Robustness in Mean-Variance Portfolio Optimization

In this paper, we discuss some of the concepts of robustness for uncertain multi-objective optimization problems. An important factor involved with multi objective optimization problems is uncertainty. The uncertainty may arise fromthe estimation of parameters in the model, error of computation, the structure of a problem, and so on. Indeed, some parameters are often unknown at the beginning of solving a multi-objective optimization problem. One of the mostimportant and popular approaches for dealing with uncertainty is robust optimization. Markowitz's portfolio optimization problem is strongly sensitive to the perturbations of input parameters. We consider Markowitz's portfolio optimization problem with ellipsoid uncertainty set and apply set-based minmax and lower robust efficiency to this problem. The concepts of robust efficiency are used in the real stock market and compared to each other. Finally, the increase and decrease effects of uncertainty set parameters on these robust efficient solutions are verified

A quadtree-polygon-based scaled boundary finite element method for image-based mesoscale fracture modelling in concrete

A quadtree-polygon scaled boundary finite element-based approach for image-based modelling of concrete fracture at the mesoscale is developed. Digital images representing the two-phase mesostructure of concrete, which comprises of coarse aggregates and mortar are either generated using a take-and-place algorithm with a user-defined aggregate volume ratio or obtained from X-ray computed tomography as an input. The digital images are automatically discretised for analysis by applying a balanced quadtree decomposition in combination with a smoothing operation. The scaled boundary finite element method is applied to model the constituents in the concrete mesostructure. A quadtree formulation within the framework of the scaled boundary finite element method is advantageous in that the displacement compatibility between the cells are automatically preserved even in the presence of hanging nodes. Moreover, the geometric flexibility of the scaled boundary finite element method facilitates the use of arbitrary sided polygons, allowing better representation of the aggregate boundaries. The computational burden is significantly reduced as there are only finite number of cell types in a balanced quadtree mesh. The cells in the mesh are connected to each other using cohesive interface elements with appropriate softening laws to model the fracture of the mesostructure. Parametric studies are carried out on concrete specimens subjected to uniaxial tension to investigate the effects of various parameters e.g. aggregate size distribution, porosity and aggregate volume ratio on the fracture of concrete at the meso-scale. Mesoscale fracture of concrete specimens obtained from X-ray computed tomography scans are carried out to demonstrate its feasibility

Application of cellular material in crashworthiness applications: an overview

Cellular foams are a modern class of materials with unique mechanical properties that have wide ranging engineering applications, in the areas of biomedical, acoustic and thermal insulation, and crashworthiness. Recently, foam materials have received increased attention for vehicle crashworthiness due to their lightweight and excellent energy absorption capabilities that allow significant weight reduction without compromising structural safety aspects. Accordingly, this paper reviews the crush and energy absorption behaviour of foam-filled structures that can be used for crashworthy design in transport engineering. In addition, the mechanical and dynamic properties of cellular material and their role on the crashworthiness performance of filled structure are discussed. Particularly, the influences of foam density and interactions, between the foam and the tubes, on the deformation mode of the filled structures are clarified. The advantages offered by the innovative foam material, which contains a density gradient, on the crashworthiness behaviour are also highlighted. Also, a brief summary of optimisation studies involving the use of foam-filled structures are presented. It was found that the cellular materials improve the crashworthiness performance when they are used as filler material in thin-walled energy absorbers due to their capability of altering the deformation mode to a more favourable one

Extending Lattice Discrete Particle Model of Concrete for Non-circular Aggregates

In this paper, Lattice-Discrete Particle Model (LDPM) of concrete has been extended in 2-D to account for the effect of non-circular aggregates. To this end, the flexible equation of super-ellipse is employed for generating aggregates in order to add the simulation possibility of a greater spectrum of aggregate samples in 2-D to lattice-Discrete particle Model. Alongside this extention, required procedures for the generation of aggregates, their packing in space, the determination of influencing region of each particle, the definition of interacting surfaces and computational points and the definition of strains are outlined. Finally, the effects of aggregates geometry on macro-scale compressive strength and softening curve and also cracking pattern of concrete under uniaxial compression are discussed