0000000000148037
AUTHOR
Paolo Vannucci
Modeling of solids
This text is the support for the course of Modeling of Solids, of the Master of Mechanics of the University Paris-Saclay - Curriculum MMM: Mathematical Methods for Mechanics, held at Versailles. The course is the continuation of the course Continuum Mechanics - Solids, and as such it is an introduction, for graduate students, to some typical topics of the theory of solid bodies. The different arguments are dealt with in a simple, succinct way, the objective being to give to students the fundamentals of each argument. Only static problems are considered, being the dynamic of structures dealt with in other courses.
Anisotropy and symmetry for elastic properties of laminates reinforced by balanced fabrics
In this article, we present a theoretical study on elastic properties of laminates composed by balanced fabric layers. Using the polar representation method for plane elastic tensors, we first describe some properties of symmetry of a general laminate composed by balanced fabrics and we write the formulas expressing positions of its axes of symmetry. Then, limiting our study to laminates composed of identical plies, we solve two problems of symmetry of the laminate elastic tensors: uncoupling and quasi-homogeneity. We found all the solutions of the uncoupling problem for the case of 3-, 4- and 5-ply laminate and all those of the quasi-homogeneity problem for the case of 4-, 5- and 6-ply lam…
A Comparative Analysis of Some Theories and Finite Elements for Sandwich Plates and Shells
In this paper we give a comparative analysis of the performance of some theories and finite elements for the calculation of composite sandwich plates and shells
The polar method as a tool for solving inverse problems of the classical laminated plate theory
Publisher Summary Fiber reinforced laminates are widely used in modem applications. For these kinds of structures, the Classical Laminated Plate Theory and its various extensions provide efficient methods for theoretical analysis, that is, when the stacking sequence, the orientations, and the properties of the individual laminas are known. For design of laminates, a very limited number of rules are available. For stiffriess design, two are currently known and used in practical applications: the Werren and Norris rule to get membrane isotropy, and the symmetrical sequence rule to suppress stretching/bending coupling. This chapter deals with the resolution of inverse problems of the Classical…
Complete in-plane elastic characterisation under tensile tests of angle-ply laminates composed of polymer-matrix layers
In this paper we present a new strategy to completely characterise the in-plane elastic properties of a large range of angle-ply laminates using only unidirectional tests. We consider laminates having the same number of identical plies in the α and – α directions. This new method uses some preceding results found by Verchery for orthotropic laminates, namely the conditions of existence of a specific direction ω, in which the shear-extension coupling is null. The characterisation of the laminate is then made using the results of three tensile tests: two in the orthotropy axes, and the third one in the ω direction, in order to have always a pure one-dimensional state of stress. We show that …
Influence of orientation errors on quasi-homogeneity of composite laminates
This paper presents a study on the effects of layer orientation defects on the property of quasi-homogeneity for composite laminates: a measure of the deviation from quasi-homogeneity, introducing the concept of degree of quasi-homogeneity, is proposed. Complete theoretical developments which lead to exact formulae in the case of a single orientation error on a layer of the laminate are showed and the results of a wide numerical analysis in the case of orientation errors randomly distributed on the stacking sequence are also presented. All the theoretical and numerical calculations are developed thanks to the polar method of representation of fourth order tensors introduced by Verchery.
A special class of uncoupled and quasi-homogeneous laminates
Abstract This paper deals with two main problems in laminate design: the search for uncoupled and quasi-homogeneous laminates. Using the polar representation method, the authors show the existence of a particular class of mathematically exact solutions to these two problems. An important feature of these solutions is that they are independent of the orientations of the layers. In fact, these orientations are not fixed by the method, and each solution determines in reality only a stacking sequence, where each layer belongs to a group of plies having the same orientation. The orientations remain undetermined, and it is up to the designer to fix them. In any event, whether the laminate is unco…
A new method for generating fully isotropic laminates
In this paper the authors propose some new kinds of isotropic laminates, made with identical anisotropic layers. In particular, these laminates satisfy some conditions which generalise the well-known Werren and Norris rules, in order to obtain fully isotropy, that is, isotropy of the three tensors A, B and D. To this purpose, the authors utilise some results found in a preceding research, namely the so-called quasi-trivial solutions. The way to form particular isotropic laminates that do not follow the Werren and Norris rule is also indicated. The paper ends with some numerical examples which illustrate the theoretical results found.
Stiffness design of laminates using the polar method
This paper is devoted to the analysis of elastic properties of anisotropic laminas using the so-called polar representation method: this is an effective mathematical tool to analyse two-dimensional elastic problems. By this method, the authors have been able to find a particular class of solutions to some special inverse problems concerning laminates made by anisotropic layers. The properties of these solutions are described and discussed, along with some general results.