Development of an unsteady aerodynamic analysis for finite-deflection subsonic cascades

An unsteady potential flow analysis, which accounts for the effects of blade geometry and steady turning, was developed to predict aerodynamic forces and moments associated with free vibration or flutter phenomena in the fan, compressor, or turbine stages of modern jet engines. Based on the assumption of small amplitude blade motions, the unsteady flow is governed by linear equations with variable coefficients which depend on the underlying steady low. These equations were approximated using difference expressions determined from an implicit least squares development and applicable on arbitrary grids. The resulting linear system of algebraic equations is block tridiagonal, which permits an efficient, direct (i.e., noniterative) solution. The solution procedure was extended to treat blades with rounded or blunt edges at incidence relative to the inlet flow

On a Lamb-type problem for a bi-axially pre-stressed incompressible elastic plate

This is a pre-copy-editing, author-produced PDF of an article accepted for publication in IMA Journal of Applied Mathematics following peer review. The definitive publisher authenticated version J. D. KAPLUNOV AND A. V. PICHUGIN (2006). On a Lamb-type problem for a bi-axially pre-stressed incompressible, IMA Journal of Applied Mathematics. 71, 171−185. OUP, is available online at: http://dx.doi.org/10.1093/imamat/hxh097The far-field response of a bi-axially pre-stressed incompressible elastic plate, subjected to an instantaneous edge impulse loading, is studied using a refined long-wave low-frequency theory. The second-order correction introduced by the refined theory is demonstrated to smooth the discontinuity associated with one of the wave-fronts predicted by the leading order hyperbolic theory. The character of the so-called quasi-front is shown to depend greatly on both the material parameters and the pre-stress and may be either classical receding or advancing. Additionally, and in contrast to the analogous problem in linear isotropic elasticity, in a pre-stressed plate the dilatational quasi-front may propagate slower than the shear wave-front. This situation is demonstrated to lead to the formation of a head-wave quasi-front

A parametric study on the buckling of functionally graded material plates with internal discontinuities using the partition of unity method

In this paper, the effect of local defects, viz., cracks and cutouts on the buckling behaviour of functionally graded material plates subjected to mechanical and thermal load is numerically studied. The internal discontinuities, viz., cracks and cutouts are represented independent of the mesh within the framework of the extended finite element method and an enriched shear flexible 4-noded quadrilateral element is used for the spatial discretization. The properties are assumed to vary only in the thickness direction and the effective properties are estimated using the Mori-Tanaka homogenization scheme. The plate kinematics is based on the first order shear deformation theory. The influence of various parameters, viz., the crack length and its location, the cutout radius and its position, the plate aspect ratio and the plate thickness on the critical buckling load is studied. The effect of various boundary conditions is also studied. The numerical results obtained reveal that the critical buckling load decreases with increase in the crack length, the cutout radius and the material gradient index. This is attributed to the degradation in the stiffness either due to the presence of local defects or due to the change in the material composition.Comment: arXiv admin note: text overlap with arXiv:1301.2003, arXiv:1107.390

On the approximation in the smoothed finite element method (SFEM)

This letter aims at resolving the issues raised in the recent short communication [1] and answered by [2] by proposing a systematic approximation scheme based on non-mapped shape functions, which both allows to fully exploit the unique advantages of the smoothed finite element method (SFEM) [3, 4, 5, 6, 7, 8, 9] and resolve the existence, linearity and positivity deficiencies pointed out in [1]. We show that Wachspress interpolants [10] computed in the physical coordinate system are very well suited to the SFEM, especially when elements are heavily distorted (obtuse interior angles). The proposed approximation leads to results which are almost identical to those of the SFEM initially proposed in [3]. These results that the proposed approximation scheme forms a strong and rigorous basis for construction of smoothed finite element methods.Comment: 14 pages, 9 figures, 1 table; International Journal for Numerical Methods in Engineering, 201

Hierarchic plate and shell models based on p-extension

Formulations of finite element models for beams, arches, plates and shells based on the principle of virtual work was studied. The focus is on computer implementation of hierarchic sequences of finite element models suitable for numerical solution of a large variety of practical problems which may concurrently contain thin and thick plates and shells, stiffeners, and regions where three dimensional representation is required. The approximate solutions corresponding to the hierarchic sequence of models converge to the exact solution of the fully three dimensional model. The stopping criterion is based on: (1) estimation of the relative error in energy norm; (2) equilibrium tests, and (3) observation of the convergence of quantities of interest

A parametric study on creep-fatigue strength of welded joints using the linear matching method

This paper presents a parametric study on creep-fatigue strength of the steel AISI type 316N(L) weldments of types 1 and 2 according to R5 Vol. 2/3 Procedure classification at 550◦C. The study is implemented using the Linear Matching Method (LMM) and is based upon a latest developed creep-fatigue evaluation procedure considering time fraction rule for creep-damage assessment. Parametric models of geometry and FE-meshes for both types of weldments are developed in this way, which allows variation of parameters governing shape of the weld profile and loading conditions. Five configurations, characterised by individual sets of parameters, and presenting different fabrication cases, are proposed. For each configuration, the total number of cycles to failure N⋆ in creep-fatigue conditions is assessed numerically for different loading cases including normalised bending moment M and dwell period t. The obtained set of N⋆ is extrapolated by the analytic function, which is dependent on M, t and geometrical parameters (α and β). Proposed function for N⋆ shows good agreement with numerical results obtained by the LMM. Thus, it is used for the identification of Fatigue Strength Reduction Factors (FSRFs) intended for design purposes and dependent on t, α, β