric representation: a theory closely related to a minimal partial-compositeness model for physics beyond the Standard Model, that was proposed by G. Ferretti. We discuss the phase structure of the lattice theory and report results for various observables of interest, including the masses of states obtained from different combinations of valence fermions and the spectrum of the Dirac operator. Finally, we comment on the extension of this type of studies to other partial-compositeness models (including, in particular, one that was recently suggested by H. Gertov et al.), which could admit lighter top-quark partners, highlighting some key features of our lattice simulation algorithm, that make it suitable for such generalizations.
TL;DR: In this paper, a discontinuous Galerkin self-dual integral equation (DG-SDIE) method is presented for accurately calculating electromagnetic scattering from objects with impedance boundary condition (IBC) surfaces.
Abstract: A discontinuous Galerkin self-dual integral equation (DG-SDIE) method is presented for accurately calculating electromagnetic scattering from objects with impedance boundary condition (IBC) surfaces. The working mechanisms of each term in the DG-SDIE formulation are studied physically and numerically. Based on the mechanisms, we propose a new efficient nonsymmetric DG-SDIE formulation (NDG-SDIE) for IBC problems. A comprehensive study is made to compare the NDG-SDIE with the previous symmetric DG-SDIE (SDG-SDIE) and antisymmetric DG-SDIE (ADG-SDIE) extension formulations for IBC. Numerical results demonstrate that NDG-SDIE is more efficient than SDG-SDIE and ADG-SDIE while generally maintaining the similar accuracy. In addition, we show that the DG methods are more attractive than the standard SDIE due to its flexible performance on large complex multiscale objects.
TL;DR: In this article, a displacement based finite element method is used to solve the analytical model and to calculate the distributions of axial and transverse shear stresses at different locations of the cantilever composite beam subjected to the transverse and the torsional loading at its free end.
Abstract: Stress analysis of thin-walled composite laminated box beams having variable stiffness is realized in this study based on an analytical model accounting for flexural-torsional coupling and warping effects. The variable stiffness of the beam is acquired by constructing laminates with curvilinear fibers having certain specific paths. The fiber paths of variable stiffness layers are classified in three groups as antisymmetric, symmetric and asymmetric. A displacement based finite element method is used to solve the analytical model and to calculate the distributions of axial and transverse shear stresses at different locations of the cantilever composite beam subjected to the transverse and the torsional loading at its free end. Numerical results obtained are compared with available results in the literature for specific cases. A detailed investigation is performed to understand the relation between the stress distributions along the cross section of the beam and the shape of curvilinear fibers for antisymmetric and symmetric cases.