Effective elastic properties of two -dimensional solids with inhomogeneities of irregular shapes

This work investigates the effective elastic properties of two-dimensional solids with inhomogeneities of various shapes. We develop a special procedure to evaluate the contribution of irregularly shaped inhomogeneities to these properties. The method can also be used to investigate the stress concentrations around the inhomogeneities. The procedure is based on the analysis of a representative volume element. We express the contribution of each inhomogeneity to the overall moduli of the composite in terms of the compliance contribution tensor. To calculate the components of this tensor, we devise a method that combines analytical and numerical approaches: Kolosov-Muskhelishvili complex variable technique and numerical conformal mapping. Application of this method to regularly shaped elastic inclusions, holes and rigid inclusions produces results that correspond well with the available analytical predictions. In the case of holes, the applicability of the finite element method is also investigated. The expressions for the effective elastic properties are first derived in the approximation of non-interacting inhomogeneities. Then the results for interacting inhomogeneities incorporating the first order approximate schemes are presented. To demonstrate the application of the method, we analyze a carbon fiber reinforced composite containing pores of irregular shapes. A two-step micromechanical procedure utilizing the concept of the compliance contribution tensor is used. We derive the closed form formulae for the contribution of fibers into the effective moduli and apply the procedure to determine the effective in-situ properties of pyrolytic carbon---a matrix phase formed during a densification process by chemical vapor infiltration

3-DIMENSIONAL GEOMETRIC SURVEY AND STRUCTURAL MODELLING OF THE DOME OF PISA CATHEDRAL

This paper aims to illustrate the preliminary results of a research project on the dome of Pisa Cathedral (Italy). The final objective of the present research is to achieve a deep understanding of the structural behaviour of the dome, through a detailed knowledge of its geometry and constituent materials, and by taking into account historical and architectural aspects as well. A reliable survey of the dome is the essential starting point for any further investigation and adequate structural modelling. Examination of the status quo on the surveys of the Cathedral dome shows that a detailed survey suitable for structural analysis is in fact lacking. For this reason, high-density and high-precision surveys have been planned, by considering that a different survey output is needed, according both to the type of structural model chosen and purposes to be achieved. Thus, both range-based (laser scanning) and image-based (3D Photogrammetry) survey methodologies have been used. This contribution introduces the first results concerning the shape of the dome derived from surveys. Furthermore, a comparison is made between such survey outputs and those available in the literature

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

Review of discontinuous Galerkin finite element methods for partial differential equations on complicated domains

The numerical approximation of partial differential equations (PDEs) posed on complicated geometries, which include a large number of small geometrical features or microstructures, represents a challenging computational problem. Indeed, the use of standard mesh generators, employing simplices or tensor product elements, for example, naturally leads to very fine finite element meshes, and hence the computational effort required to numerically approximate the underlying PDE problem may be prohibitively expensive. As an alternative approach, in this article we present a review of composite/agglomerated discontinuous Galerkin finite element methods (DGFEMs) which employ general polytopic elements. Here, the elements are typically constructed as the union of standard element shapes; in this way, the minimal dimension of the underlying composite finite element space is independent of the number of geometrical features. In particular, we provide an overview of hp-version inverse estimates and approximation results for general polytopic elements, which are sharp with respect to element facet degeneration. On the basis of these results, a priori error bounds for the hp-DGFEM approximation of both second-order elliptic and first-order hyperbolic PDEs will be derived. Finally, we present numerical experiments which highlight the practical application of DGFEMs on meshes consisting of general polytopic elements