Simulation of Steel Reinforcement on the Nonlinear Behaviour of Slender Glulam Beam Columns by Using the Newton-Raphson Method

The current theory in NF EN 1995-1-1/NA of Eurocode 5, which is based on maximum deflection, has been investigated on softwoods. Therefore, this theory is not adapted for slender glulam beam columns made of tropical hardwood species from the Congo Basin. This maximum deflection is caused by a set of loads applied to the structure. However, Eurocode 5 doesn’t provide how to predict this deflection in case of long-term load for such structures. This can be done by studying load-displacement (P-Δ) behaviour of these structures while taking into account second order effects. To reach this goal, a nonlinear analysis has been performed on a three-dimensional beam column embedded on both ends. Since conducting experimental investigations on large span structural products is time-consuming and expensive especially in developing countries, a numerical model has been implemented using the Newton-Raphson method to predict load-displacement (P-Δ) curve on a slender glulam beam column made of tropical hardwood species. On one hand, the beam has been analyzed without wood connection. On the other hand, the beam has been analyzed with a bolted wood connection and a slotted-in steel plate. The load cases considered include self-weight and a uniformly applied long-term load. Combinations of serviceability limit states (SLS) and ultimate limit states (ULS) have also been considered, among other factors. A finite-element software RFEM 5 has been used to implement the model. The results showed that the use of steel can reduce displacement by 20.96%. Additionally, compared to the maximum deflection provided by Eurocode 5 for softwoods, hardwoods can exhibit an increasing rate of 85.63%. By harnessing the plastic resistance of steel, the bending resistance of wood can be increased by 32.94%.

Evaluation of site response characteristic using nonlinear method （Case study： Babol, Iran）

In this the present study, an attempt has been made to evaluate the seismic hazard considering local site effects by carrying out detailed geotechnical site characterization in Babol, Iran. Use of geotechnical data and synthesis of drilling data extracted from the Babol＇s subsurface database have enabled authors to determine the geotechnical properties of each site. These data are consisted of twenty five boreholes up to depth of 40 m. Based on the obtained data from geotechnical investigation the study area is divided to five zones. Dynamic analysis was performed in time domain, using fully nonlinear model by PLAXIS. A series of analysis in the study area showed the site period, ranging from 0.4 to 0.8 s. Finally the obtained response spectra from fully nonlinear method were compared with site response spectra of Iran＇s 2800 （earthquake） code.

Improved Nonlinear Equation Method for Numerical Prediction of Jominy End-Quench Curves

Without considering the effects of alloying interaction on the Jominy end-quench curves, the prediction resuits obtained by YU Bai-hai＇s nonlinear equation method for multi-alloying steels were different from those experimental ones reported in literature. Some alloying elements have marked influence on Jominy end-quench curves of steels. An improved mathematical model for simulating the Jominy end-quench curves is proposed by introducing a parameter named alloying interactions equivalent （Le）. With the improved model, the Jominy end-quench curves of steels so obtained agree very well with the experimental ones.

NONLINEAR TIME TRANSFORMATION METHOD FOR STRONG NONLINEAR OSCILLATION SYSTEMS

In this paper,a nonlinear time transformation method is presented for the analysis of strong nonlinear oscillation systems.This method can be used to study the limit cycle behavior of the autonomous systems and to analyze the forced vibration of a strong nonlinear system.

TOPOLOGY SYNTHESIS OF GEOMETRICALLY NONLINEAR COMPLIANT MECHANISMS USING MESHLESS METHODS

This paper presents a new method for topology optimization of geometrical nonlinear compliant mechanisms using the element-free Galerkin method （EFGM）. The EFGM is employed as an alternative scheme to numerically solve the state equations by fully taking advantage of its capability in dealing with large displacement problems. In the meshless method, the imposition of essential boundary conditions is also addressed. The popularly studied solid isotropic material with the penalization （SIMP） scheme is used to represent the nonlinear dependence between material properties and regularized discrete densities. The output displacement is regarded as the objective function and the adjoint method is applied to finding the sensitivity of the design functions. As a result, the optimization of compliant mechanisms is mathematically established as a nonlinear programming problem, to which the method of moving asymptotes （MMA） belonging to the sequential convex programming can be applied. The availability of the present method is finally demonstrated with several widely investigated numerical examples.

Variational iteration solving method for El Nio phenomenon atmospheric physics of nonlinear model

A class of E1 Niйo atmospheric physics oscillation model is considered. The E1 Niйo atmospheric physics oscillation is an abnormal phenomenon involved in the tropical Pacific ocean-atmosphere interactions. The conceptual oscillator model should consider the variations of both the eastern and western Pacific anomaly patterns. An E1 Niйo atmospheric physics model is proposed using a method for the variational iteration theory. Using the variational iteration method, the approximate expansions of the solution of corresponding problem are constructed. That is, firstly, introducing a set of functional and accounting their variationals, the Lagrange multiplicators are counted, and then the variational iteration is defined, finally, the approximate solution is obtained. From approximate expansions of the solution, the zonal sea surface temperature anomaly in the equatorial eastern Pacific and the thermocline depth anomaly of the sea-air oscillation for E1 Niйo atmospheric physics model can be analyzed. E1 Niйo is a very complicated natural phenomenon. Hence basic models need to be reduced for the sea-air oscillator and are solved. The variational iteration is a simple and valid approximate method.

REMARKS ON NONLINEAR GALERKIN METHOD FOR KURAMOTO-SIVASHINSKY EQUATION

This paper is concentrated on a nonlinear Galerkin method with sm small- scale components for Kuramoto-Sivashmsky equation, in which convergence results and the analysis of error estimates are given, The conclusion shows that this choce of modes is efficient .for The method modifred.

Expanding the Tanh-Function Method for Solving Nonlinear Equations

In this paper, using the tanh-function method, we introduce a new approach to solitary wave solutions for solving nonlinear PDEs. The proposed method is based on adding integration constants to the resulting nonlinear ODEs from the nonlinear PDEs using the wave transformation. Also, we use a transformation related to those integration constants. Some examples are considered to find their exact solutions such as KdV- Burgers class and Fisher, Boussinesq and Klein-Gordon equations. Moreover, we discuss the geometric interpretations of the resulting exact solutions.

A Family of Fifth-order Iterative Methods for Solving Nonlinear Equations

In this paper, we present and analyze a family of fifth-order iterative methods free from second derivative for solving nonlinear equations. It is established that the family of iterative methods has convergence order five. Numerical examples show that the new methods are comparable with the well known existing methods and give better results in many aspects.

Stability of average acceleration method for structures with nonlinear damping

The energy approach is used to theoretically verify that the average acceleration method （AAM）, which is unconditionally stable for linear dynamic systems, is also unconditionally stable for structures with typical nonlinear damping, including the special case of velocity power type damping with a bilinear restoring force model. Based on the energy approach, the stability of the AAM is proven for SDOF structures using the mathematical features of the velocity power function and for MDOF structures by applying the virtual displacement theorem. Finally, numerical examples are given to demonstrate the accuracy of the theoretical analysis.

Full－range nonlinear analysis of fatigue behaviors of reinforced concrete structures by finite element method

The offshore reinforced concrete structures are always subject to cyclic load, such as wave load.In this paper a new finite element analysis model is developed to analyze the stress and strain state of reinforced concrete structures including offshore concrete structures, subject to any number of the cyclic load. On the basis of the anal ysis of the experimental data,this model simplifies the number of cycles-total cyclic strain curve of concrete as three straight line segments,and it is assumed that the stress-strain curves of different cycles in each segment are the same, thus the elastoplastic analysis is only needed for the first cycle of each segment, and the stress or strain corresponding to any number of cycles can be obtained by superposition of stress or strain obtained by the above e lastoplastic analysis based on the cyclic numbers in each segment.This model spends less computer time,and can obtain the stress and strain states of the structures after any number of cycles.The endochronic-damage and ideal offshore concrete platform subject to cyclic loading are experimented and analyzed by the finite element method based on the model proposed in this paper. The results between the experiment and the finite element analysis are in good agreement,which demonstrates the validity and accuracy of the proposed model.

Advanced method to estimate reliability-based sensitivity of mechanical components with strongly nonlinear performance function

Based on the random perturbation technique for reliability sensitivity design,some realistic reliability-based sensitivity issues are discussed,some of which have a structure of high nonlinear performance functions.Combining the related theories of the moment method of the reliability analysis,the matrix differential,and the Kronecker algebra,the reliability-based sensitivity method based on the perturbation method is modified if the first four moments of random variables are given.Meanwhile,a reliability-based sensitivity computation method is proposed.Some examples are used to show that using this method can effectively improve the accuracy of the reliability-based sensitivity computation and offer a reliable theoretic basis in engineering.

Legendre Rational Spectral Method for Nonlinear Klein-Gordon Equation

A Legendre rational spectral method is proposed for the nonlinear Klein-Gordon equation on the whole line. Its stability and convergence are proved. Numerical results coincides well with the theoretical analysis and demonstrate the e?ciency of this approach.

Generalized Extended tanh-function Method for Traveling Wave Solutions of Nonlinear Physical Equations

In this paper, the generalized extended tanh-function method is used for constructing the traveling wave solutions of nonlinear evolution equations. We choose Fisher＇s equation, the nonlinear schr＆#168;odinger equation to illustrate the validity and ad-vantages of the method. Many new and more general traveling wave solutions are obtained. Furthermore, this method can also be applied to other nonlinear equations in physics.

INTERPOLATION PERTURBATION METHOD FORSOLVING NONLINEAR PROBLEMS

In this paper, using the interpolation perturbation method. the author seeks tosolve several nonlinear problems. Numerical examples show that the method Df thispaper has good accuracy.

Seismic fluid identification using a nonlinear elastic impedance inversion method based on a fast Markov chain Monte Carlo method

Elastic impedance inversion with high efficiency and high stability has become one of the main directions of seismic pre-stack inversion. The nonlinear elastic impedance inversion method based on a fast Markov chain Monte Carlo （MCMC） method is proposed in this paper, combining conventional MCMC method based on global optimization with a preconditioned conjugate gradient （PCG） algorithm based on local optimization, so this method does not depend strongly on the initial model. It converges to the global optimum quickly and efficiently on the condition that effi- ciency and stability of inversion are both taken into consid- eration at the same time. The test data verify the feasibility and robustness of the method, and based on this method, we extract the effective pore-fluid bulk modulus, which is applied to reservoir fluid identification and detection, and consequently, a better result has been achieved.

Some new solutions derived from the nonlinear (2+1)-dimensional Toda equation-an efficient method of creating solutions

This paper presents a new and efficient approach for constructing exact solutions to nonlinear differential-difference equations （NLDDEs） and lattice equation. By using this method via symbolic computation system MAPLE, we obtained abundant soliton-like and/or period-form solutions to the （2＋1）-dimensional Toda equation. It seems that solitary wave solutions are merely special cases in one family. Furthermore, the method can also be applied to other nonlinear differential-difference equations.

New Modification of Fixed Point Iterative Method for Solving Nonlinear Equations

In this paper, we have modified fixed point method and have established two new iterative methods of order two and three. We have discussed their convergence analysis and comparison with some other existing iterative methods for solving nonlinear equations.

A SIMPLE FAST METHOD IN FINDING PARTICULAR SOLUTIONS OF SOME NONLINEAR PDE

The 'trial function method' ( TFM for short) and a routine way in finding traveling,wave solutions to some nonlinear partial differential equations( PDE for short), wer explained. Two types of evolution equations are studied, one is a generalized Burgers or KdV equation, the other is the Fisher equation with special nonlinear forms of its reaction rate term. One can see that this method is simple, fast and allowing further extension.

Self-adaptive one-dimensional nonlinear finite element method based on element energy projection method

The element energy projection （EEP） method for computation of super- convergent resulting in a one-dimensional finite element method （FEM） is successfully used to self-adaptive FEM analysis of various linear problems, based on which this paper presents a substantial extension of the whole set of technology to nonlinear problems. The main idea behind the technology transfer from linear analysis to nonlinear analysis is to use Newton＇s method to linearize nonlinear problems into a series of linear problems so that the EEP formulation and the corresponding adaptive strategy can be directly used without the need for specific super-convergence formulation for nonlinear FEM. As a re- sult, a unified and general self-adaptive algorithm for nonlinear FEM analysis is formed. The proposed algorithm is found to be able to produce satisfactory finite element results with accuracy satisfying the user-preset error tolerances by maximum norm anywhere on the mesh. Taking the nonlinear ordinary differential equation （ODE） of second-order as the model problem, this paper describes the related fundamental idea, the imple- mentation strategy, and the computational algorithm. Representative numerical exam- ples are given to show the efficiency, stability, versatility, and reliability of the proposed approach.