Nth-order Fuzzy Differential Equations Under Generalized Differentiability

In this paper, the multiple solutions of Nth-order fuzzy differential equations by the equivalent integral forms are considered. Also, an Existence and uniqueness theorem of solution of Nth-order fuzzy differential equations is proved under Nth-order generalized differentiability in Banach space

A note on “Numerical solutions of fuzzy differential equations by extended Runge–Kutta-like formulae of order 4”

In this note we show that the example presented in a recent paper by Ghazanfari et al. is incorrect. Namely, the “exact solution” suggested by the authors is not solution of the given fuzzy differential equation (FDE). Indeed, the authors have proposed an exact solution which is independent from the initial condition. So, we obtain the correct exact solution using the characterization theorem proposed by Bede et al. under Seikkala differentiability. Also, some details are given for the mentioned example

Nearest interval-valued approximation of interval-valued fuzzy numbers

In this paper, we proposed a new interval-valued approximation of interval-valued fuzzy numbers, which is the best one with respect to a certain measure of distance between interval-valued fuzzy numbers. Also, a set of criteria for interval-valued approximation operators is suggested

An improved Runge-Kutta method for solving fuzzy differential equations under generalized differentiability

In this paper, a new Runge-Kutta method be presented which has the fifth order local truncation error with lower function evaluation in comparison with classical one's. Also we use the generalized derivative instead of Seikkala's derivative to illustrate the efficiency of this derivative. The method's applicability is illustrated by solving a linear first order fuzzy differential equation

Experimental and Numerical Studies of Stress Distribution in an Expanding Pin Joint System

Pin joints are widely used mechanisms in different industrial machineries such as aircrafts, cranes, ships, and offshore drilling equipment providing a joint with possibility of relative rotation about one single axis. The rigidity of the joint and its service lifetime depend on the clamping force in the contact region that is provided by the applied torque. However, due to the tolerance needed for insertion of a pin in the equipment support bore, the pin is prone to relative displacement inside the bore. The amplitude of this relative displacement usually increases as time passes and since the material of the support often has lower quality grade than the pin, it leads to creation of slack in the equipment and malfunctioning of the machine. An Expanding Pin System (EPS) can be a solution to this problem where the split sleeve expands to remove the gap while the joint is torqued. Therefore, slack in the joint system disappears and 360° contact area could be achieved, providing a better stress distribution and preventing the stress localization. Determining the EPS preload and the resulting contact pressure and stresses in the joint parts are important to avoid damaging to the contact surfaces of the joints and making the dismantling of the EPS difficult. Therefore, finding the amount of the required torque is a compromise between preventing slack in the EPS and prohibiting damage to the joint parts. Stress analysis in this study is performed based on the industrially recommended torque for the EPS type under study. This article reports the study conducted on the stress distribution and the magnitude of stresses exerted to the equipment support when EPS is installed on the machine. To achieve this purpose and to investigate the stress distribution in the joint, both experimental and finite element (FE) methods were used. The experimental results show how much of the applied energy to the EPS in the form of torque is spent to expand the split sleeve and test boss and also to overcome friction. The finite element analysis provides magnitude and distribution of stresses in the EPS components.publishedVersio

On a numerical solution for fuzzy fractional differential equation using an operational matrix method

In the current manuscript we suggest an approach to obtain the solutions of the fuzzy fractional differential equations (FFDEs). We found the operational matrix within the modified Laguerre functions. In this way the investigated equations are turned into a set of algebraic equations. We provide examples to illustrate both accuracy and simplicity of the suggested approach

Numerical study on vibratory extraction of offshore wind turbine monopile foundations under sandy seabed condition

The wind industry has experienced a rapid growth in Europe over the last decades. The early generation turbines were designed for a life of 20–25 years. Decommissioning of offshore wind turbines is becoming more important since many of these installed assets are approaching their end of lifetime. In this study, using vibratory extraction of monopile foundations instead of current practice of cutting them is investigated numerically. Correct estimation of extraction force helps operators to choose suitable vibro-hammer and vessel (or crane-barge), which leads to reduction of decommissioning costs. A Coupled Eulerian-Lagrangian (CEL) approach of ABAQUS/Explicit combined with a modified Mohr-Coulomb (MMC) model are used to find the pile shaft resistance during total removal operation under saturated dense sand condition. The MMC model captures the nonlinear pre-peak hardening and post-peak softening of the dense sand which is not modelled by conventional Mohr-Coulomb model. The VUSDFLD subroutine, which is a user-defined framework, has been used to implement the MMC model into CEL analysis. A parametric study is conducted to analyze how the characteristics of the vibro-hammer, such as its frequency, eccentric moment, and the extraction rate influence the results. The present numerical results show that using proper frequency results in reduction of soil resistance to less than 25% of the initial resistance. However, appropriate hammer with enough eccentric moment and suitable extraction rate, are vital to ensure soil degradation. The results show that the proposed methodology is both robust and straightforward and it has the potential to reduce computational time which is efficient for engineering applications.publishedVersio

Computing the eigenvalues and eigenvectors of a fuzzy matrix

Computation of fuzzy eigenvalues and fuzzy eigenvectors of a fuzzy matrix is a challenging problem. Determining the maximal and minimal symmetric solution can help to find the eigenvalues. So, we try to compute these eigenvalues by determining the maximal and minimal symmetric solution of the fully fuzzy linear system $widetilde{A}widetilde{X}= widetilde{lambda} widetilde{X}.

A fractional multistep method for solving a class of linear fractional differential equations under uncertainty

The objective of this research has been devoted to solve linear fuzzy fractional differential equations (FFDEs) of the Caputo sense. The basic idea is to develop a fractional linear multistep method for solving linear FFDEs under fuzzy fractional generalized differentiability. For safely illustrating the advantages and potential of the presented method, a comparison with the fractional Euler method has to be analyzed in depth. We are interested in using a simple method to obtain gripping results