The field of nonlinear optics has developed rapidly since its beginning in 1961. This development is in both the theory of nonlinear effects and the theory of nonlinear interactions in solids, and in the applications of nonlinear devices. This review discusses nonlinear interactions in solids and the resultant nonlinear coupling of electromagnetic waves that leads to second harmonic generation,...

This paper develops repetitive and iterative learning control design and analysis for back stepping controlled nonlinear systems. To precisely track periodic or finite duration trajectories for nonlinear systems, back stepping control is first designed to render closed loop stability and, in theory, asymptotic tracking performance. However, due to the sensitivity to the unmodelled dynamics plan...

nonlinear analyses allow simulating, in a more realistic way, the behaviour of structuressubjected to several types of complex loading conditions such as earthquakes. however, it isrecognized that these analyses normally generate a considerable amount of results, a factorthat difficult its interpretation. over the last years, considerable progresses have been made instructural nonlinear behavio...

In the context of nonlinear finite element (FE) method, this paper presents a computational framework for ‘exact’ response sensitivity analysis of soil-structural interaction (SSI) systems based on the direct differentiation method (DDM). The DDM requires analytically differentiating the FE algorithm for the response computation with respect to material, geometry or loading parameters, involvin...

Solution capabilities for twoand three-dimensional nonlinear finite element analysis of concrete structures are presented. The concrete material is modeled including the triaxial nonlinear stress-strain behavior, tensile cracking, axon-stiff~~g, compression crushing and str~n-sof~ng. The results of various sample analyses are given to demonstrate the constitutive model and the solution strategi...

For this purpose a finite element model specifically developed for the nonlinear analysis of steel-concrete composite beams is adopted. This finite element model includes material nonlinearity of slab concrete, reinforcement steel, beam steel as well as slabbeam nonlinear partial interaction due to the deformable shear connection. The inclusion of the partial interaction in the composite beam m...

Within the context of the Maxwell Garnett model, we calculate the nonlinear susceptibility of a composite optical material comprised of spherical inclusion particles contained within a host material. We allow both constituents to respond nonlinearly and to exhibit linear absorption. Our treatment takes complete account of the tensor nature of the nonlinear interaction, under the assumption that...