Search results for "Marsaglia polar method"
showing 5 items of 5 documents
Anisotropy and symmetry for elastic properties of laminates reinforced by balanced fabrics
2001
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…
The polar method as a tool for solving inverse problems of the classical laminated plate theory
2000
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…
Influence of orientation errors on quasi-homogeneity of composite laminates
2003
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
2001
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…
Stiffness design of laminates using the polar method
2001
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.