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Failure of the materials occurs once the stress intensity factor (SIF) overtakes the material fracture toughness. At this level, the crack will grow rapidly resulting in unstable crack growth until a complete fracture happens. The SIF calculation of the materials can be conducted by experimental, theoretical and numerical techniques. Prediction of SIF is crucial to ensure safety life from the material failure. The aim of the simulation study is to evaluate the accuracy of SIF prediction using finite element analysis.

The bootstrap resampling method is employed in S-version finite element model (S-FEM) to generate the random variables in this simulation analysis. The SIF analysis studies are promoted by bootstrap S-version Finite Element Model (BootstrapS-FEM). Virtual crack closure-integral method (VCCM) is an important concept to compute the energy release rate and SIF. The semielliptical crack shape is applied with different crack shape aspect ratio in this simulation analysis. The BootstrapS-FEM produces the prediction of SIFs for tension model.

The mean of BootstrapS-FEM is calculated from 100 samples by the resampling method. The bounds are computed based on the lower and upper bounds of the hundred samples of BootstrapS-FEM. The prediction of SIFs is validated with Newman–Raju solution and deterministic S-FEM within 95 percent confidence bounds. All possible values of SIF estimation by BootstrapS-FEM are plotted in a graph. The mean of the BootstrapS-FEM is referred to as point estimation. The Newman–Raju solution and deterministic S-FEM values are within the 95 percent confidence bounds. Thus, the BootstrapS-FEM is considered valid for the prediction with less than 6 percent of percentage error.

The bootstrap resampling method is employed in S-FEM to generate the random variables in this simulation analysis.

The multisource uncertainties, including material dispersion, load fluctuation and geometrical tolerance, have crucial effects on fatigue performance of turbine bladed disks. In view of the aim of this paper, it is essential to develop an advanced approach to efficiently quantify their influences and evaluate the fatigue life of turbine bladed disks.

In this study, a novel combined machine learning strategy is performed to fatigue assessment of turbine bladed disks. Proposed model consists of two modeling phases in terms of response surface method (RSM) and support vector regression (SVR), namely RSM-SVR. Two different input sets obtained from basic variables were used as the inputs of RSM, then the predicted results by RSM in first phase is used as inputs of SVR model by using a group data-handling strategy. By this way, the nonlinear flexibility of SVR inputs is improved and RSM-SVR model presents the high-tendency and efficiency characteristics.

The accuracy and tendency of the RSM-SVR model, applied to the fatigue life estimation of turbine bladed disks, are validated. The results indicate that the proposed model is capable of accurately simulating the nonlinear response of turbine bladed disks under multisource uncertainties, and SVR-RSM model provides an accurate prediction strategy compared to RSM and SVR for fatigue analysis of complex structures.

The results indicate that the proposed model is capable of accurately simulate the nonlinear response of turbine bladed disks under multisource uncertainties, and SVR-RSM model provides an accurate prediction compared to RSM and SVRE for fatigue analysis of turbine bladed disk.

To improve the accuracy of parameter prediction for small-sample data, considering the existence of error in samples, the error circle is introduced to analyze original samples.

The influence of surface roughness on fatigue life is discussed. The error circle can treat the original samples and extend the single sample, which reduces the influence of the sample error.

The S-N curve obtained by the error circle method is more reliable; the S-N curve of the Bootstrap method is more reliable than that of the Maximum Likelihood Estimation (MLE) method.

The parameter distribution and characteristics are statistically obtained based on the surface roughness, surface roughness factor and intercept constant. The original sample is studied by an error circle and discussed using the Bootstrap and MLE methods to obtain corresponding S-N curves. It provides a more trustworthy basis for predicting the useful life of products.

Since the most of structures and structural components suffers from cyclic loadings, the study on the fatigue failure due to the crack growth has a great importance. The purpose of this paper is to present a three-dimensional fatigue crack growth simulation of embedded cracks using s-version finite element method (SFEM). Using the numerical results, the validity of the fitness-for-service (FFS) code evaluation method is verified.

In this paper, three-dimensional fatigue crack propagation analysis of embedded cracks is performed using the SFEM. SFEM is a numerical analysis method in which the shape of the structure is represented by a global mesh, and cracks are modeled by local meshes independently. The independent global and local meshes are superimposed to obtain the displacement solution of the problem simultaneously.

The fatigue crack growth of arbitrary shape of cracks is slow compared to that of the simplified circular crack and the crack approximated based on the FFS code of the Japan Society of Mechanical Engineers (JSME). The results tell us that the FFS code of JSME can provide a conservative evaluation of the fatigue crack growth and the residual life time.

This paper presents a three-dimensional fatigue crack growth simulation of embedded cracks using SFEM. Using this method, it is possible to apply mixed mode loads to complex shaped cracks that are closer to realistic conditions.

Mechanical issues related to the information and growth of small cracks are considered to play a major role in very high cycle fatigue (VHCF) for metallic materials. Further efforts on better understanding in early stage of a crack are beneficial to estimating and preventing catastrophic damage for a long period service.

Dependent on the ultrasonic loading system, a novel method of in situ photomicroscope is established to study the crack behaviors in VHCF regime.

This in situ photomicroscope method provides advantages in combination with fatigue damage monitoring at high magnification, a large number of cycles, and efficiency. Visional investigation with attached image proceeding code proves that the method has high resolution on both size and time, which permits reliable accuracy on small crack growth rate. It is observed that the crack propagation trends slower in the overall small crack stage down to the level of 10–11 m/cycle. Strain analysis relays on a real-time recording which is applied by using digital image correlation. Infrared camera recording indicates the method is also suitable for thermodynamic study while growth of damage.

Benefiting from this method, it is more convenient and efficient to study the short crack propagation in VHCF regime.

This article aims to present a direct solution to handle linear constraints in finite element (FE) analysis without penalties or the Lagrange multipliers introduced.

First, the system of linear equations corresponding to the linear constraints is solved for the leading variables in terms of the free variables and the constants. Then, the reduced system of equilibrium equations with respect to the free variables is derived from the finite-dimensional virtual work equation. Finally, the algorithm is designed.

The proposed procedure is promising in three typical cases: (1) to enforce displacement constraints in any direction; (2) to implement local refinements by allowing hanging nodes from element subdivision and (3) to treat non-matching grids of distinct parts of the problem domain. The procedure is general and suitable for 3D non-linear analyses.

The algorithm is fitted only to the Galerkin-based numerical methods.

The proposed procedure does not need Lagrange multipliers or penalties. The tangential stiffness matrix of the reduced system of equilibrium equations reserves positive definiteness and symmetry. Besides, many contemporary Galerkin-based numerical methods need to tackle the enforcement of the essential conditions, whose weak forms reduce to linear constraints. As a result, the proposed procedure is quite promising.

Gives a bibliographical review of the error estimates and adaptive finite element methods from the theoretical as well as the application point of view. The bibliography at the end contains 2,177 references to papers, conference proceedings and theses/dissertations dealing with the subjects that were published in 1990‐2000.

The ability to characterise highly conducting objects, that may also be highly magnetic, by the complex symmetric rank–2 magnetic polarizability tensor (MPT) is important for metal detection applications including discriminating between threat and non-threat objects in security screening, identifying unexploded anti-personnel landmines and ordnance and identifying metals of high commercial value in scrap sorting. Many everyday non-threat items have both a large electrical conductivity and a magnetic behaviour, which, for sufficiently weak fields and the frequencies of interest, can be modelled by a high relative magnetic permeability. This paper aims to discuss the aforementioned idea.

The numerical simulation of the MPT for everyday non-threat highly conducting magnetic objects over a broad range of frequencies is challenging due to the resulting thin skin depths. The authors address this by employing higher order edge finite element discretisations based on unstructured meshes of tetrahedral elements with the addition of thin layers of prismatic elements. Furthermore, computer aided design (CAD) geometrical models of the non-threat and threat object are often not available and, instead, the authors extract the geometrical features of an object from an imaging procedure.

The authors obtain accurate numerical MPT characterisations that are in close agreement with experimental measurements for realistic physical objects. The assessment of uncertainty shows the impact of geometrical and material parameter uncertainties on the computational results.

The authors present novel computations and measurements of MPT characterisations of realistic objects made of magnetic materials. A novel assessment of uncertainty in the numerical predictions of MPT characterisations for uncertain geometry and material parameters is included.

A system for doing finite element computations in parallel is described. It is general purpose in the sense that it can be used across a wide range of finite element applications and in the sense that it is not restricted to any particular parallel hardware. Its performance on computers ranging from clusters of PCs to massively parallel high performance machines is illustrated.

A bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view is given. The bibliography at the end of the paper contains 1,726 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1996‐1999.