Various Equivalent Nonlinear Static Analysis procedures have recently been introduced for seismic assessment of tall buildings. Here, iterative linear Equivalent method is proposed for seismic Analysis of concrete dams. Regarding important differences between the behavior of concrete dams and high-rise buildings, basic concepts and main steps of this Analysis technique are developed to make it applicable for this kind of structures. In comparison with well-known push-over Analysis, independency of the results from the lateral load pattern is one of the main advantages of this method. Other important achievements contain: estimating structure's damping and considering the interaction between water, structure and foundation. The proposed method is implemented and verified for Pine Flat dam which shows acceptable results.

Nonlinear Static procedure (NSP) is a common technique to predict seismic demands on various building structures by subjecting a monotonically increasing horizontal loading (pushover) to the structure. Therefore, the pushover Analysis is an important part of each NSP. Accordingly, the current paper aims at investigating the efficiency of various algorithms of lateral load patterns applied to the structure in NSPs. In recent years, fundamental advances have been made in the NSPs to enhance the response of NSPs toward Nonlinear time history Analysis (NTHA). Among the NSPs, the philosophy of "Adaptive procedures" has been focused by many researchers. In the case of utilizing Adaptive procedures, the use of incremental force vector considering the effects of higher modes of vibration and stiffness deteriorations is possible and seems that it can lead to a good prediction of seismic response of structures. In this study, a new Adaptive procedure called energy-based Adaptive pushover Analysis (EAPA) is implemented based on the work done by modal forces in each level of the structure during the Analysis and is examined for steel moment resisting frames (SMRFs). EAPA is inspired by force-based Adaptive pushover (FAP) and story shear-based Adaptive pushover (SSAP). FAP has applied modal forces directly into load patterns; SSAP, on the other hand, has implemented the energy method in system`s capacity curve for measuring the Equivalent movement. EAPA has enforced the concept of energy directly in load pattern; so that by using the modal forces-movements an energy-based Adaptive algorithm is obtained. Hence, the effects of higher modes, deterioration in stiffness and strength, and characteristics of a specific site are incorporated and reflected in applied forces on the structure. Results obtained from the method proposed a desirable accordance with the extracted results from NTHA over the height of the structure.

Progressive collapse studies generally assess the performance of the structure under gravity and blast loads, while earthquakes may also lead to the progressive collapse of a damaged structure. In this study, the progressive collapse response of concentrically braced dual systems with steel moment-resisting frames was assessed under seismic loads through pushover Analysis using triangular and uniform lateral load patterns. Two different bracing types (X and inverted V braces) were considered, and their performances were compared under different lateral load patterns using the Nonlinear Static alternate path method recommended in the Unified Facilities Criteria (UFC) guideline. Eventually, the seismic progressive collapse resistance of models was compared to their progressive collapse response under gravity loads. These studies showed that models under the seismic progressive collapse loads satisfied UFC acceptance criteria and limited rehabilitation objective. The structures had better performance under seismic progressive collapse than models under gravity loads because of more resistance, ductility, suitable load redistribution, and more structural elements that participated in load redistribution. Furthermore, despite studies on progressive collapse under gravity loads, the dual system with X braces showed better progressive collapse performance (more resistance, residual reserve strength ratio and ductility) under seismic loads than the model with inverted V braces.

Friction is a Nonlinear phenomenon which has destructive effects on performance of control systems. To obviate these effects, friction compensation is an effectual solution. In this paper, an Adaptive technique is proposed in order to eliminate limit cycles as one of the undesired behaviors due to presence of friction in control systems which happen frequently. The proposed approach works for Nonlinear dynamic and Static friction models and is applicable to a wide range of different mechanical systems. It is also applied to a simple inverted pendulum on a cart as a highly Nonlinear under-actuated system. A Nonlinear optimal controller based on the approximate solution of Hamilton-Jacobi-Bellman partial differential equation is designed to fulfill our control objectives and achieve preferable performance compared to those of the linear optimal controllers. It causes to have more accuracy in system's response and positioning in the presence of friction. Simulation result approve the effectiveness of both the presented technique and controller.

In recent years some multi-mode pushover procedures taking into account higher mode effects, have been proposed. The responses of considered modes are combined by the quadratic combination rules, while using the elastic modal combination rules in the inelastic phases is not valid. Here, an optimum weighted mode combination method for Nonlinear Static Analysis is presented. Genetic algorithm is used for optimization of the modal weight. The proposed procedure is applied for a sample building. The results show that the resulted response from the proposed method has minimal error in comparison with the response of the Nonlinear time history Analysis.

This investigation presents material Nonlinear Analysis of a cantilever bar element made of functionally graded material with porosity properties. The material properties of bar element are considered as changing though axial direction based on the Power-Law distribution and uniform porosity distribution. The stress-strain relation of the material is considered as a Nonlinear property according to a Power-Law function. The cantilever bar element is subjected to a point load at the free end. In order to obtain more realistic solution for the Nonlinear problem and axially material distribution, Nonlinear finite element method is used. In the obtaining of finite element equations, the virtual work principle is used and, after linearization step, the tangent stiffness matrix and residual vector are obtained. In the Nonlinear solution process, the incremental force method is implemented and, each load step, the Nonlinear equations are solved by using the Newton-Raphson iteration method. In the numerical results, effects of material Nonlinearity parameters, porosity coefficients, material distribution parameter and aspect ratios on Nonlinear Static deflections of the bar are presented and discussed. The obtained results show that the material Nonlinear behaviour of the bar element is considerably affected with porosity and material graduation.

This paper presents a force (flexibility) based formulation for Nonlinear Static Analysis of reinforced concrete plane frames. Nonlinear behavior of concrete and steel fibers based on a simple one-dimensional constitutive law is considered. Navier- Bernoulli theory is accepted in different sections and the effect of bond-slip is, thus, neglected. The section flexibility and stiffness matrices are extracted by direct integration of tangential modulus of materials all over the sections. Flexibility, stiffness and residual force vector of elements are estimated, using principle of virtual work and based on a force (flexibility) formulation. An iterative algorithm used to satisfy the proposed convergence criterion. Presented samples show accuracy and efficiency of the proposed method in contrast to other existing numerical and experimental results.    

This paper addresses the semi-analytical modeling and stability Analysis of coupled slosh-tank dynamics within a multi-body system framework using the Homotopy Perturbation Method (HPM). The sloshing motion of the liquid inside the tank is represented using an Equivalent pendulum model, which allows for a more accurate depiction of the dynamics involved. Nonlinear equations of motion are derived using the Lagrangian approach to account for lateral and longitudinal excitations, explicitly focusing on compressive oscillations.Our model investigates the influence of critical parameters, including viscous damping, amplitude, and excitation frequency. These parameters are examined at two specific points, one within and one outside the stability regions, to understand their effects on the overall system behavior. The study demonstrates that viscous damping is particularly significant in moving points from unstable to stable regions compared to other principal parameters.Simulations are conducted to visualize stability phenomena through stability diagrams, phase portraits, and time histories of sloshing amplitude. The results obtained using HPM are compared to those from the numerical Runge-Kutta method, validating the analytical approach. This comparison highlights the effectiveness of HPM in accurately capturing the dynamics and stability characteristics of coupled slosh-tank systems, offering valuable insights into the design and control of such systems.

Genetic algorithm (GA) is one of the meta-heuristic optimization algorithms. In this paper, the effects of spectral dynamic and Equivalent Static Analysis methods on the calculated optimum weight of the frame are investigated by the means of GA. In the Equivalent Static Analysis, the applied lateral load and design constraints are considered according to ASCE and LRFD-AISC specifications. The internal forces of the frame members are calculated using finite element method. Analysis and optimization of the frame are performed using a program written in MATLAB programming language. Three types of selection including stochastic selection, tournament selection, and ranking selection as well as three different types of crossover, single point, two-point, and continuous crossover are utilized in this study. Moreover, a comparison between Equivalent Static Analysis and spectral dynamic Analysis is presented. The results indicate that the difference between the optimum weight of the structure analyzed by spectral dynamic and Equivalent Static methods increases as the applied load is increased.