International Journal of Computational Engineering Science

Simple engineering analysis based on stress and momentum correspondence principles and the Rayleigh quotient approximation is used to derive error convergence rates and estimates for dynamic beam models based on the Timoshenko beam theory. These predictions are verified by carrying out numerical computations.

Convective heat transport affects the thermal field and drag coefficient in a head-disk assembly significantly. The flow structure and the temperature distribution in ventilated disk passage are being investigated thoroughly in the present work. Two computational methods are used namely: finite volume method (FVM) and finite element method (FEM). Both are based on the Navier–Stokes partial differential equations but with different algorithms and meshes. With different settings of operating conditions on disk, the following important parameters are considered: inlet Reynolds number, rotational speed, shroud clearance and wall temperature. Both co-rotating and counter-rotating disks are also being studied. The former is based on FORTRAN code and the latter on FASTFLO PDE calculator. All the codes are run on a SGI UNIX workstation. It is found that both the Corolis force and centrifugal-buoyancy have important effects on the flow structure and heat transfer due to the rotatinal speed and inlet velocity. Nusselt number decreases along the radius, especially near the disk outer edge. It decreases more rapidly along the radius and the absolute value is much greater for nonventilated disks. The predicted friction coefficients (C_f) are also very different in both cases. For the ventilated case, C_f varies rapidly. While in the nonventilated case, C_f is rather constant when rotational speed (Ω) is low (< 100 rpm). However, when Ω is higher (> 800 rpm), C_f varies appreciably along the radius. Finally, the shroud clearance has the pronunced effects only in the high-Re flow. The results are compared, discussed and their agreement is good.

The bending of a rectangular elastic plate under uniform distributed load and simply supported at the corners by equal-leg angles is studied analytically. The width of the supporting legs can be varied symmetrically about the plate axes giving mixed boundary conditions with supported and free edges. The solution is set up by using the Le'vy–Na'dai approach and the mixed boundary equation at the edges are written in the form of dual series equations. By choosing the proper finite integral transform, the dual series equations can be written as a system of inhomogeneous Fredholm integral equations. The inhomogeneous Fredholm integral equations are reduced to a set of inhomogeneous algebraic simultaneous equations by using Simpson's rule and solved by Picard iteration. The deflection along the middle line of the rectangular plate with various lengths of simple support legs has been calculated.

Performance analysis of a reversible micro-pump system is obtained by numerical simulations. The unsteady incompressible Navier–Stokes equations are solved in a moving micro-pump system using a spectral h/p element algorithm, employing an arbitrary Lagrangian Eulerian (ALE) formulation on structured/unstructured meshes. The performance of the micro-pump is evaluated as a function of the Reynolds number and the geometric parameters. The volumetric flowrate is shown to increase as a function of the Reynolds number. The unsteady traction forces on the pump membrane and the vorticity dynamics within the pump cavity are presented.

A numerical study is performed to investigate unsteady natural convection heat transfer and fluid flow in a cavity under reduced gravity. Consideration is given to the influence of Marangoni convection on the thermal and velocity fields in a two-dimensional square cell. Here, it consists of two opposing vertical side walls held at constant but different temperature with the horizontal lower wall insulated and the upper face treated as nondeformable adiabatic free surface. The fluid temperature gradient in the cavity in the absence of Marangoni force under the reduced gravity is substantially decreased near the hot and cold vertical walls and the dominant heat transfer mechanism switches from convection into conduction, as time progresses. On the contrary, the corresponding flow pattern and isotherms are similar to that under normal gravity condition, resulting in a slight deterioration of the heat transfer performance, if Marangoni force drives the flow in the cavity. Therefore the unsteady natural convection in the system considered is affected by the Marangoni force level.

Comprehensive quasistatic, small deformation finite element analysis and photoelastic studies were made of multiple contact between discs. Two aspects of the work were examined. The first was concerned with the finite element implementation of the variational inequalities approach to treat the general contact problem. Quadratic programming and Lagrange multipliers were used to identify the candidate contact surface and to solve the resulting nonlinear equations. The solution strategy was based upon the use of a two-step algorithm, which guaranteed the accurate imposition of the active kinematic contact constraints and evaluated the contact forces without the use of special contact elements. The second aspect of work was concerned with the application of an enhanced image-processing technique to obtain the stress field resulting from an automated photoelastic rig. A hybrid method was also employed to determine the contact forces between the multiple discs. The results revealed close agreement between experimentally determined contact values and finite element predictions. Furthermore, they indicated load redistribution and load sharing as well as the influence of interfacial friction.

In this paper we present some analytical integration formulae for computing integrals of rational functions of bivariate polynomial numerator with linear and bilinear denominator over a 2-square |ξ| = 1, |η| = 1 in the local parametric space (ξ, η). These integrals arise in finite element formulations of second order partial differential equations of plane and axisymmetric problems in continuum mechanics to computer the components of element stiffness matrices. In case of a rational integrals of n-th degree bivariate polynomial numerator with a linear of bilinear denominator there are exactly rational integrals of monomial numerators with the same linear denominator. By an expansion it is shown that these integrals can be computed in two ways, accordingly we have presented an explicit and a recursive scheme. By use of the recursive scheme such integrals can be computed efficiently with less computational effort whenever (n + 1) integrals of order zero to n in one of the variates are known by explicit integration formulae. Integration formulae from zeroth to octic order are, for clarity and reference summarized in tabular forms. Finally to show the application of the derived formulae three application examples to compute the Prandtl stress function values and the torsional constant k are considered. A computer code based on the present integration scheme to obtain the element stiffness matrices for plane problems is also developed.

This paper describes a new laminated composite plate theory and associated finite element model that allow variable through-the-thickness refinement, as needed, to capture higher-order thickness effects and interlaminar stresses in laminated composite and sandwich panels. The theory and finite element model utilize a new zig-zag sublaminate concept, in which each computational layer (or sublaminate) contains several, even many, physical layers. Within each sublaminate, a high-order zig-zag kinematic assumption is employed, providing very high accuracy, even when the entire laminate is modeled using only a single sublaminate. The accuracy and efficienty of the model are thus adaptable, depending upon the number of sublaminates used. In order to facilitate through-the-thickness refinement, the finite element model is cast in the form of an eight-noded brick-type element, with displacements and rotations as nodal degrees-of-freedom. At interlaminar element boundaries, interlaminar shear traction degrees-of-freedom are also present, so that transverse shear stress continuity can be enforced through the entire thickness of the laminate, irrespective of the thickness discretization chosen. Numerical examples are presented to demonstrate the effectiveness of the current model for the analysis of laminated composite and sandwich panels that are very thick or thin.