P. Bar-Yoseph

On the accuracy of interlaminar stress calculation in laminated plates

Abstract A new method for analyzing the free edge stress field in composite laminates is developed. This method is based on a composite expansion and assumed stress approach. Laminates of the type [ ± 45/0]s and [ ± 45]s are modeled. A posteriori error estimates for the interlaminar shear stress in an angle-ply laminate are presented.

Space-time spectral element method for solution of second-order hyperbolic equations

Abstract A two-field mixed-hybrid spectral element formulation in time and space is presented. Explicit (STSEE) and implicit (STSEI) algorithms are developed and used to solve a second-order scalar hyperbolic equation. The algorithms were analyzed and their characteristics in terms of truncation error and stability are presented. This analysis was confirmed by numerical results. The improvement in accuracy in comparison with semi-discrete schemes is remarkable.

Interlaminar stress analysis for laminated plates containing a curvilinear hole

Abstract This study presents a variational-perturbation approach for the three-dimensional stress analysis around a curvilinear cutout in composite laminates. The solution is based on a composite expansion and assumed stress finite element methods. Stress field solutions for angleply and cross-ply laminates containing an elliptical hole have been presented. The effects of the ellipse aspect ratio and the fiber orientation on the interlaminar shear stress magnitude have been investigated. A failure criterion based on the interlaminar distortional energy function has been suggested. According to this criterion, it was found that, for angle-ply laminates containing an elliptical hole, a delamination failure initiation occurs at a point along the perpendicular to the direction of loading.

Rectangular hybrid shell element for analysing folded plate structures

Abstract A new rectangular hybrid stress element for analysing folded plate structures is presented. The new four-node element, which is based on the classical hybrid stress method, is called the hybrid coupling element and is generated by a combination of a hybrid plane stress element and a hybrid plate bending element. An invariant equilibrated stress field in each element and an inter-element compatible boundary displacement field are assumed independently in this model. Two additional degrees of freedom at the two nodes which lie along the line of intersection of two planes enable the displacement compatibility. They correspond to the rotation about the local z -axis of the element and are called ‘drilling’ degrees of freedom. The new hybrid finite element system has been used for an investigation of the response of a variety of elastic mountings and has yielded reliable results compared with classical methods. Finally, the advantages of such mountings in engineering design are emphasized.

Adaptive mesh generation based on multi-resolution quadtree representation

An advanced CAD model is required for efficient, real-time adaptive generation of FE meshes. In this paper, a discrete level of detail (LOD) method for reconstructing progressive multiresolution models is proposed. With this approach, the model is reconstructed a priori so that any level of detail can be accessed directly, in real time, according to application requirements. The mesh is generated adaptively according to geometrical or analysis error indicators, where even at lower levels of resolution, critical areas are preserved. The method has been extended to progressive time and geometrical models for simulation and is demonstrated by several examples. Copyright

Mixed-hybrid finite strip method for folded plate structures

Abstract The present work proposed a new mixed-hybrid finite strip formulation for stress analysis of long folded plates combined with rectangular simply supported panels. The formulations evolved coupled in-plane and flexural stresses, while the model for the plate bending followed the Mindlin plate. A comparison with other numerical methods and an exact solution highlight the advantages of the proposed method.

The effect of material non-linearity on the interlaminar stress field in composite laminates

Abstract This paper presents a new approach for interlaminar stress analyses near the free edge. The material non-linear analysis is based on an improved material model which depends on the secant energy function. The stress field solution is obtained by an asymptotic-variational approach in which the solution is composed of interior and edge layer solutions. A first order approximation in the interior region, gives rise to a set of equations which coincides with the classical lamination theory equations using non-linear stress-strain relations. Good correlations with experimental results have been found for single and angle ply laminates. In the edge layer, the solution is based upon a composite expansion and assumed stress finite element methods. The interlaminar stress analysis is based upon a non-linear shear modulus. The solution is found to be in a qualitative agreement with an independent solution. By using the proposed approach one can identify angle ply laminates which are the most sensitive to interlaminar shear failure.

Asymptotic and finite element approximations for heat transfer in rotating compressible flow over an infinite porous disk

Abstract The laminar boundary layer equations for the compressible flow due to the finite difference in rotation and temperature rates are solved for the case of uniform suction through the disk. The effects of viscous dissipation on the incompressible flow are taken into account for any rotation rate, whereas for a compressible fluid they are considered only for a disk rotating in a stationary fluid. For the general case, the governing equations are solved numerically using a standard finite element scheme. Series solutions are developed for those cases where the suction effect is dominant. Based on the above analytical and numerical solutions, a new asymptotic finite element scheme is presented. By using this scheme one can significantly improve the pointwise accuracy of the standard finite element scheme.

Variational asymptotic study of a cylindrical embedded delamination in composites

Abstract New mixed variational analyses of a cylindrical embedded delamination in composite laminated plates are presented. The method of composite expansion, along with the Hellinger-Reissner variational formulation, is employed to derive new finite strip schemes for the interior and edge layer problems. Numerical results for a flat embedded delamination, part-through hole and a through-thickness hole are presented for symmetric and asymmetric plates under membrane or bending loading. Numerical results of the new two-dimensional mixed-hybrid finite strip scheme are presented to show the strips behavior characteristics regarding spectral accuracy, finite element convergence and the satisfaction of equilibrium conditions.

The interdependence of hygrothermal processes and elasto-viscoplastic behavior in polymer-dominated multi-material systems

Abstract An analytical numerical method was developed to predict the time-dependent mechanical behavior of polymer-dominated multi-material systems. The method takes into account the interdependence of stress, strain, moisture diffusion and heat conduction, and it provides stress, strain, moisture and temperature distributions through the system as functions of time, when the external hygrothermal-mechanical conditions are given. In addition it requires the input of empirical stress-strain-time relationships as well as stress-diffusion coupling coefficients. Following experimental evaluation of the necessary coefficients a set of nonlinear coupled differential equations is solved numerically by the finite strip method, which was found to be efficient and accurate for the purpose. The experimental results of the deformation behavior and moisture concentration in an asymmetrical Epoxy-Aluminum model exposed to different hygrothermomechanical histories show a good correlation with analytical prediction.