Aggressive submodelling of stress concentrations

For some finite element analyses of stresses in engineering components, low‐order elements can be preferred. This choice, however, results in slow convergence, especially at key stress concentrations. To overcome this difficulty, submodelling of stress concentrators can be employed. With submodelling, a subregion within the original global configuration and centred on the stress concentrator of interest is analysed by itself, with a consequent reduction in computation. The more aggressive the submodelling, the smaller the subregion and the greater the computational savings. To realize such savings in actuality, it is necessary that appropriate boundary conditions be applied to the subregion. Some of these boundary conditions must be drawn from a global analysis of the original configuration: then it is essential to ensure that such boundary conditions are determined sufficiently accurately. This paper describes a procedure for being reasonably certain that such is the case. The procedure is evaluated on a series of test problems and demonstrated on a contact application. Results show that good engineering estimates of peak stresses can be obtained even in regions of unusually high stress gradients. Furthermore, these estimates can be obtained in return for quite moderate levels of computational effort. Copyright © 1999 John Wiley & Sons, Ltd.     

GENERALIZED LAMINATE THEORIES BASED ON DOUBLE SUPERPOSITION HYPOTHESIS

There was a tremendous advantage of using the generalized co-ordinate system to express various types of laminate theories. With two layer-dependent terms of both the zeroth- and the first-order of thickness co-ordinate, a generalized zigzag theory was presented in a previous study. Due to its success in laminate analysis, the feasibility of assigning the two high-order terms, i.e. the second- and the third-order terms, of the generalized zigzag theory as layer-dependent variables was of primary interest. It was found that a so-called global–local superposition technique could be used for expressing the laminate theories in an explicit manner, namely recursive equations, to retain the advantage of numerical efficiency. Based on the superposition technique, the fundamental roles of the individual terms are identified. It is concluded that not only the completeness of the terms, but also the inclusion of as many terms as possible, is important to a laminate theory. It then is the goal of this study to look into a laminate theory which can satisfy the requirement of completeness and include all the first-, second- and third-order terms in an assumed displacement field. A special technique, namely hypothesis for double superposition, is presented to achieve the goal. The feasibility of the hypothesis is demonstrated in this study. Although not verified mathematically, the hypothesis seems to be capable of giving accurate and efficient laminate theories. © 1997 by John Wiley & Sons, Ltd.     

Refined global–local higher-order theory for angle-ply laminated plates under thermo-mechanical loads and finite element model

To analyze angle-ply laminated composite and sandwich plates coupled bending and extension under thermo-mechanical loading, a refined global–local higher-order theory considering transverse normal strain is presented in this work. Hitherto, present theory for angle-ply laminates has never been reported in the literature, and this theory can satisfy continuity of transverse shear stresses at interfaces. In addition, the number of unknowns in present model is independent of layer numbers of the laminate. Based on this theory as well as methodology of the refined triangular discrete Kirchhoff plate element, a triangular laminated plate element satisfying the requirement of C¹ continuity is presented. Numerical results show that the present refined theory can accurately analyze the bending problems of angle-ply composite and sandwich plates as well as thermal expansion problem of cross-ply plates, and the present refined theory is obviously superior to the existing global–local higher-order theory proposed by Li and Liu [Li XY, Liu D. Generalized laminate theories based on double superposition hypothesis. Int J Numer Meth Eng 1997;40:1197–212]. After ascertaining the accuracy of present model, the distributions of displacements and stresses for angle-ply laminated plates under temperature loads are also given in present work. These results can serve as a reference for future investigations.     

VARIABLE KINEMATIC MODELLING OF LAMINATED COMPOSITE PLATES

A displacement-based variable kinematic global–local finite element model is developed using hierarchical, multiple assumed displacement fields at two different levels: (1) at the element level, and (2) at the mesh level. The displacement field hierarchy contains both a conventional plate expansion (2-D) and a full layerwise (3-D) expansion. Depending on the accuracy desired, the variable kinematic element can use various terms from the composite displacement field, thus creating a hierarchy of different elements having a wide range of kinematic complexity and representing a number of different mathematical models. The VKFE is then combined with the mesh superposition technique to further increase the computational efficiency and robustness of the computational algorithm. These models are used to analyse a number of laminated composite plate problems that contain localized subregions where significant 3-D stress fields exist (e.g. free-edge effects).