Three-dimensional nonlinear finite element analysis of dovetail joints in aeroengine discs

Three-dimensional nonlinear finite element analysis is made of the dovetail region in aeroengine compressor disc assemblies using contact elements. The study is devoted to examining the effect of the critical geometrical features, such as flank length, flank angle, fillet radii and skew angle upon the resulting stress field. Frictional conditions at the interface between the disc and the blade are also examined. The finite element predictions were validated using three-dimensional photoelastic stress freezing results. Comparisons with the two-dimensional finite element analysis made earlier by Papanikos and Meguid (Fatigue Fract. Eng. Mater. Struct. 17 (5) (1994) 539–550) of the same geometry reveal certain inadequacies. Specifically, the earlier analysis underestimates the maximum equivalent stress along the interface by as much as 40%. This could have serious implications concerning the safety margins of the disc assembly.     

Convergence analysis of an upwind finite volume element method with Crouzeix-Raviart element for non-selfadjoint and indefinite problems

In this paper we construct an upwind finite volume element scheme based on the Crouzeix-Raviart nonconforming element for non-selfadjoint elliptic problems. These problems often appear in dealing with flow in porous media. We establish the optimal order H ¹-norm error estimate. We also give the uniform convergence under minimal elliptic regularity assumption      

A two-level additive Schwarz method for the Morley nonconforming element approximation of a nonlinear biharmonic equation

In this paper, we consider the well known Morley nonconformingelement approximation of a nonlinear biharmonic equation whichis related to the well-known two-dimensional Navier–Stokesequations. Firstly, optimal energy and H¹-norm estimates areobtained. Secondly, a two-level additive Schwarz method is presentedfor the discrete nonlinear algebraic system. It is shown thatif the Reynolds number is sufficiently small, the two-levelSchwarz method is optimal, i.e. the convergence rate of theSchwarz method is independent of the mesh size and the numberof subdomains.     

An alternative alpha finite element method with discrete shear gap technique for analysis of laminated composite plates

This paper presents an alternative alpha finite element method using triangular meshes (AαFEM) for static, free vibration and buckling analyses of laminated composite plates. In the AαFEM, an assumed strain field is carefully constructed by combining compatible strains and additional strains with an adjustable parameter α which can produce an effectively softer stiffness formulation compared to the linear triangular element. The stiffness matrices are obtained based on the strain smoothing technique over the smoothing domains and the constant strains on triangular sub-domains associated with the nodes of the elements. The discrete shear gap (DSG) method is incorporated into the AαFEM to eliminate transverse shear locking and an improved triangular element termed as AαDSG3 is proposed. Several numerical examples are then given to demonstrate the effectiveness of the AαDSG3.     

An improved GPS method with a new pseudo-peripheral nodes finder in finite element analysis

Finding pseudo-peripheral nodes with the largest eccentricity is important in matrix bandwidth and profile reduction algorithms in finite element analysis. A heuristic parameter, called the “width-depth ratio” and denoted by κ, is presented for finding the pseudo-peripheral nodes with larger pseudo-diameter compared with the GPS (Gibbs-Poole-Stockmeyer) pseudo-peripheral nodes finder. A novel nodes renumbering algorithm is thus developed by using our nodes finder based on GPS method. Simulations show that proposed nodes finder is reliable and effective in locating the proper pseudo-peripheral nodes with larger pseudo-diameters. A shielded microstrip line is given as an example to testify the ability of the proposed algorithm in application. The results, including time, pseudo-diameter, bandwidths and profiles, all indicate that our method is more competitive than GPS algorithm to be used as the nodes renumbering algorithm.     

Applications of the three dimensional finite element alternating method

This paper describes some recent applications of the three dimensional finite element alternating method (FEAM). The problems solved involve surface flaws in various types of structure. They illustrate how the FEAM can be used to analyze problems involving mechanical and thermal loads, residual stresses, bonded to composite patch repairs, and fatigue.     

Finite element error analysis of a variational multiscale method for the Navier-Stokes equations

The paper presents finite element error estimates of a variational multiscale method (VMS) for the incompressible Navier–Stokes equations. The constants in these estimates do not depend on the Reynolds number but on a reduced Reynolds number or on the mesh size of a coarse mesh. This work is partially supported by NSF grants DMS9972622, DMS20207627 and INT9814115.     

Error estimates of the finite element method for the exterior Helmholtz problem with a modified DtN boundary condition

A priori error estimates in the H¹- and L²-norms are established for the finite element method applied to the exterior Helmholtz problem, with modified Dirichlet-to-Neumann (MDtN) boundary condition. The error estimates include the effect of truncation of the MDtN boundary condition as well as that of discretization of the finite element method. The error estimate in the L²-norm is sharper than that obtained by the author [D. Koyama, Error estimates of the DtN finite element method for the exterior Helmholtz problem, J. Comput. Appl. Math. 200 (1) (2007) 21-31] for the truncated DtN boundary condition.     

The two-grid interpolating element free Galerkin (TG-IEFG) method for solving Rosenau-regularized long wave (RRLW) equation with error analysis

The two-grid method is a technique to solve the linear system of algebraic equations for reducing the computational cost. In this study, the two-grid procedure has been combined with the EFG method for solving nonlinear partial differential equations. The two-grid FEM has been introduced in various forms. The well-known two-grid FEM is a three-step method that has been proposed by Bajpai and Nataraj (Comput. Math. Appl. 2014;68:2277–2291) that the new proposed scheme is an ecient procedure for solving important nonlinear partial differential equations such as Navier–Stokes equation. By applying shape functions of IMLS approximation in the EFG method, a new technique that is called interpolating EFG (IEFG) can be obtained. In the current investigation, we combine the two-grid algorithm with the IEFG method for solving the nonlinear Rosenau-regularized long-wave (RRLW) equation. In other hand, we demonstrate that solutions of steps 1, 2, and 3 exist and are unique and also we achieve an error estimate for them. Moreover, three test problems in one- and two-dimensional cases are given which support accuracy and efficiency of the proposed scheme.     

Finite element dynamic analysis of unsymmetric composite laminated beams with shear effect and rotary inertia under the action of moving loads

The finite element dynamic response of an unsymmetric composite laminated orthotropic beam, subjected to moving loads, has been studied. One-dimensional finite element based on classical lamination theory, first-order shear deformation theory, and higher-order shear deformation theory having 16, 20 and 24 degrees of freedom, respectively, are developed to study the effects of extension, bending, and transverse shear deformation. The theories also account for the Poisson effect, thus, the lateral strains and curvatures can be expressed in terms of the axial and transverse strains and curvatures and the characteristic couplings (bend–stretch, shear–stretch and bend–twist couplings) are not lost. The dynamic response of symmetric cross-ply and unsymmetric angle-ply laminated beams under the action of a moving load have been compared to the results of an isotropic simple beam. The formulation also has been applied to the static and free vibration analysis.     

The determining equations for the nonclassical method of the nonlinear differential equation(s) with arbitrary order can be obtained through the compatibility

In this paper, firstly we show that the determining equations of the (1+1) dimension nonlinear differential equation with arbitrary order for the nonclassical method can be derived by the compatibility between the original equation and the invariant surface condition. Then we generalize this result to the system of the (m+1) dimension differential equations. The nonlinear Klein–Gordon equation, the (2+1)-dimensional Boussinesq equation and the generalized Nizhnik–Novikov–Veselov equation serve as examples illustrating this method.