Design of stiffened panels for stress and buckling via topology optimization

This paper investigates the weight minimization of stiffened panels simultaneously optimizing sizing, layout, and topology under stress and buckling constraints. An effective topology optimization parameterization is presented using multiple level-set functions. Plate elements are employed to model the stiffened panels. The stiffeners are parametrized by implicit level-set functions. The internal topologies of the stiffeners are optimized as well as their layout. A free-form mesh deformation approach is improved to adjust the finite element mesh. Sizing optimization is also included. The thicknesses of the skin and stiffeners are optimized. Bending, shear, and membrane stresses are evaluated at the bottom, middle, and top surfaces of the elements. A p-norm function is used to aggregate these stresses in a single constraint. To solve the optimization problem, a semi-analytical sensitivity analysis is performed, and the optimization algorithm is outlined. Numerical investigations demonstrate and validate the proposed method.

On Some Applications of Kakutani’s Fixed Point Theorem in Game Theory

In this paper, we discuss some major applications of Kakutani’s fixed point theorem in game theory. In the course of research work we mostly use the idea of mathematical set, functions, topological properties and Brouwer’s fixed point theorem to make the Kakutani’s fixed point theorem more conspicuous. In the key point of idea, we include how this theory can play the effective role to highlight new fixed point results and their applications in different fields of game theory.

Quantitative approximation by nonlinear convolution operators of Landau-Choquet type

By using the concept of Choquet nonlinear integral with respect to a monotone set function, we introduce the nonlinear convolution operators of Landau-Choquet type, with respect to a family of submodular set functions. Quantitative approximation results in terms of the modulus of continuity are obtained with respect to some particular possibility measures. For some subclasses of functions we prove that these Landau-Choquet type operators can have essentially better approximation properties than their classical correspondents.