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This paper deals with identification of optimal fiber orientations and laminate thicknesses in maximum stiffness and minimum weight design of laminated composite beams. The structural response is evaluated using beam finite elements which correctly account for the influence of the fiber orientation and cross section geometry. The resulting finite element matrices are significantly smaller than those obtained using equivalent finite element models. This modeling approach is therefore an attractive alternative in computationally intensive applications at the conceptual design stage where the focus is on the global structural response. An optimization strategy is presented which aims at enabling the use of fiber angles as continuous design variables albeit the problems may have many local minima. A sequence of closely related problems with an increasing number of design variables is treated. The design found for a problem in the sequence is projected to generate the starting point for the next problem in the sequence. Numerical results are presented for cantilever beams with different geometries and load cases. The results indicate that the devised strategy is well suited for finding optimal fiber orientations and laminate thicknesses in the design of slender laminated composite structures. [ABSTRACT FROM AUTHOR]

This paper presents a multiresolution topology optimization (MTOP) scheme to obtain high resolution designs with relatively low computational cost. We employ three distinct discretization levels for the topology optimization procedure: the displacement mesh (or finite element mesh) to perform the analysis, the design variable mesh to perform the optimization, and the density mesh (or density element mesh) to represent material distribution and compute the stiffness matrices. We employ a coarser discretization for finite elements and finer discretization for both density elements and design variables. A projection scheme is employed to compute the element densities from design variables and control the length scale of the material density. We demonstrate via various two- and three-dimensional numerical examples that the resolution of the design can be significantly improved without refining the finite element mesh. [ABSTRACT FROM AUTHOR]

Abstract  We consider the optimal design of two- (2D) and three-dimensional (3D) flow domains using the lattice Boltzmann method (LBM) as an approximation of Navier-Stokes (NS) flows. The problem is solved by a topology optimization approach varying the effective porosity of a fictitious material. The boundaries of the flow domain are represented by potentially discontinuous material distributions. NS flows are traditionally approximated by finite element and finite volume methods. These schemes, while well established as high-fidelity simulation tools using body-fitted meshes, are effected in their accuracy and robustness when regular meshes with zero-velocity constraints along the surface and in the interior of obstacles are used, as is common in topology optimization. Therefore, we study the potential of the LBM for approximating low Mach number incompressible viscous flows for topology optimization. In the LBM the geometry of flow domains is defined in a discontinuous manner, similar to the approach used in material-based topology optimization. In addition, this non-traditional discretization method features parallel scalability and allows for high-resolution, regular fluid meshes. In this paper, we show how the variation of the porosity can be used in conjunction with the LBM for the optimal design of fluid domains, making the LBM an interesting alternative to NS solvers for topology optimization problems. The potential of our topology optimization approach will be illustrated by 2D and 3D numerical examples. [ABSTRACT FROM AUTHOR]