Abstract: A formulation of postbuckling analysis of end supported rods under self-weight has been presented by the variational method. The variational formulation involving the strain energy due to bending and the potential energy of the self-weight, are expressed in terms of the intrinsic coordinates. The variational formulation is accomplished by introducing the Lagrange multiplier technique to impose the boundary conditions. The finite element method is used to derive a system of nonlinear equations resulting from the stationary of the total potential energy and then Newton-Raphson iterative procedure is applied to solve this system of equations. The numerical results demonstrate the postbluckled configurations of end supported rods under self-weight. This finite element method based on variational formulation expressed in term of intrinsic coordinate is highly recommended for postbuckling analysis of end-supported rods under self-weight.
Abstract: Role of piezoelectric energy harvesters has gained interest in supplying power for micro devices such as health monitoring sensors. In this study, in order to enhance the piezoelectric energy harvesting in capturing energy from broader range of excitation and to improve the mechanical and electrical responses, bimorph piezoelectric energy harvester beam with magnetic mass attached at the end is presented. In view of overcoming the brittleness of piezo-ceramics, functionally graded piezoelectric layers comprising of both piezo-ceramic and piezo-polymer is employed. The nonlinear equations of motions are derived using energy method and then solved analytically using perturbation scheme. The frequency responses of the forced vibration case are obtained for the near resonance case. The nonlinear dynamic responses of the MEMS scaled functionally graded piezoelectric energy harvester in this paper may be utilized in different design scenarios to increase the efficiency of the harvester.
Abstract: A semi-implicit phase field method for droplet evolution is proposed. Using the phase field Cahn-Hilliard equation, we are able to track the interface in multiphase flow. The idea of a semi-implicit finite difference scheme is reviewed and employed to solve two nonlinear equations, including the Navier-Stokes and the Cahn-Hilliard equations. The use of a semi-implicit method allows us to have larger time steps compared to explicit schemes. The governing equations are coupled and then solved by a GMRES solver (generalized minimal residual method) using modified Gram-Schmidt orthogonalization. To show the validity of the method, we apply the method to the simulation of a rising droplet, a leaky dielectric drop and the coalescence of drops. The numerical solutions to the phase field model match well with existing solutions over a defined range of variables.
Abstract: The main focus of this manuscript is to provide a
highly efficient two-point sixth-order family of super-Halley type
methods that do not require any second-order derivative evaluation
for obtaining simple roots of nonlinear equations, numerically. Each
member of the proposed family requires two evaluations of the given
function and two evaluations of the first-order derivative per iteration.
By using Mathematica-9 with its high precision compatibility, a
variety of concrete numerical experiments and relevant results are
extensively treated to confirm t he t heoretical d evelopment. From
their basins of attraction, it has been observed that the proposed
methods have better stability and robustness as compared to the other
sixth-order methods available in the literature.
Abstract: The main objective of the present article is to explore the state of mixed convection nanofluid flow of gyrotactic microorganisms from an isothermal vertical wedge in porous medium. In our pioneering investigation, the easiest possible boundary conditions have been employed, in other words when the temperature, the nanofluid and motile microorganisms’ density have been considered to be constant on the wedge wall. Adding motile microorganisms to the nanofluid tends to enhance microscale mixing, mass transfer, and improve the nanofluid stability. Upon the Oberbeck–Boussinesq approximation and non-similarity transmutation, the paradigm of nonlinear equations are obtained and tackled numerically by using the R.K. Gill and shooting methods to obtain the dimensionless velocity, temperature, nanoparticle concentration and motile microorganisms density together with the reduced Sherwood, Nusselt, and numbers. Bioconvection parameters have strong effect upon the motile microorganism, heat, and volume fraction of nanoparticle transport rates. In the case when bioconvection is neglected, the obtained computations were found in very good agreement with the previous published data.
Abstract: In this paper we present the efficient parallel
implementation of elastoplastic problems based on the TFETI (Total
Finite Element Tearing and Interconnecting) domain decomposition
method. This approach allow us to use parallel solution and compute
this nonlinear problem on the supercomputers and decrease the
solution time and compute problems with millions of DOFs. In
our approach we consider an associated elastoplastic model with
the von Mises plastic criterion and the combination of linear
isotropic-kinematic hardening law. This model is discretized by
the implicit Euler method in time and by the finite element
method in space. We consider the system of nonlinear equations
with a strongly semismooth and strongly monotone operator. The
semismooth Newton method is applied to solve this nonlinear
system. Corresponding linearized problems arising in the Newton
iterations are solved in parallel by the above mentioned TFETI. The
implementation of this problem is realized in our in-house MatSol
packages developed in MatLab.
Abstract: Unmanned aircraft systems (UAS) are playing
increasingly prominent roles in defense programs and defense
strategies around the world. Technology advancements have
enabled the development of it to do many excellent jobs as
reconnaissance, surveillance, battle fighters, and communications
relays. Simulating a small unmanned aerial vehicle (SUAV)
dynamics and analyzing its behavior at the preflight stage is too
important and more efficient. The first step in the UAV design is
the mathematical modeling of the nonlinear equations of motion. .
In this paper, a survey with a standard method to obtain the full
non-linear equations of motion is utilized, and then the
linearization of the equations according to a steady state flight
condition (trimming) is derived. This modeling technique is
applied to an Ultrastick-25e fixed wing UAV to obtain the valued
linear longitudinal and lateral models. At the end the model is
checked by matching between the behavior of the states of the nonlinear
UAV and the resulted linear model with doublet at the
control surfaces.
Abstract: In order to evaluate the performance of a unified power
flow controller (UPFC), mathematical models for steady state and
dynamic analysis are to be developed. The steady state model is
mainly concerned with the incorporation of the UPFC in load flow
studies. Several load flow models for UPFC have been introduced
in literature, and one of the most reliable models is the decoupled
UPFC model. In spite of UPFC decoupled load flow model simplicity,
it is more robust compared to other UPFC load flow models and it
contains unique capabilities. Some shortcoming such as additional
set of nonlinear equations are to be solved separately after the load
flow solution is obtained. The aim of this study is to investigate the
different control strategies that can be realized in the decoupled load
flow model (individual control and combined control), and the impact
of the location of the UPFC in the network on its control parameters.
Abstract: Flood wave propagation in river channel flow can be enunciated by nonlinear equations of motion for unsteady flow. It is difficult to find analytical solution of these non-linear equations. Hence, in this paper verification of the finite element model has been carried out against available numerical predictions and field data. The results of the model indicate a good matching with both Preissmann scheme and HEC-RAS model for a river reach of 29km at both sites (15km from upstream and at downstream end) for discharge hydrographs. It also has an agreeable comparison with the Preissemann scheme for the flow depth (stage) hydrographs. The proposed model has also been applying to forecast daily discharges at 400km downstream in the Indus River from Sukkur barrage of Sindh, Pakistan, which demonstrates accurate model predictions with observed the daily discharges. Hence, this model may be utilized for flood warnings in advance.
Abstract: The tension leg platform (TLP) is a vertically moored structure with excess buoyancy. The TLP is regarded as moored structure in horizontal plan, while inherit stiffness of fixed platform in vertical plane. In this paper, a numerical study using modified Morison equation was carried out in the time domain to investigate the influence of nonlinearities due to hydrodynamic forces and the coupling effect between surge, sway, heave, roll, pitch and yaw degrees of freedom on the dynamic behavior of TLP's. The stiffness of the TLP was derived from a combination of hydrostatic restoring forces and restoring forces due to cables and the nonlinear equations of motion were solved utilizing Newmark’s beta integration scheme. The effect of tethers length and wave characteristics such as wave period and wave height on the response of TLP's was evaluated.
Only uni-directional waves in the surge direction was considered in the analysis. It was found that for short wave periods (i.e. 10 sec.), the surge response consisted of small amplitude oscillations about a displaced position that is significantly dependent on tether length, wave height; whereas for longer wave periods, the surge response showed high amplitude oscillations about that is significantly dependent on tether length.
Abstract: This paper presents a new function expansion method for finding traveling wave solutions of a nonlinear equations and calls it the G G -expansion method, given by Wang et al recently. As an application of this new method, we study the well-known Sawada-Kotera-Kadomtsev-Petviashivili equation and Bogoyavlensky-Konoplechenko equation. With two new expansions, general types of soliton solutions and periodic solutions for these two equations are obtained.
Abstract: In this paper, we are concerned with the further study for system of nonlinear equations. Since systems with inaccurate function values or problems with high computational cost arise frequently in science and engineering, recently such systems have attracted researcher-s interest. In this work we present a new method which is independent of function evolutions and has a quadratic convergence. This method can be viewed as a extension of some recent methods for solving mentioned systems of nonlinear equations. Numerical results of applying this method to some test problems show the efficiently and reliability of method.
Abstract: In the present article, nonlinear vibration analysis of
single layer graphene sheets is presented and the effect of small
length scale is investigated. Using the Hamilton's principle, the three
coupled nonlinear equations of motion are obtained based on the von
Karman geometrical model and Eringen theory of nonlocal
continuum. The solutions of Free nonlinear vibration, based on a one
term mode shape, are found for both simply supported and clamped
graphene sheets. A complete analysis of graphene sheets with
movable as well as immovable in-plane conditions is also carried out.
The results obtained herein are compared with those available in the
literature for classical isotropic rectangular plates and excellent
agreement is seen. Also, the nonlinear effects are presented as
functions of geometric properties and small scale parameter.
Abstract: In this article the homotopy continuation method (HCM) to solve the forward kinematic problem of the 3-PRS parallel manipulator is used. Since there are many difficulties in solving the system of nonlinear equations in kinematics of manipulators, the numerical solutions like Newton-Raphson are inevitably used. When dealing with any numerical solution, there are two troublesome problems. One is that good initial guesses are not easy to detect and another is related to whether the used method will converge to useful solutions. Results of this paper reveal that the homotopy continuation method can alleviate the drawbacks of traditional numerical techniques.
Abstract: For the last years, the variants of the Newton-s method with cubic convergence have become popular iterative methods to find approximate solutions to the roots of non-linear equations. These methods both enjoy cubic convergence at simple roots and do not require the evaluation of second order derivatives. In this paper, we present a new Newton-s method based on contra harmonic mean with cubically convergent. Numerical examples show that the new method can compete with the classical Newton's method.
Abstract: The critical period for weed control (CPWC) is the period in the crop growth cycle during which weeds must be controlled to prevent unacceptable yield losses. Field studies were conducted in 2005 and 2006 in the University of Birjand at the south east of Iran to determine CPWC of corn using a randomized complete block design with 14 treatments and four replications. The treatments consisted of two different periods of weed interference, a critical weed-free period and a critical time of weed removal, were imposed at V3, V6, V9, V12, V15, and R1 (based on phonological stages of corn development) with a weedy check and a weed-free check. The CPWC was determined with the use of 2.5, 5, 10, 15 and 20% acceptable yield loss levels by non-linear Regression method and fitting Logistic and Gompertz nonlinear equations to relative yield data. The CPWC of corn was from 5- to 15-leaf stage (19-55 DAE) to prevent yield losses of 5%. This period to prevent yield losses of 2.5, 10 and 20% was 4- to 17-leaf stage (14-59 DAE), 6- to 12-leaf stage (25-47 DAE) and 8- to 9-leaf stage (31-36 DAE) respectively. The height and leaf area index of corn were significantly decreased by weed competition in both weed free and weed infested treatments (P
Abstract: A new, rapidly convergent, numerical procedure for
internal loading distribution computation in statically loaded, singlerow,
angular-contact ball bearings, subjected to a known combined
radial and thrust load, which must be applied so that to avoid tilting
between inner and outer rings, is used to find the load distribution
differences between a loaded unfitted bearing at room temperature,
and the same loaded bearing with interference fits that might
experience radial temperature gradients between inner and outer
rings. For each step of the procedure it is required the iterative
solution of Z + 2 simultaneous nonlinear equations – where Z is the
number of the balls – to yield exact solution for axial and radial
deflections, and contact angles.
Abstract: This paper present the harmonic elimination of hybrid
multilevel inverters (HMI) which could be increase the number of
output voltage level. Total Harmonic Distortion (THD) is one of the
most important requirements concerning performance indices.
Because of many numbers output levels of HMI, it had numerous
unknown variables of eliminate undesired individual harmonic and
THD nonlinear equations set. Optimized harmonic stepped waveform
(OHSW) is solving switching angles conventional method, but most
complicated for solving as added level. The artificial intelligent
techniques are deliberation to solve this problem. This paper presents
the Particle Swarm Optimization (PSO) technique for solving
switching angles to get minimum THD and eliminate undesired
individual harmonics of 15-levels hybrid multilevel inverters.
Consequently it had many variables and could eliminate numerous
harmonics. Both advantages including high level of inverter and
Particle Swarm Optimization (PSO) are used as powerful tools for
harmonics elimination.
Abstract: A family of improved secant-like method is proposed in this paper. Further, the analysis of the convergence shows that this method has super-linear convergence. Efficiency are demonstrated by numerical experiments when the choice of α is correct.