Search results for "Linear"
showing 10 items of 7165 documents
Some consistency issues in multi-criteria decision making
2017
The complexity of decision-making problems included under the multi-criteria decision-making (MCDM) paradigm has favored the proliferation of many schools of thought and varied methodologies. It has not yet been possible to prove the supremacy of any of these approaches. Moreover, in some cases it is difficult to combine the theoretical validity of the approximations with their practical appropriateness. It seems that rigor and applicability are two opposing concepts, something that should not be so. It is our responsibility to bridge the gap. To reduce the gap between theory and practice and use effective methodological approaches, it is necessary to combine the rigor and objectivity of tr…
Fatigue Design of Roller Bearing for Large FPSO Turrets
2012
The present report presents the fatigue design and a fatigue life prediction method for large roller bearings applied in the turret turn table for large Floating Production Storage and Offloading (FPSO) units. The contact point between wheel and rail in these bearings is subjected to a multi-axial stress situation and both surface wear and fatigue cracking may occur. Stress analyses with contact elements are carried out and a methodology based on the Dang Van fatigue criterion is adopted. The criterion is based on an equivalent stress defined as a combination of the fluctuation of the shear stress from its mean value and the associated hydrostatic stress at a critical plane at any time. The…
Comparison of Variance and Damage Indicator Methods for Prediction of the Fracture Plane Orientation in Multiaxial Fatigue
1999
ABSTRACT Two methods that enable prediction of the fracture plane orientation are presented and compared in this paper. The first one is a statistical approach, which is based on the variance of an equivalent stress. It is assumed that the fracture plane is the one where the variance of a linear combination of the shear and normal stresses acting on this plane is maximum. The second one uses the so-called damage indicator of a multiaxial fatigue criterion, which is based on the research of the critical plane. The formulation of the criterion involves shear and normal stress amplitudes and mean normal stress. The fracture plane is the critical plane; That is to say the one where the damage i…
Application of time–stress superposition to nonlinear creep of polyamide 66 filled with nanoparticles of various sizes
2007
The long-term tensile creep of polyamide 66 and its nanocomposites filled with 1 vol.% TiO2 nanoparticles 21 and 300 nm in diameter is studied. It is assumed that the dominant mechanisms of creep deformation are of viscoelastic nature, while the contribution of plastic strains is not essential in the stress (< 0.6 of the ultimate stress) and time (about 100 hours) ranges considered. The creep isochrones obtained show that the materials exhibit a nonlinear viscoelastic behaviour and the degree of nonlinearity is reduced significantly by incorporation of the nanoparticles. The evolution of viscoelastic strains is less pronounced for the nanocomposite filled with smaller nanoparticles. Smooth …
Mohr-cyclides, a 3D representation of geological tensors: The examples of stress and flow
2008
Mohr-circles are commonly used to represent second-rank tensors in two dimensions. In geology, this mainly applies to stress, flow, strain and deformation. Three-dimensional second rank tensors have been represented by sets of three Mohr-circles, mainly in the application of stress. This paper demonstrates that three-dimensional second rank tensors can in fact be represented in a three-dimensional reference frame by Mohr surfaces, which are members of the cyclide family. Such Mohr-cyclides can be used to represent any second rank tensor and are exemplified with the stress and flow tensors.
Influence of data input in the evaluation of Stress Intensity Factors from Thermoelastic Stress Analysis
2021
Abstract Thermoelastic Stress Analysis (TSA) is applied to evaluate the Stress Intensity Factor (SIF), T-stress and J-Integral in a Single-Edge-Notched-Tension sample undergoing fatigue cycling. The Williams’ series stress formulation and a least-square fitting (LSF) procedure are used to obtain the SIF and the T-stress. The evaluation is carried out with the aim to investigate the influence of the input data in the system of equations solved with the LSF, and in particular: the number of coefficients used in the Williams’ series and the choice and position of the fitted experimental data points. Three algorithms for the determination of the crack tip position are also evaluated: a coarse g…
A unifying variational framework for stress gradient and strain gradient elasticity theories
2015
Abstract Stress gradient elasticity and strain gradient elasticity do constitute distinct continuum theories exhibiting mutual complementary features. This is probed by a few variational principles herein presented and discussed, which include: i) For stress gradient elasticity, a (novel) principle of minimum complementary energy and an (improved-form) principle of stationarity of the Hellinger–Reissner type; ii) For strain gradient elasticity, a (known) principle of minimum total potential energy and a (novel) principle of stationarity of the Hu–Washizu type. Additionally, the higher order boundary conditions for stress gradient elasticity, previously derived by the author (Polizzotto, Int…
Nonlinear Nonhomogeneous Elliptic Problems
2019
We consider nonlinear elliptic equations driven by a nonhomogeneous differential operator plus an indefinite potential. The boundary condition is either Dirichlet or Robin (including as a special case the Neumann problem). First we present the corresponding regularity theory (up to the boundary). Then we develop the nonlinear maximum principle and present some important nonlinear strong comparison principles. Subsequently we see how these results together with variational methods, truncation and perturbation techniques, and Morse theory (critical groups) can be used to analyze different classes of elliptic equations. Special attention is given to (p, 2)-equations (these are equations driven…
THE MINIMIZING TOTAL VARIATION FLOW WITH MEASURE INITIAL CONDITIONS
2004
In this paper we obtain existence and uniqueness of solutions for the Cauchy problem for the minimizing total variation flow when the initial condition is a Radon measure in ℝN. We study limit solutions obtained by weakly approximating the initial measure μ by functions in L1(ℝN). We are able to characterize limit solutions when the initial condition μ=h+μs, where h∈L1(ℝN)∩L∞(ℝN), and μs=αℋk⌊ S,α≥0,k is an integer and S is a k-dimensional manifold with bounded curvatures. In case k<N-1 we prove that the singular part of the solution does not move, it remains equal to μs for all t≥0. In particular, u(t)=δ0 when u(0)=δ0. In case k=N-1 we prove that the singular part of the limit solution …
Maximal Operators with Respect to the Numerical Range
2018
Let $\mathfrak{n}$ be a nonempty, proper, convex subset of $\mathbb{C}$. The $\mathfrak{n}$-maximal operators are defined as the operators having numerical ranges in $\mathfrak{n}$ and are maximal with this property. Typical examples of these are the maximal symmetric (or accretive or dissipative) operators, the associated to some sesquilinear forms (for instance, to closed sectorial forms), and the generators of some strongly continuous semi-groups of bounded operators. In this paper the $\mathfrak{n}$-maximal operators are studied and some characterizations of these in terms of the resolvent set are given.