Nonlinear Analysis

This paper addresses the efficiency of thermal insulation layers applied to protect structural elements strengthened by fiber-reinforced polymers (FRP) in the case of fire event. The paper presents numerical modeling and nonlinear analysis of reinforced concrete (RC) columns externally strengthened by FRP and protected by thermal insulation layers when subjected to elevated temperature specified by standard fire tests, in order to predict their residual capacity and fire endurance. The adopted numerical approach uses commercial software includes heat transfer, variation of thermal and mechanical properties of concrete, steel reinforcement, FRP and insulation material with elevated temperature. The numerical results show good agreement with published results of full-scale fire tests. A parametric study was conducted to investigate the influence of several variables on the structural response and residual capacity of insulated FRP-confined columns loaded by service loads when exposed ...

The expected seismic losses of structures with Rotational Friction Dampers (RFDs) are assessed by the Endurance Time (ET) method considering the optimal frictional moment of the devices. A practical method is proposed to obtain the optimal frictional moment of the dampers in multi-story structures at multiple seismic hazard levels. The ET method is used as the analytical tool in this research due to its ability to reduce the number of required analyses and providing good estimations of structural responses at various hazard levels. In order to investigate the effectiveness of the dampers, the life cycle costs of a weak steel structure equipped with optimal RFDs are compared with a standard structure with optimal RFDs and without RFDs. To this end, a comprehensive performance evaluation is performed on the structures based on FEMA P-58 methodology. The ET method is also used as a tool to assess the structural responses in the framework of this methodology. The probability of collapse, fatalities, and expected damage costs are estimated utilizing a Monte Carlo procedure considering uncertainties. Also, a cost-benefit analysis is performed to determine the payback period of investment for the additional cost of the rotational friction damping systems.

In the present study, a general nonlinear one-dimensional finite element beam model is developed for the analysis of composite beams. The proposed model is based on the partial interaction theory of composite beams where the flexibility of shear connectors is allowed. By using a layered approach for the composite beam cross-section and including the material nonlinear behavior of concrete, steel, shear connector and reinforcing steel, the proposed method of analysis is capable of predicting the response of composite beams throughout the elastic, inelastic and ultimate load ranges in one complete analysis. Numerical case studies are presented to demonstrate the validity and applicability of the present method. The results are compared with experimental and analytical or numerical results obtained by other investigators. Also the results are compared with ANSYS package results. The maximum differences in deflection and slip for the examples considered are 12% and 14% respectively when compared with ANSYS and 5% and 11% when compared with experimental work. Accordingly, the proposed nonlinear finite element model represents an efficient and simple tool for the full range analysis of composite beams.

Suction anchors may be subjected to quasihorizontal, quasivertical or inclined loading depending on the type of structure and the water depth. The loading conditions can give rise to horizontal and vertical loads, and moments. To achieve the best performance, suction anchors may be used in different ways. A single cylindrical unit is normally used for typical floaters, and to achieve higher load resistance a cluster of several attached cylinders may be installed. They may also be used with external wings to optimize the horizontal holding capacity by an enlarged projected area. The behaviour of the suction anchor subjected to lateral and pullout loading is presented in this paper. This is to observe the effects of the external wings on the failure mechanism and ultimate capacity of the foundation. The general-purpose finite element program DIANA is being used for this study. A nonlinear analysis was performed on a three dimensional model formed using eight-node isoparametric solid brick elements. The soil was modelled as an elastic perfectly plastic material with von Mises yield criterion for saturated clay. Both load control and displacement control analyses were used for this study.

www.civil.iitb.ac.in/~dns/IACMAG08/pdfs/M47.pdf

For $p\geq 2$ , let $E$ be a 2-uniformly smooth and $p$ -uniformly convex real Banach space and let $A:E\rightarrow E^{\ast }$ be a Lipschitz and strongly monotone mapping such that $A^{-1}(0)\neq \emptyset$ . For given $x_{1}\in E$ , let $\{x_{n}\}$ be generated by the algorithm $x_{n+1}=J^{-1}(Jx_{n}-\unicode[STIX]{x1D706}Ax_{n})$ , $n\geq 1$ , where $J$ is the normalized duality mapping from $E$ into $E^{\ast }$ and $\unicode[STIX]{x1D706}$ is a positive real number in $(0,1)$ satisfying suitable conditions. Then it is proved that $\{x_{n}\}$ converges strongly to the unique point $x^{\ast }\in A^{-1}(0)$ . Furthermore, our theorems provide an affirmative answer to the Chidume et al. open problem [‘Krasnoselskii-type algorithm for zeros of strongly monotone Lipschitz maps in classical Banach spaces’, SpringerPlus4 (2015), 297]. Finally, applications to convex minimization problems are given.

In the present paper, a performance analysis of an 18 levels IMS system building, built in Santiago de Cuba city, which is classified as very high seismic hazard level for the new Cuban code, is carried out using the static nonlinear analysis method, known as the pushover analysis in the specialized literature. A retrospective of this method and their basic objectives are also given, and his use in Cuba as well. To perform the analysis, a characterization of their components, material used in the time of construction of the building, loads analysis, including the prestressed load was done. To obtain the structure´s response and his corresponding performance level, various artificial earthquakes compatibles with the seismicity of the region, according with the seismic demand levels specified by the Cuban code, were determined and included in the analysis, even the El Centro earthquake, which is recognized as a transcendental earthquake by specialists worldwide.
The potential formations of plastic hinges were defined according to the building´s characteristics, which their occurrence was corroborate according with the structure´s results. Geometric model was obtain using SAP2000 v16 software, and using the program´s capabilities, different  eatures of the structure were determined, including, dynamic response, capacity curve, hinge formation mechanism, story drifts, and
maximum building´s drift, according to different levels of demand. Remarkable results of the performance objectives in the analyzed structure were obtained for each earthquake, as follows: for the earthquakes compatible with the seismicity of the zone, the classification was Fully Operational for the Occasional event, and for the events Rare,
and Very Rare the classification was Operational, fulfilling the objectives established according to the importance of the building.

A simply supported bridge is modelled to investigate the effect of a strain rate dependent modulus of elasticity on the dynamic response of the structure to a moving load. The bridge is modelled as a one-dimensional discretized finite element beam and the moving load is represented by a point force. A constant modulus of elasticity is traditionally employed when simulating the dynamic response of structures under moving loads. In this paper, a time-variant modulus is used to calculate strains and displacements and compare them to the traditional approach for different speeds and bridge spans. The time-variant modulus is obtained from the strain rate of the structure which is used in turn to update the strain. The results show significant changes in the modulus and in the resulting load effect as load magnitude and speed increase.

Multivalued fractals are considered as fixed-points of certain induced union operators, called the Hutchinson–Barns-ley operators, in hyperspaces of compact subsets of the original spaces endowed with the Hausdorff metric. Various approaches are presented for obtaining the existence results, jointly with the information concerning the topological structure of the set of multivalued fractals. According to the applied fixed-point principles, we distinguish among metric , topological and TarskiÕs multivalued fractals. Finite families of condensing and (locally) compact maps as well as of different sorts of contractions are examined with this respect. In particular, continuation principle for multivalued frac-tals is established for (locally) compact maps. Multivalued fractals are also generated implicitly by means of differential inclusions. A randomization of the deterministic results is indicated. Numerical aspects of computer generated multi-valued fractals are discussed in detail.

This is a short survey on some recent as well as classical results and open problems in smoothness and renormings of Banach spaces. Applications in general topology and nonlinear analysis are considered. A few new results and new proofs are included. An effort has been made that a young researcher may enjoy going through it without any special pre-requisites and

The so-called ‘least squares regression’ for mathematical modeling is a widely used technique.  It’s so common that one might think nothing could be improved to the algorithm anymore.  But it can.  By minimizing the squares of the differences between measured and predicted values not only in the vertical, but also in the horizontal direction.  I call this ‘multidirectional regression’.  The difference is very significant, especially for power function models, often used in biomedical sciences.  And it makes the regression invariant if the dependent and independent variables are switched.  This was a neglected problem with the traditional method.  The Body Mass Index and the Corpulence Index and their correlation with body fat percentage are studied here as an example showing that this regression technique produces better results.

Controlling seismic damage and improving performance are creative ideas of earthquake designing in which uses definite demonstrating of the structure together with techniques. One of the most important tools to dissipate energy is dampers that are able to reduce vibrations. Especially Fluid Viscous dampers (FVD) which are used to investigate the response of Reinforced Concrete building when they are subjected to lateral load like seismic. A structure might be viewed as serviceable in the event where it can be satisfied by transferring loads to foundation. Since earthquake loads are imposed on a structure, vibrations occur. To resist responses and absorb energy, Fluid Viscous Dampers is used. With Equivalent Static, Response Spectrum and Time history method, it is vital to identify characteristics by (ETABS) finite element program where Models having ordinary RC moment-resisting frame by square column cross-sections with and without FVD. In this evaluation, it is utilized in linear and non-linear analysis where ETABS, Version (18.0.2), has been used. The results are shown that dampers (FVD) dramatically reduce the lateral deflection and enhance the performance of the structure. They also cause a decrease in Time period of maximum Psuedo Spectral Acceleration (PSA) in Response spectrum curves, increasing the story stiffness and decreasing the story Shear. Therefore, adding FVD to RC buildings is effective utilization due to its dissipation of energy.

This paper provides an overview of the US Army Corps of Engineers' guidance for seismic design and evaluation of concrete dams, as presented in the Engineer Manual EM1110-2-6053. The re- quirements to design and evaluate concrete dams to have a predictable performance for specified levels of seismic hazard are discussed. The seismic input and performance levels associated with serviceability, damage control, and collapse prevention are defined. The analysis and evaluation procedures and acceptance criteria for each performance level are described. They consist of linear and nonlinear procedures for estimation of seismic response and acceptance criteria that use demand-capacity ratios, damage control thresholds, and irrecoverable level of movements and post-earthquake stability condition to assess dam safety. Finally, an example is provided to demonstrate the application of the manual to seismic evaluation of a concrete gravity dam.

The Perona-Malik equation is a formally ill-posed parabolic equation for which simple discretizations are nevertheless numerically found to be stable. After discussing the background of this paradox in computer vision, this paper shows the nonexistence of weak solutions even in those cases where computations are successful, and introduces a notion of generalized solutions for this equation, which do evolve smoothly and possess many of the features of numerical calculations.