George Michaelov

An efficient approach for computing residual stresses in welded joints

Although the finite element method has emerged as one of the most attractive approaches for computing residual stresses in welded joints, its application to practical analysis and design problems has been hampered by computational difficulties. These difficulties do not arise in modeling the complex constitutive response of melting and solidifying metal; rather, they occur mostly because of the enormous computational size of any practical problem resulting primarily from the three-dimensional (3D) modeling of a welding process. Although two-dimensional (2D) modeling has been used widely in residual stress problems, current belief holds that 2D analysis cannot render accurate residual stresses that occur due to welding. This study investigates the residual stress fields in a welded T-joint, comparing those computed by 3D models with those computed by 2D models. The study shows that the temperature distribution in the central zone of the joint can be captured successfully by a 2D finite element model and a technique that takes into account the heat transfer balance and welding speed. The residual stresses in the plane of the 2D model computed by this method show fairly good agreement with those computed by the 3D model. More substantial differences are observed in the out-of-plane stresses, which are attributed primarily to the different mechanical boundary conditions in the out-of-plane direction of the 2D and the 3D models. All analyses in this investigation are performed with the finite element code ABAQUS.

Spectral characteristics of nonstationary random processes — a critical review

Abstract This article analyzes the approaches to defining “spectral characteristics” derived from the spectral functions of nonstationary random processes. The processes considered are those for which an evolutionary power spectrum as designated by Priestley can be defined. Two basic approaches to defining spectral characteristics are reviewed. The first, characterized as geometric, leads to Vanmarkes spectral moments, which have proven to be very useful characteristics for stationary processes. However, these moments may be infinite for nonstationary processes, which creates problems for applications. The second approach, viewed as nongeometric, is based on Di Paolas pre-envelope covariances. The advantages and deficiencies of both approaches are discussed. It is also shown that the nongeometric spectral characteristics can be directly defined from the frequency domain as integrals of the one-sided auto- and cross-spectra of the evolutionary process and its derivatives. These nongeometric spectral characteristics are then used in defining parameters that characterize the central frequency and the bandwidth of evolutionary processes. To this end, the probability distributions of the process envelope are analyzed. It is demonstrated that suitable central frequencies and bandwidth factors can be defined from the probability density functions of the derivatives of the envelope and the phase.

Spectral characteristics of nonstationary random processes—response of a simple oscillator

Abstract A nongeometric approach for defining spectral characteristics of evolutionary (nonstationary) processes is applied to the transient stochastic response of a simple oscillator with modulated white noise excitation. The first three nonstationary spectral characteristics of the response are considered. Although the nongeometric spectral characteristics can generally be defined as integrals of the one-sided evolutionary auto- and cross-spectra of the nonstationary process and its derivatives, the study exploits their time-domain definitions as the variances and the covariance of the response and an “auxiliary” process. The approach is applied to three particular excitation functions which have simple analytical forms. Each of these functions has been frequently studied in the past, and/or has potential for use in modeling a variety of practical engineering problems. Approximate expressions for the first three spectral characteristics of the response are developed by neglecting small oscillatory terms. Based on these expressions, approximations are derived for the central frequency and the bandwidth factor of the response.

Fatigue of welded steel joints under wideband loadings

Abstract Fatigue tests were conducted on high-strength welded steel cruciform-shaped specimens subjected to random loadings to investigate the effects of loading intensity, nonnormality and frequency bandwidth on the rate of fatigue damage accumulation. The test result are compared with predictions made using the Rayleigh approximation and rainflow analysis in terms of cycles and times to failure. Results indicate that nonnormality can significantly increase the rate of fatigue damage accumulation and result in nonconservative fatigue life estimates if it is effect is not accounted for properly. Likewise, frequency content was also found to influence the rate of fatigue damage accumulation, but to a lesser extent than nonnormality.

Stochastic fatigue damage accumulation in a T-welded joint accounting for the residual stress fields

Abstract The residual stresses that occur as a result of nonhomogeneous heating and cooling during welding may have a significant effect on the accumulation of fatigue damage in a welded joint. The problem is complicated not because of the complex spatial distribution of the residual stress fields, but because those fields typically change under an applied load. The present study considers the effect of residual stresses on fatigue damage accumulation in a welded joint subjected to stochastic loading. The influence of residual stresses on stochastic fatigue damage accumulation is accounted for by a simple approach based on an elastic–perfectly-plastic material model and the Gerber correction factor. The model assumes that the residual stress remaining at the critical location depends on the largest nominal stress ever endured by a welded joint. The model predicts that the residual stresses during stochastic loading randomly decay to zero. The effect of material yielding is additionally investigated by considering an elastic–plastic material model with linear kinematic hardening. The residual stresses in this case are computed through Monte Carlo simulations. It is demonstrated that the effect of material hardening is to reduce the rate of residual stress decay and thus to accelerate the rate of fatigue damage accumulation.

Vibration control of structures using adjustable slippage elements

Abstract A new method for passive control of structural vibrations is introduced and investigated. The method is based on providing nonlinearity to the stiffness of a structure by installing elements with adjustable slippage in the proper locations. An adjustable slippage element (ASE) is a mechanical link with a two-branch elastic force–displacement response. The slippage threshold, which is the transition point between the two branches, can be adjusted within a relatively broad range, and can thus control the shape of the force–displacement curve of the element. An ASE can be used to rearrange the elastic restoring forces in the structure protected, and can be used separately or in combination with other passive control systems such as conventional damping devices. A structure equipped with such elements may gain enhanced dynamic performance, because the ASE redistributes elastic and plastic deformations, decreases force transmissibility, and improves resonance escape properties. These effects are achieved by separating the characteristic displacement within the ASE device among four prestressed elastic springs. The relative deformation between these elastic springs is controlled by their designed stiffness and also by the level of prestressing. The latter also controls the value of the slippage threshold of the device. The present study investigates the behavior and effectiveness of the proposed elements by considering a single-degree-of-freedom (SDOF) system equipped with an ASE and subjected to harmonic loading and earthquake base excitation.

Fractile levels for non-stationary extreme response of linear structures

A new method is developed for computing fractile levels of non-stationary extreme response of linear structures subjected to stationary, Gaussian white noise. The technique relies on suitable approximation of the integral which gives the number of level crossing by the response process and on simplifications of the second-order response statistics. Two approaches are investigated for obtaining closed form expressions for the fractile levels based on the Poisson approximation of the extreme value distribution. The better of these techniques is then extended to provide fractile levels based on the Vanmarcke approximation of the extreme value distribution. The results from the closed form expressions show very good agreement with corresponding numerical solutions of the non-linear equations for the Poisson and Vanmarcke fractile levels.