A New Beam Finite Element for Static Bending Analysis of Slender Transversely Cracked Beams on Two-Parametric Soils

This paper derives an original finite element for the static bending analysis of a transversely cracked uniform beam resting on a two-parametric elastic foundation. In the simplified computational model based on the Euler–Bernoulli theory of small displacements, the crack is represented by a linear rotational spring connecting two elastic members. The derivations of approximate transverse displacement functions, stiffness matrix coefficients, and the load vector for a linearly distributed load along the entire beam element are based on novel cubic polynomial interpolation functions, including the second soil parameter. Moreover, all derived expressions are obtained in closed forms, which allow easy implementation in existing finite element software. Two numerical examples are presented in order to substantiate the discussed approach. They cover both possible analytical solution forms that may occur (depending on the problem parameters) from the same governing differential equation of the considered problem. Therefore, several response parameters are studied for each example (with additional emphasis on their convergence) and compared with the corresponding analytical solution, thus proving the quality of the obtained finite element.

Pure Nash Equilibria in Resource Graph Games

This paper studies the existence of pure Nash equilibria in resource graph games, a general class of strategic games succinctly representing the players’ private costs. These games are defined relative to a finite set of resources and the strategy set of each player corresponds to a set of subsets of resources. The cost of a resource is an arbitrary function of the load vector of a certain subset of resources. As our main result, we give complete characterizations of the cost functions guaranteeing the existence of pure Nash equilibria for weighted and unweighted players, respectively. For unweighted players, pure Nash equilibria are guaranteed to exist for any choice of the players’ strategy space if and only if the cost of each resource is an arbitrary function of the load of the resource itself and linear in the load of all other resources where the linear coefficients of mutual influence of different resources are symmetric. This implies in particular that for any other cost structure there is a resource graph game that does not have a pure Nash equilibrium. For weighted games where players have intrinsic weights and the cost of each resource depends on the aggregated weight of its users, pure Nash equilibria are guaranteed to exist if and only if the cost of a resource is linear in all resource loads, and the linear factors of mutual influence are symmetric, or there is no interaction among resources and the cost is an exponential function of the local resource load. We further discuss the computational complexity of pure Nash equilibria in resource graph games showing that for unweighted games where pure Nash equilibria are guaranteed to exist, it is coNP-complete to decide for a given strategy profile whether it is a pure Nash equilibrium. For general resource graph games, we prove that the decision whether a pure Nash equilibrium exists is Σ p 2 -complete.

Balancing Loads among MEC Servers by Task Redirection to Enhance the Resource Efficiency of MEC Systems

To improve the resource efficiency of multi-access edge computing (MEC) systems, it is important to distribute the imposed workload evenly among MEC servers (MECSs). To address this issue, we propose a task redirection method to balance loads among MECSs in a distributed manner. In conventional methods, a congested MECS selects only one MECS to which it redirects tasks. By contrast, the proposed method enables a congested MECS to distribute its tasks to a set of MECSs, the loads of which are lower than that of the congested MECS by determining the number of tasks that it redirects to each selected MECS. We prove that our task redirection method drives a MEC system to a state where the resulting MECS load vector is lexicographically minimal. Through extensive simulation studies, we show that compared with the conventional methods, the proposed method can achieve the smallest load difference between the load of the MECS, the load of which is the highest, and that of the MECS, the load of which is the smallest. By lexicographically minimizing the MECS load vector, the proposed method decreases the average task blocking rate when the task offload rate is high. In addition, we show that the proposed method outperforms the conventional methods in terms of the number of tasks, the delay requirements of which are not satisfied.

Lethal and Sublethal Effects of Flupyradifurone on Bemisia tabaci MED (Hemiptera: Aleyrodidae) Feeding Behavior and TYLCV Transmission in Tomato

Pesticides primarily affect target organisms via direct toxicity, but may also alter the feeding behaviors of surviving individuals in ways that alter their effect on host plants. The latter impact is especially important when pests can transmit plant pathogens. The Mediterranean (MED) population of the sweetpotato whitefly Bemisia tabaci Gennadius (Hemiptera: Aleyrodidae) transmits Tomato yellow leaf curl virus (TYLCV), a pathogen that can be economically devastating in field and greenhouse cropping systems. We first assessed the impact of sublethal (LC15) and label concentrations of flupyradifurone, a butenolide-derived insecticide, on the feeding behavior of TYLCV-infected MED on tomato. We next measured the effect of flupyradifurone on plant TYLCV load, vector transmission efficiency, and MED survival. Both the LC15 and label flupyradifurone concentrations dramatically altered MED feeding and caused the near cessation of both salivation and phloem ingestion (necessary for viral transmission and acquisition, respectively). Both concentrations also significantly reduced plant TYLCV load, and the label rate of flupyradifurone sharply decreased TYLCV transmission while killing >99% of MED. As the first report of pesticide-induced changes in the feeding behavior of viruliferous Bemisia, our findings highlight the potential importance of chemically driven feeding cessation in the control of TYLCV and other Bemisia-transmitted plant pathogens.

Analytical Model of Two-Directional Cracking Shear-Friction Membrane for Finite Element Analysis of Reinforced Concrete

There are a multitude of existing material models for the finite element analysis of cracked reinforced concrete that provide reduced shear stiffness but do not limit shear strength. In addition, typical models are not based on the actual physical behavior of shear transfer across cracks by shear friction recognized in the ACI 318 Building Code. A shear-friction model was recently proposed that was able to capture the recognized cracked concrete behavior by limiting shear strength as a yielding function in the reinforcement across the crack. However, the proposed model was formulated only for the specific case of one-directional cracking parallel to the applied shear force. This study proposed and generalized an orthogonal-cracking shear-friction model for finite element use. This was necessary for handling the analysis of complex structures and nonproportional loading cases present in real design and testing situations. This generalized model was formulated as a total strain-based model using the approximation that crack strains are equal to total strains, using the proportional load vector, constant vertical load, and modified Newton–Raphson method to improve the model’s overall accuracy.

Dynamics of Plane Waves in a Semi-Bounded Electro-Magneto-Elastic Medium

The problem of harmonic oscillations in electro-electromagnetic composites is studied. Oscillations can be initiated by the extended load vector, including the horizontal and vertical components of mechanical displacements, and electrical induction distributed on top of the surface. Boundary conditions assume full mechanical coupling for all layers of the structure. Electrical conditions on the surface top can be both electrically open, and electrically shorted. Magnetic conditions are similar to electric ones and describe the continuity of fields in between two mediums, or indicate the isolation of the magnetic field between them. The Green's function of electro–magneto–elastic medium is constructed. Phase velocities are obtained for various geometric proportions and materials.

Well-posedness of the fractional Zener wave equation for heterogeneous viscoelastic materials

Zener’s model for viscoelastic solids replaces Hooke’s law σ = 2με(u) + λ tr(ε(u)) I, relating the stress tensor σ to the strain tensor ε(u), where u is the displacement vector, μ > 0 is the shear modulus, and λ ≥ 0 is the first Lamé coefficient, with the constitutive law (1 + τDt) σ = (1 + ρDt)[2με(u) + λ tr(ε(u)) I], where τ > 0 is the characteristic relaxation time and ρ ≥ τ is the characteristic retardation time. It is the simplest model that predicts creep/recovery and stress relaxation phenomena. We explore the well-posedness of the fractional version of the model, where the first-order time-derivative Dt in the constitutive law is replaced by the Caputo time-derivative $\begin{array}{} D_t^\alpha \end{array} $ with α ∈ (0, 1), μ, λ belong to L∞(Ω), μ is bounded below by a positive constant and λ is nonnegative. We show that, when coupled with the equation of motion ϱü = Div σ + f, considered in a bounded open Lipschitz domain Ω in ℝ3 and over a time interval (0, T], where ϱ ∈ L∞(Ω) is the density of the material, assumed to be bounded below by a positive constant, and f is a specified load vector, the resulting model is well-posed in the sense that the associated initial-boundary-value problem, with initial conditions u(0, x) = g(x), u̇(0, x) = h(x), σ(0, x) = S(x), for x ∈ Ω, and a homogeneous Dirichlet boundary condition, possesses a unique weak solution for any choice of g ∈ [$\begin{array}{} \mathrm{H}^1_0 \end{array} $(Ω)]3, h ∈ [L2(Ω)]3, and S = ST ∈ [L2(Ω)]3×3, and any load vector f ∈ L2(0, T; [L2(Ω)]3), and that this unique weak solution depends continuously on the initial data and the load vector.

Material-Oriented Shape Functions for FGM Plate Finite Element Formulation

A four-noded finite element of a moderately thick plate made of functionally graded material (FGM) is presented. The base element is rectangular and can be extended to any shape using a transformation based on NURBS functions. The proposed 2D shape functions are consistent with the physical interpretation and describe the states of element displacement caused by unit displacements of nodes. These functions depend on the FGM’s material parameters and are called material-oriented. The shape function matrix is based on a superposition displacement field of two plate strips with 1D exact shape functions. A characteristic feature of the proposed formulation is full coupling of the membrane and bending states in the plate. The analytical form of the stiffness matrix and the nodal load vector was obtained, which leads to the numerical efficiency of the formulation. The element has been incorporated into Abaqus software with the use of Maple program. The finite element shows good convergence properties for different FGM models in the transverse direction to the middle plane of the plate. During derivation of the 2D plate element the formally exact 1D finite element for transverse nonhomogeneous FGM plate strip was developed.

Analysis of Fatigue Damage Accumulation in Structural Materials under Quasi-Random Load

The spectrum of stresses at a hazardous point on bearing metal structures of mining, road-building and transporting machines, as a rule, is random by nature. Objective complexity of the fatigue process and variety of fatigue crack nucleation mechanisms are the main causes of errors in prediction of their lifespan, along with an experimentally untestable hypothesis of linear summation of damages. The method of complete stress-strain diagrams uses a representative parameter of the fatigue process, selected in accordance with the results of testing, carried out on trained thin specimens of a specific material. The summation of fatigue damages is based on experimental kinematic curves, whose intersection with a load vector is used as a criterion of fatigue failure. It is shown that the approach proposed to calculate the lifespan gives certain advantages, as far as individual properties of the material are concerned, and when it comes to describing the kinetics of the fatigue process and determining the limiting state of the material in a structure.

Influence of Anchor Connector Stiffness on Displacement-Internal Force of Steel-Concrete Frame

In the article, the author introduces how to determine the equivalent hardness of steel-concrete composite beam element, stiffness matrix and nodal load vector of steel-concrete beam element. Thereby, to build and solve the problem of analyzing the structural steel frame of concrete considering the anchor stiffness, programming and clarifying the impact of anchor stiffness associated with displacement - internal force of the frame