Probabilistic Elastic-plastic Fracture Mechanics Analysis of Propagation of Cracks in Pipes under Internal Pressure

This study presents a three dimensional finite element method analysis of semi-elliptical surface cracks in pipes under internal pressure load. In the elastic–plastic case, estimates of the J-integral are presented for various ratios including crack depth to pipe thickness (a/t) and strain hardening index in the (R-O) Ramberg-Osgood (n).  Finally, failure probability is accessed by a statistical analysis for uncertainties in loads and material properties, and structural reliability and crack size. The Monte Carlo method is used to predict the distribution function of the mechanical response. According to the obtained results, we note that the stress variation and the crack size are important factors influencing on the distribution function of (J/Je)

Vibration Analysis of Viscoelastic FGM Nanoscale Plate Resting on Viscoelastic Medium Using Higher-order Theory

The present article aims essentially to present an analytical and numerical method which makes it possible to study the damped vibrations of viscoelastic FGM nanoplates resting on viscoelastic foundations. A new model for the higher-order shear deformation plate theory is coupled with the internal Kelvin - Voigt viscoelastic model and the three-parameter viscoelastic foundation model for the purpose of reducing and minimizing the vibration response of the system. It is widely admitted that the mechanical properties of these new functionally gradient materials (FGMs) vary according to the thickness of the plate and depend on its volume fraction. The use of FGM plates seems to be an ideal solution for the study of free vibrations because of their multifunctionality that is fully integrated with the nonlocal Eringen effect. The dynamic response of such a complex system has been investigated by varying the aspect ratio of the plate, the mechanical characteristics of the material used, the internal and external damping and the foundation rigidity. The results obtained, with and without the nonlocal effect, were compared with those of different models of higher-order theories and under various boundary conditions; they were found to be in good agreement with those reported in the literature

(R1899) Asymptotic Normality of the Conditional Hazard Function in the Local Linear Estimation Under Functional Mixing Data

In this study, we are interested in using the local linear technique to estimate the conditional hazard function for functional dependent data where the scalar response is conditioned by a functional random variable. The asymptotic normality of this constructed estimator is demonstrated under some extreme conditions. Our estimator’s performance is demonstrated through simulations

Buckling of composite non local or gradient connected beams

International audienceThe buckling of an axially loaded elastic composite beam with a nonlocal core or a nonlocal connection system is studied in this paper. The composite beam or the sandwich beam is composed of two Euler–Bernoulli beams with a nonlocal elastic interaction. This nonlocal interaction is physically based on the Reissner's model based on three-parameters' interaction function. The energy equations are first presented, and the differential equations are rigorously obtained from a variational principle. We show that the connection model can be expressed in an integral format, therefore, inducing the nonlocal character of this beam elastic interaction model. Furthermore, the variational format of this nonlocal composite model is given, leading to meaningful natural and higher-order boundary conditions. The system of these differential equations can be reduced to a single 10th-order differential equation. We present an exact method to solve this stability problem, based on Ferrari or Cardano's method. The solution can be fully simplified in case of specific boundary conditions with symmetrical considerations. The stability domain is analytically characterized in the loading space for the pinned–pinned boundary conditions. The correspondence between the buckling of the nonlocal composite column and the shear composite column is discussed. Finally, it is shown that the Timoshenko beam model is a nonlocal integral model

Nonparametric Estimation of the Conditional Distribution Function For Surrogate Data by the Regression Model

The main objective of this paper is to estimate the conditional cumulative distribution using the nonparametric kernel method for a surrogated scalar response variable given a functional random one. We introduce the new kernel type estimator for the conditional cumulative distribution function (cond-cdf) of this kind of data. Afterward, we estimate the quantile by inverting this estimated cond-cdf and state the asymptotic properties. The uniform almost complete convergence (with rate) of the kernel estimate of this model and the quantile estimator is established. Finally, a simulation study completed to show how our methodology can be adopted

Numerical prediction of the ductile damage for axial cracks in pipe under internal pressure

This study presents a numerical prediction of the ductile damage for axial cracks in pipe subjected to internal pressure. The three dimensional finite element methods used to evaluate the J-integral. The effect of the external radius (Rext),the thickness (t), length crack (a) , the applied loads (P) and the crack position of the pipes has studied. The Monte Carlo method was used to determine the probabilistic characteristics of the J-integral. It’s also used later to predict the failure probability based on initiation of the crack growth. We note that the crack size and the geometries of the pipe are an important factor influencing on the durability of the pipe

Analysis of the crack-crack interaction effect initiated in aeronautical structures and repaired by composite patch

In this work, we analyze three - dimensionally, by the finite element method, the performance of the repair of aeronautical structures damaged by cracking and repaired by patch of composite materials. The effect of crack-crack interaction according to their position and interdistance was analyzed. The criterion of rupture retained for this study is the factor of intensity of constraints. We show that this factor increases considerably and reaches a critical threshold when the two cracks develop towards each other. The repair of such damage using a composite patch ensures the stability of this structure during the commissioning process. The sharp fall in the stress intensity factor is characteristic of this stability