Moving Least-squares Technique Research Articles

Bi-iterative moving enhanced model for probability-based transient LCF life prediction of turbine blisk

The low cycle fatigue (LCF) life of aeroengine turbine blisk endures uncertain and transient loads from multi-physical fields, so that it is necessary to evaluate the LCF life for improving the safety of turbine blisk and aeroengine from a probabilistic perspective. In this paper, bi-iterative moving enhanced modeling (BIMEM) approach is developed to conduct the probability-based transient LCF prediction of turbine blisk with fluid-thermal-structural interaction, by integrating extremum thought, Kriging model, moving least squares (MLS) technique and modified particle swarm optimization (MPSO) algorithm. The extremum thought is used to simplify the processes of transient responses of turbine blisk into extremum values in time domain. Both MLS technique and Kriging model are employed to establish the relationship functions between output response and input parameters, for deriving transient reliability sensitivity analysis of turbine blisk LCF life. The MPSO algorithm is applied to find the optimal values of hyperparameters in Kriging model with the effective samples; from the probability-based transient LCF prediction of turbine blisk, it is illustrated that turbine blisk reliability degree is 0.9986, when the allowable value of LCF life is 2968 cycles; and the primary factor affecting turbine blisk LCF life is strength coefficient, followed by gas temperature, fatigue strength exponent, and so forth; the developed BIMEM approach is better in modeling precision and simulation efficiency in the probabilistic-based LCF life prediction, relative to other methods. The efforts of this paper offer a promising way for the health evaluation and prediction of complex structures besides turbine blisk.

Moving least-squares aided finite element method (MLS-FEM): A powerful means to consider simultaneously velocity and pressure discontinuities of multi-phase flow fields

We suggest a strategy to consider discontinuities in the two-phase flow calculations. Our approach comprises enhancing the shape functions of the finite element method (FEM) with the moving least-squares (MLS) interpolation functions. The new shape functions correlate a parameter at any arbitrary point to its surrounding nodes instead of an element's nodes. We name this strategy the "moving least-squares" aided "finite element method" (MLS-FEM).In a previous paper Mostafaiyan et al., we have employed the concept of the MLS-FEM to develop the PMLS (pressure shape function enhanced by the MLS interpolation functions) method, which predicts pressure discontinuities due to the surface tension forces. We take another additional step to consider velocity and pressure discontinuities in a domain with two different fluids. Therefore, we use the MLS technique to enhance the pressure (P) and velocity (V) shape functions. We name this scheme PVMLS (pressure and velocity shape functions enhanced by the MLS technique).We validate the PVMLS method with a stationary drop problem (as a benchmark). We show that the previous PMLS method fails to predict an accurate pressure or smooth streamlines by increasing the Capillary number and deviating from the unit viscosity ratio. However, the PVMLS method provides more accurate results since it considers velocity as a discontinuous parameter. Also, we compare the results of the PVMLS method at very high viscosity ratios (undeformable fluid) with a boundary-fitted single-phase problem. The reported similarities between the predicted pressure values and streamlines in both strategies demonstrate the reliability of the PVMLS method. Finally, we discuss that by employing the PVMLS method to calculate the velocity field, the interface advection will be more mass-conservative.

Moving least-squares aided finite element method (MLS-FEM): A powerful means to predict pressure discontinuities of multi-phase flow fields and reduce spurious currents

A technique based on the finite element method (FEM) is developed to precisely predict the pressure jump due to the surface tension forces in two-phase flow problems. In this method, the FEM shape functions of the active elements (the elements containing both phases) are enhanced by the aid of the moving least-squares (MLS) interpolation functions and used in the FEM calculations. Therefore, this technique is named as moving least-squares aided finite element method (MLS-FEM).The enhanced shape function correlates the value of any unknown parameters (e.g., the velocity, pressure, or stress values) at any arbitrary point inside an active element to its surrounding nodes. When the enhancement is performed only for the pressure (P) shape functions, we briefly name the MLS-FEM as the PMLS method (pressure shape function enhanced by the MLS technique). In this case, it would be possible to predict the pressure discontinuities in a two-phase flow domain.To assess the performance of the PMLS method in the calculation of the velocity components and pressure values in two-phase flow fields, the stationary drop problem is investigated. The results show that by employing the PMLS method, not only the magnitude of the spurious current is significantly reduced but also the pressure jump approaches toward its analytical value, without any pressure fluctuation at the interface. It is also explained that the method can be used to evaluate the extent of the drop deformation in a structured or an unstructured meshing system. Finally, the limitation of the introduced method is discussed, which is the basis for further developments.

A meshless collocation scheme for inverse heat conduction problem in three-dimensional functionally graded materials

This short communication documents the first attempt to apply the generalized finite difference method (GFDM) for inverse heat conduction analysis of functionally graded materials (FGMs). The fact that the GFDM is a meshless collocation method makes it particularly attractive in solving problems with complex geometries and high dimensions. By employing the Taylor series expansion and the moving least-squares technique, the method produces sparse and banded matrix which makes it possible to perform large-scale simulations. Three benchmark examples are provided to demonstrate the accuracy and adaptability of the GFDM approach in solving the inverse Cauchy problems. The convergence and stability of the method with respect to the amount of noise added into the input data are analyzed.

Limit analysis of plates and slabs using a meshless equilibrium formulation

AbstractA meshless Element‐Free Galerkin (EFG) equilibrium formulation is proposed to compute the limit loads which can be sustained by plates and slabs. In the formulation pure moment fields are approximated using a moving least‐squares technique, which means that the resulting fields are smooth over the entire problem domain. There is therefore no need to enforce continuity conditions at interfaces within the problem domain, which would be a key part of a comparable finite element formulation. The collocation method is used to enforce the strong form of the equilibrium equations and a stabilized conforming nodal integration scheme is introduced to eliminate numerical instability problems. The combination of the collocation method and the smoothing technique means that equilibrium only needs to be enforced at the nodes, and stable and accurate solutions can be obtained with minimal computational effort. The von Mises and Nielsen yield criteria which are used in the analysis of plates and slabs, respectively, are enforced by introducing second‐order cone constraints, ensuring that the resulting optimization problem can be solved using efficient interior‐point solvers. Finally, the efficacy of the procedure is demonstrated by applying it to various benchmark plate and slab problems. Copyright © 2010 John Wiley & Sons, Ltd.

Analyzing the interaction between collinear interfacial cracks by an efficient boundary element-free method

A new traction boundary integral equation is presented for analyzing the interaction effect of any number of collinear interface cracks in a two-dimensional bimaterial. The dislocation densities on every crack surface are expressed in the products of the characteristic terms and the weight functions, and the unknown weight functions are approximated using the moving least-squares technique based on the constructed orthogonal basis functions. An efficient numerical integral method is employed to evaluate the Cauchy principal integrals that appear in the meshless method. The boundary element-free method is established, and a series of numerical results is presented. The interaction between the collinear interfacial cracks is analyzed.