The paper is concerned with the optimal design of two dimensional, in-plane loaded structural elements and three dimensional bodies, made of aleotropic materials, with regard to both the elastic and the ultimate behaviour. Sec. 2 is devoted to finding the local orientations of the material symmetry axes in 3D orthotropic solids, corresponding to extreme values of the global elastic stiffness. These orientations are shown to be such that collinearity of principal stress and principal strains is achieved throughout the body. In the particular case of transversely isotropic or cubic materials, optimal orientations are shown to depend both on a material parameter and the strain field. A certain orientation of the material symmetry axes may correspond either to a minimum or to a maximum in the elastic stiffness, depending on whether the material has ‘high’ or ‘low shear modulus’. These results are then specialized to plane orthotropic bodies, in which case the theoretical findings obtained by other authors are recovered. In the plane case, also simultaneous optimization of fiber orientation and density is dealt with. Sec. 3 concerns optimal limit design of plastic 2D in-plane loaded orthotropic structures. Fiber orientation and density are assumed as design variables. Here again, necessary optimality conditions are analytically found and their mechanical interpretation is studied. Analogies with both the numerical results of other authors and the elastic case are observed and discussed as well.
On the optimal design of bodies with material symmetries
TALIERCIO, ALBERTO
1994-01-01
Abstract
The paper is concerned with the optimal design of two dimensional, in-plane loaded structural elements and three dimensional bodies, made of aleotropic materials, with regard to both the elastic and the ultimate behaviour. Sec. 2 is devoted to finding the local orientations of the material symmetry axes in 3D orthotropic solids, corresponding to extreme values of the global elastic stiffness. These orientations are shown to be such that collinearity of principal stress and principal strains is achieved throughout the body. In the particular case of transversely isotropic or cubic materials, optimal orientations are shown to depend both on a material parameter and the strain field. A certain orientation of the material symmetry axes may correspond either to a minimum or to a maximum in the elastic stiffness, depending on whether the material has ‘high’ or ‘low shear modulus’. These results are then specialized to plane orthotropic bodies, in which case the theoretical findings obtained by other authors are recovered. In the plane case, also simultaneous optimization of fiber orientation and density is dealt with. Sec. 3 concerns optimal limit design of plastic 2D in-plane loaded orthotropic structures. Fiber orientation and density are assumed as design variables. Here again, necessary optimality conditions are analytically found and their mechanical interpretation is studied. Analogies with both the numerical results of other authors and the elastic case are observed and discussed as well.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
