Torsion Theory Research Articles

Tor-tilting and weak silting theories in comodule categories

In this paper, we introduce and investigate Tor-tilting comodules and weak silting comodules, providing a generalization of the established tilting and silting theories in the comodule category. Our exploration yields a comprehensive understanding of their fundamental properties, including their associated torsion theories. We delve into not only the relations between Tor-tilting and weak silting comodules but also the connections among them and (co) tilting as well as (co) silting comodules. Additionally, we define Tor-tilting coflat comodules and Tor-tilting coflat dimensions. Finally, we explore Tor-tilting and weak silting objects in the morphism category, demonstrating their equivalence.

Homotopy torsion theories

In the context of categories equipped with a structure of nullhomotopies, we introduce the notion of homotopy torsion theory. As special cases, we recover pretorsion theories as well as torsion theories in multi-pointed categories and in pre-pointed categories. Using the structure of nullhomotopies induced by the canonical string of adjunctions between a category A and the category Arr(A) of arrows, we give a new proof of the correspondence between orthogonal factorization systems in A and homotopy torsion theories in Arr(A), avoiding the request on the existence of pullbacks and pushouts in A. Moreover, such a correspondence is extended to weakly orthogonal factorization systems and weak homotopy torsion theories.

Neutron stars in scalar torsion theories with non minimal coupling

We explore the existence and configurations of static and slowly rotating neutron stars (NSs) within a specific truncation of teleparallel scalar torsion theory. In this model, a scalar field ϕ is non-minimally coupled to the torsion scalar as ξTϕ 2, in the presence of the scalar potential V(ϕ) = -μ 2 ϕ 2/2 + λϕ 4/4. We establish the hydrostatic equilibrium equations for the static scenario and numerically solve them for both interior and exterior regions, employing appropriate boundary conditions near the center and at a distant location far away from the star's surface. Radial profiles of metric functions and the scalar field, alongside mass-radius diagrams, are plotted, utilizing four different realistic equations of state (EOS). Our results align closely with observational constraints from the GW170817 event, revealing a maximal mass of 2.37 M ⊙ achieved with the BSk21 EOS for a coupling parameter ξ = 0.25. Extending our analysis to encompass slow rotation, we establish the relationship between the star's moment of inertia and its mass. Furthermore, we explore future observations of NSs utilizing the redshift surface observable. Finally, we demonstrate the validity of the universality relation between the two forms of normalized moment of inertia within teleparallel scalar torsion theory with non minimal coupling.

A new theoretical method for torsional-flexural vibrations response of thin-walled beams with closed cross-sections under uniform distributed moving load

This article presents a new theoretical method for the torsional-flexural vibration response of a thin-walled beam with closed cross sections under a uniformly distributed moving load. Based on Vlasov’s theory and restrained torsion theory, a comprehensive equation of motion for torsional flexural vibration is established by considering the effects of additional torque caused by the change of the shear center and the center of mass and the warpage coefficient. Using the Fourier transform, Laplace transform, and their inverse transformations, the torsional-flexural vibration response expression of thin-walled beams with closed cross-sections under a uniformly distributed moving load was derived. The results calculated by the analytical solutions in this study were compared with those from finite element method, demonstrating the reliability and superiority of the analytical solutions. Compared with the method that ignores the warpage coefficient, the lateral displacement and torsion angle of the beam calculated by the proposed theoretical method decreased by more than 12.00%. The effect of the cross-sectional properties on the natural frequency of the torsional-flexural vibration of thin-walled beams is analyzed, and the results show that the moment of inertia and mass per unit length have a considerable influence on the torsional-flexural frequency, which increases with the moment of inertia and decreases with an increase in the mass per unit length. The influences of the load magnitude, load velocity, and load eccentricity on the dynamic response were further investigated. According to the results, the lateral displacement of the beam increased significantly with increases in the load eccentricity and load magnitude. In practical engineering, the conclusions of this study can be used to limit the torsional-flexural vibration response of simple maglev support bridges to ensure the safety of vehicles and passengers.

Comodule theories in Grothendieck categories and relative Hopf objects

We develop the categorical algebra of the noncommutative base change of a comodule category by means of a Grothendieck category S. We describe when the resulting category of comodules is locally finitely generated, locally noetherian or may be recovered as a coreflective subcategory of the noncommutative base change of a module category. We also introduce the category SHA of relative (A,H)-Hopf modules in S, where H is a Hopf algebra and A is a right H-comodule algebra. We study the cohomological theory in SHA by means of spectral sequences. Using coinduction functors and functors of coinvariants, we study torsion theories and how they relate to injective resolutions in SHA. Finally, we use the theory of associated primes and support in noncommutative base change of module categories to give direct sum decompositions of minimal injective resolutions in SHA.

Asymmetric Folded Plate with Parallel Edges in Validation of their Static Behavior by Combining Vlasov Torsion Theory with Bernoulli Bending Theory

Aims: A new hybrid procedure that combines the Vlasov torsion theory with the Bernoulli bending theory is presented herein, to demonstrate qualitatively and quantitatively the operation of asymmetric folded plates with parallel edges, which are loaded with gravity static loads. Background: A recently proposed technique based on Vlasov torsion theory is used for the exact calculation of the Principal Elastic Reference System in a reinforced concrete folded plate having an asymmetric thin-walled open cross-section with parallel edges. Moreover, the warping moment (or bi-moment) concept of the Vlasov theory is combined with the pure-bending around two axes, according to the Bernoulli bending theory, to determine the normal stresses along the longitudinal dimension of the folded plate. Methods: Τhe warping properties of a thin-walled open cross-section are determined by calculating: (a) the elastic characteristics (elastic center, principal axes) of the section, (b) the principal start point, the sectorial coordinates, the wrapping moment of inertia and the wrapping stiffness of the section. Finally, the normal stresses along the longitudinal dimension are calculated considering the bi-axes flexure with the bi-moment phenomenon. Results: Τhe exact solution of normal stresses at the middle section of an examined folded plate along the longitudinal dimension is found by combining the Bernoulli bending theory for prismatic beams and the Vlasov torsion theory for thin-walled open sections. Conclusion: The current procedure can be used as a benchmark analysis method of asymmetric folded plates in order to evaluate the reliability of the results of various analysis F.E.M. software, covering an open issue of the structural analysis of special structures.

Numerical studies on the torsional behavior of octagonal concrete‐filled linked double steel tubes

AbstractThe concrete confinement is improved in octagonal concrete‐filled double steel tubular (OCFLDST) columns by linking the steel tubes with steel plates and thereby it enhances ductility. It has the potential to improve the torsional resistance in concrete‐filled steel tubular cross‐sections. This paper investigates the torsional behavior of OCFLDST through analytical and numerical investigations. The numerical model for OCFLDST is developed in ABAQUS and validated using test data available in the literature for axial loading conditions. The validated model is then subjected to pure torsion to study the torsional behavior of OCFLDST. In comparison with bare steel tubes, concrete filling of linked steel tubes has increased the torsional resistance by 33%. Further, parametric studies are conducted to understand the influence of various parameters like yield strength and thickness of the outer steel tube, compressive strength of concrete, the thickness of the linking plates, and axial load ratio. The numerical results are compared with the proposed expression for finding the torsional capacity based on St. Venant's torsion theory. The proposed capacity prediction is in good agreement with the numerical results.

On torsion theories and open classes of linear modular lattices

Given a ring R, a bijection exists between torsion theories and idempotent radicals. Further, the class of hereditary torsion theories contains the skeleton of the open classes. In this work, we extend the notions and main results in R-Mod about torsion classes, torsion-free classes, and open classes to the category of linear lattices, whose objects are complete modular lattices and whose morphisms are linear morphisms.

The transformation matrix in the 7DOFs beam formulation

A non-negligible percentage of steel products for civil and industrial constructions is realised with members characterised by a mono-symmetric cross-section. The non-coincidence between the centroid and the shear centre reflects in a quite complex behaviour that is remarkably influenced by the warping effects. Usually, frame design is based on the output data of commercial Finite Element Analysis Packages (FEAPs) but only few of them offer a refined beam element formulation able to reproduce the response of non-bisymmetric cross-section members (like the 7 degrees of freedom, DOFs, beam element). As a consequence, warping effects are usually neglected in routine design, leading in several cases to assess non-correct internal stresses, global displacements and critical buckling multipliers.This paper is focussed on mono-symmetric cross-section members and deals with the influence of the interaction between axial force, bending moments and bimoment in linear elastic range. In particular, the two strategies that FE developers usually adopt, in the 7 DOFs beam formulation, to pass from the local to the global reference system are herein shortly introduced and discussed. The effects of the associated transformation matrices have been investigated in few examples, also reproduced via closed expressions derived from the mixed torsion theory and FE shell models. Paper outcomes show that the results in terms of generalised displacements, internal forces and, consequently, stress distribution along the member cross-section are significantly different, strictly depending on the adopted transformation matrix. The importance of a correct evaluation of the bimoment distribution is stressed also by the fact that the new edition of the EN1993-1-1, expected in the next months, includes also the bimoment contribution for member checks.

An extension of $S$--noetherian rings and modules

For any commutative ring $A$ we introduce a generalization of $S$--noetherian rings using a here\-ditary torsion theory $\sigma$ instead of a multiplicatively closed subset $S\subseteq{A}$. It is proved that totally noetherian w.r.t. $\sigma$ is a local property, and if $A$ is a totally noetherian ring w.r.t $\sigma$, then $\sigma$ is of finite type.

Accurate Modeling and Wave Propagation Analysis of Cracked Slender Structural Members by the Spectral Element Method

The analysis of elastic wave propagation in cracked structures is very useful in the crack detection by the ultrasonic guided wave method. This study presents an accurate spectral element modeling method for cracked slender structural members by using refined waveguide models and a more realistic crack model. Firstly, a spatial spectral beam element model is established for uncracked slender structural member based on the Love rod theory, the modified Timoshenko beam theory, and the Saint-Venant’s torsion theory. Then, the complete local additional flexibility matrix for crack in the structural member with rectangular cross section is derived from the theory of elastic fracture mechanics, and a two-node condensed spectral element model considering the stiffness coupling effect caused by the crack is established for cracked slender structural member. The wave response in cracked structures is solved by the numerical inverse Laplace transformation method. A thorough comparison of the wave responses in cracked structural member evaluated by the presented spectral element model and the 3D solid finite element model is given in the numerical example, which verifies the accuracy and high efficiency of the presented method.

Some aspects about the lattice [τg,χ] and the torsion theories of Kaplansky-type

In this manuscript, we define when a torsion theory, which is a generalization of Goldie’s torsion theory, is of the type I, II, or III, according to Kaplansky’s theory of types, and we establish some structure theorems of regular, right self-injective rings using the torsion theories of Kaplansky-type. We study the properties that each of these torsion theories has and their influence on the lattice of generalizations of Goldie’s torsion theory, locating several subintervals of which contain no atoms nor coatoms, thus extending our knowledge of the lattice structure of .

Supercomputers against strong coupling in gravity with curvature and torsion

Many theories of gravity are spoiled by strongly coupled modes: the high computational cost of Hamiltonian analysis can obstruct the identification of these modes. A computer algebra implementation of the Hamiltonian constraint algorithm for curvature and torsion theories is presented. These non-Riemannian or Poincaré gauge theories suffer notoriously from strong coupling. The implementation forms a package (the ‘Hamiltonian Gauge Gravity Surveyor’ – HiGGS) for the xAct tensor manipulation suite in Mathematica. Poisson brackets can be evaluated in parallel, meaning that Hamiltonian analysis can be done on silicon, and at scale. Accordingly HiGGS is designed to survey the whole Lagrangian space with high-performance computing resources (clusters and supercomputers). To demonstrate this, the space of ‘outlawed’ Poincaré gauge theories is surveyed, in which a massive parity-even/odd vector or parity-odd tensor torsion particle accompanies the usual graviton. The survey spans possible configurations of teleparallel-style multiplier fields which might be used to kill-off the strongly coupled modes, with the results to be analysed in subsequent work. All brackets between the known primary and secondary constraints of all theories are made available for future study. Demonstrations are also given for using HiGGS – on a desktop computer – to run the Dirac–Bergmann algorithm on specific theories, such as Einstein–Cartan theory and its minimal extensions.

Torsion theories connected by a heart and hearts of intervals

Torsion theories connected by a heart and hearts of intervals

Consistent pairs of $ \mathfrak{s} $-torsion pairs in extriangulated categories with negative first extensions

<abstract><p>As a generalization of a consistent pair of $ t $-structures on triangulated categories, we introduced the notion of a consistent pair of $ \mathfrak{s} $-torsion pairs in the extriangulated setup. Let $ (\mathcal{T}_{i}, \mathcal{F}_{i}) $ be an $ \mathfrak{s} $-torsion pair in an extriangulated category with a negative first extension for any $ i = 1, 2 $. By using the consistent pair, we gave a criterion for $ (\mathcal{T}_{1}\ast\mathcal{T}_{2}, \mathcal{F}_{1}\cap\mathcal{F}_{2}) $ to be an $ \mathfrak{s} $-torsion pair. Our results were then applied to the torsion theory induced by $ \tau $-rigid modules.</p></abstract>

Numerical Model for a Geometrically Nonlinear Analysis of Beams with Composite Cross-Sections

This paper presents a beam model for a geometrically nonlinear stability analysis of the composite beam-type structures. Each wall of the cross-section can be modeled with a different material. The nonlinear incremental procedure is based on an updated Lagrangian formulation where in each increment, the equilibrium equations are derived from the virtual work principle. The beam model accounts for the restrained warping and large rotation effects by including the nonlinear displacement field of the composite cross-section. First-order shear deformation theories for torsion and bending are included in the model through Timoshenko’s bending theory and a modified Vlasov’s torsion theory. The shear deformation coupling effects are included in the model using the six shear correction factors. The accuracy and reliability of the proposed numerical model are verified through a comparison of the shear-rigid and shear-deformable beam models in buckling problems. The obtained results indicated the importance of including the shear deformation effects at shorter beams and columns in which the difference that occurs is more than 10 percent.

Small pairs of abelian p-groups

The aim of this paper is to introduce and investigate small pairs of abelian p-groups, defined by means of small homomorphisms and by analogy with torsion theories and cotorsion pairs. Non-trivial small pairs live inside the two classes of thick p-groups and thin p-groups. Since these groups, as well as small homomorphisms, have been investigated long time ago, in the first part of the paper we survey known results on these topics, adding some new results. A relevant role in the study of small pairs is played by the classes of fully-thick and fully-thin groups and by the groups which are at the same time thick and thin. This last class of groups is large enough to guarantee the existence of 22c different small pairs. Connections with a Corner's classical realization theorem for endomorphism rings of separable p-groups and the recent topic of groups with minimal full inertia are established.

Gradual and Fuzzy Modules: Functor Categories

The categorical treatment of fuzzy modules presents some problems, due to the well known fact that the category of fuzzy modules is not abelian, and even not normal. Our aim is to give a representation of the category of fuzzy modules inside a generalized category of modules, in fact, a functor category, Mod−P, which is a Grothendieck category. To do that, first we consider the preadditive category P, defined by the interval P=(0,1], to build a torsionfree class J in Mod−P, and a hereditary torsion theory in Mod−P, to finally identify equivalence classes of fuzzy submodules of a module M with F-pair, which are pair (G,F), of decreasing gradual submodules of M, where G belongs to J, satisfying G=Fd, and ∪αF(α) is a disjoint union of F(1) and F(α)\G(α), where α is running in (0,1].

Center of Stiffness, Principal Axes and Principal Start Point of Thin-Walled Open-Sections of Cores: A New Modified Calculation Technique Based on Vlasov Torsion Theory

The present paper deals with the exact calculation of the Principal Elastic Reference System of R/C Cores, which have thin-walled open section. A new modified technique based on Vlasov torsion theory is developed that examines the warping phenomenon of cores. The exact position of the elastic center (or shear center) of a core and the orientation of the principal axes of elasticity, as well as the exact calculation of warping constant, are special parameters since, on the one hand it strongly affects the in plan stiffness distribution of the building members, and on the other hand it affects the values of the building eigen-frequencies and mode-shapes. These parameters are particularly critical in seismic design of asymmetric multistorey buildings. Based on Vlasov torsion theory of cores with thin-walled open sections, a repetitive mathematical procedure about the calculation of the location of the elastic center of core and the principal start point of the section is proposed. This new modified technique can be applied to cores of any shape. Afterwards, the exact diagram of sectorial coordinates of the section, as well as the warping constant, are calculated. All the above-mentioned parameters are very useful in the simulation of the cores in numerical models that are going to use in linear and nonlinear seismic analysis of the structures. Knowing all mentioned parameters, the numerical accuracy of the finite element method on cores can be checked. Finally, a numerical example, where the proposed new modified technique is applied on a fully asymmetric core, is presented.

Stability analysis of shear deformable cross-ply laminated composite beam-type structures

This paper presents a shear deformable beam model for the nonlinear stability analysis of composite beam-type structures. Each wall of the cross-section is stacked in the cross-ply scheme. The incremental equilibrium equations are derived in the framework of an updated Lagrangian formulation. Hooke’s law is assumed to be valid. The nonlinear displacement field of the composite cross-section accounts for the restrained warping and the large rotation effects. The shear deformation effects are included through Timoshenko’s bending theory and modified Vlasov’s torsion theory. Additional shear correction factors due to the bending-torsion coupling occurring at asymmetric cross-sections are introduced in the analysis. The accuracy and reliability of proposed numerical mode are verified on benchmark examples, and the obtained results confirm that it can be classified as a shear locking-free model.