Singular Integral Equations. By N.I. Muskhelishvili. Translated fromthe 2nd Russian edition by J.R.M. Radok. Pp. 447. F1. 28.50. 1953. (Noordhoff, Groningen)

Mathematica--A System for Doing Mathematics by Computer.

Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates

Composites science and technology

THE appearance of a treatise in English upon the mathematical theory of elasticity is an event the potential importance of which may be judged by the that the author, in his frequent suggestions for collateral reading, refers to only three such, those of Southwell, Timoshenko, and Love. In spirit and content Sokolnikoff}s book differs greatly from each and all of these. It may be described by a possible sub-title: “A pure mathematician surveys topics related to certain problems in the mathematical theory of elasticity”. It is symptomatic of the change in outlook of American mathematics over the past few decades. Mathematical Theory Of Elasticity Prof. I. S. Sokolnikoff with the collaboration of Asst. Prof. R. D. Speche. Pp. xi + 373. (New York and London: McGraw-Hill Book Co., Inc., 1946.) 22s. 6d.

Mathematical Theory Of Elasticity

The influence at micromechanical scale of thermal residual stresses, originating in the cooling down associated to the curing process of fibrous composites, on inter-fibre failure under transverse compression is studied. In particular, the effect of these stresses on the appearance of the first debonds is discussed analytically; later steps of the damage mechanism are analysed by means of a single fibre model, making use of the Boundary Element Method. The results are evaluated applying Interfacial Fracture Mechanics concepts. The conclusions obtained show, at least in the case of dilute fibre packing, the effect of thermal residual stresses on the appearance and initiation of growth to be negligible, and the morphology of the damage not to be significantly affected in comparison with the case in which these stresses are not considered. Experimental tests are carried out, the results agreeing with the conclusions derived from the numerical analysis.

Effect of thermal residual stresses on the matrix failure under transverse compression at micromechanical level – A numerical and experimental study

Micromechanical study on the influence of scale effect in the first stage of damage in composites

Detailed characterization of linear elastic stress states at corners and crack tips requires knowledge of the stress singularity orders, the characteristic angular functions and the generalized stress intensity factors (GSIF). Typically a high accuracy is found in the literature for the evaluation of the stress singularity orders and characteristic angular functions (numerically computed from analytical expressions in most cases). Nevertheless, GSIF values, evaluated by means of a numerical model using FEM or BEM and usually by postprocessing the results, are often reported with a lower level of confidence. A robust procedure is presented in this work for the evaluation of the GSIF at multimaterial corners. The procedure is based on a simple least squares technique involving stresses and/or displacements, computed by BEM, at the neighborhood of the corner tip. A careful verification of the robustness and accuracy of the procedure using a few benchmark problems in the literature has been carried out. Applications of the procedure developed to the evaluation of GSIFs appearing at corners in metal-composite adhesive lap joints are presented.

A least squares procedure for the evaluation of multiple generalized stress intensity factors at 2D multimaterial corners by BEM

A general expression for estimating the location of the first interpenetration point in the open model of interface cracks that, for a fixed reference system, can be directly applied to all material combinations is presented.

On the estimation of the first interpenetration point in the open model of interface cracks

This paper deals with recovery of potential gradient (∇u) in the resolution of the two-dimensional Laplace equation by boundary element method. The emphasis is placed on ∇u-recovery near and on the boundary, where error behaviour and convergence rate are studied in detail. Conventional hypersingular (HS) and strongly singular (SS) boundary integral representations (BIRs) of ∇u are compared with two recovery procedures recently introduced by Mantic, Graciani and Paris, Comput. Methods Appl. Mech. Engrg (1999) 178, pp. 267–289: DSC – a local smoothing procedure, and SSC - applying SS BIR with the integral density obtained previously from DSC. The theoretical analysis of error of ∇u recovered by ∇u-BIRs presented is supported by numerical examples. The numerical study of convergence carried out using an h-refinement of (quasi)uniform meshes of linear boundary elements shows a slow convergence rate, O(h) or less, of HS and SS BIRs in comparison with superconvergence rate O(h2) of DSC (only on the boundary) and SSC near the boundary and at element centres and junctions between elements. A slow convergence rate is obtained by all approximations at boundary corners, SSC clearly providing the most accurate results. Superconvergent results of HS and SS BIRs are only obtained in a particular case of evaluation of tangential derivative of potential on a straight part of the boundary.

Federico París

Papers

Effect of thermal residual stresses on the matrix failure under transverse compression at micromechanical level – A numerical and experimental study

Micromechanical study on the influence of scale effect in the first stage of damage in composites

A least squares procedure for the evaluation of multiple generalized stress intensity factors at 2D multimaterial corners by BEM

On the estimation of the first interpenetration point in the open model of interface cracks

A critical study of hypersingular and strongly singular boundary integral representations of potential gradient