A multidomain spectral collocation method for the Stokes problem

A multidomain spectral collocation scheme is proposed for the approximation of the two-dimensional Stokes problem. It is shown that the discrete velocity vector field is exactly divergence-free and we prove error estimates both for the velocity and the pressure

On the optimal design of bodies with material symmetries

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

Parallel algorithms for the capacitance matrix method in domain decompositions

We characterize the capacitance matrix associated with domain decompositions by spectral collocation methods for the solution of elliptic problems. Richardson and conjugate gradient iterations with preconditioners wel suited for computation in a parallel environment are discussed. The spectral properties of the preconditioned capacitance matrix are analyzed, also for the case of substructures with internal vertices. © 1988 Instituto di Elaborazione della Informazione del CNR