One of the most important issues in controller design and analysis of a nonlinear system is its degree of Nonlinearity. Helbig et al. proposed a method in which the system, along with a linear reference model (which is the sum of a couple of first order transfer functions), is stimulated with a set of input patterns. The outputs of these systems are then compared and the Nonlinearity measure of the system is obtained as the normalized difference between the outputs of these two systems. In this paper, the linear reference model is replaced with two simpler linear ones. The proposed method has been used for assessment of the Nonlinearity measure of various nonlinear systems that are used as standard benchmarks by the nonlinear process control research community. The results show that, despite the use of this simpler model with less parameters, the calculated Nonlinearity measure is almost similar to the one obtained by Helbig's method. Furthermore, the Nonlinearity measure obtained by the proposed method can be calculated very much faster.

In this paper, the bi-directional evolutionary structural optimization (BESO) method is used to find optimal layouts of 3D prestressed concrete beams. Considering the element sensitivity number as the design variable, the mathematical formulation of topology optimization is developed based on the ABAQUS finite element software package. The surface-to-surface contact with a small sliding between concrete and prestressing steels is assumed to accurately model the prestressing effects. The concrete constitutive model used is the concrete damaged plasticity (CDP) model in ABAQUS. The integration of the optimization algorithm and finite element analysis (FEA) tools is done by using the ABAQUS scripting interface. A pretensioned prestressed simply supported beam is modeled to show capabilities of the proposed method in finding optimal topologies of prestressed concrete beams. Many issues relating to topology optimization of prestressed concrete beams such as the effects of prestressing stress, geometrical discontinuities and height constraints on optimal designs and strut-and-tie models (STMs) are studied in the example. The results show that the proposed method can efficiently be used for layout optimization of prestressed concrete beams.

Because of difficulty in inspection and retrofit of foundation in comparison with other elements, the common design philosophy is to avoid any nonlinear deformation in the foundation. This paper shows that by employing controlled foundation Nonlinearity, in predetermined sections with arrangements for inspection and retrofit, it is possible to reduce seismic demand on superstructure. Localizing nonlinear deformation to pre-specified zones in the foundation, it is possible to avoid wide spread nonlinear deformation across various members in the superstructure in the case of strong ground motions. To evaluate the efficiency of the proposed model, the response of steel braced frames is examined on rigid foundation, rocking elastic foundation and finally on rocking foundation with controlled nonlinear deformation. Results show that while rocking could be used to protect the superstructure elements from possible overloading during large earthquakes for low-rise structures; it has no remarkable effect on the response of high-rise structures. However, the proposed model with Nonlinearity in the foundation could be used in both cases (low-rise and high-rise structures) to effectively control the response of structure.