نشریه روش های عددی در مهندسی
سال سی و هشتم شماره 1 (تابستان 1398)

The behavior of many types of fluids can be simulated using differential equations. There are many approaches to solve differential equations, including analytical and numerical methods. However, solving an ill-posed high-order differential equation is still a major challenge. Generally, the governing differential equations of a viscoelastic nanofluid are ill-posed; hence, their solution is a challenging task. In addition, the presence of very tiny nanoparticles (lower than 100 nm) induces new heat and mass transfer mechanisms which can increase the complexity of the behavior of the viscoelastic nanofluids. Therefore, creating or developing new analytical or semi-analytical approaches to solve the governing equations of these types of nanofluids is highly demanded. In the present study, by using a new idea and utilizing an optimization approach, a new solution approach has been presented to solve the governing equations of viscoelastic nanofluids. By using the optimization method, a basic initial guess was changed toward an optimized solution satisfying all boundary conditions and the governing equations. The results indicate the robustness and accuracy of the presented method in dealing with the high-order ill-posed governing differential equations of viscoelastic nanofluids.

In this paper, nonlinear modal interactions caused by one-to-three internal resonance in a beam-mass-spring-damper system are investigated based on nonlinear system identification. For this purpose, the equations governing the transverse vibrations of the beam and mass are analyzed via the multiple scale method and the vibration response of the system under primary resonance is extracted. Then, the frequency behavior of the vibration response is studied by Fourier and Morlet wavelet transforms. In order to perform the nonparametric identification of the time response, mono-frequency intrinsic mode functions are derived by the advanced empirical mode decomposition. In this approach, masking signals are utilized in order to avoid mode mixing caused by modal interaction. After analyzing the frequency behavior of each mode function, slow flow dynamics of the system is established and intrinsic modal oscillators for reconstructing the corresponding intrinsic mode are extracted. Finally, by analyzing the beating phenomenon in a simple one-degree-of-freedom system, it is shown that the internal resonance causes beating only under the circumstance that the slope of the logarithmic amplitude of oscillator force is nonzero. The results, therefore, show that depending on the periodic, pseudo-periodic, and chaotic behavior of the response, modal interactions might be stationary or non-stationary. Moreover, the chaotic behavior occurs mostly in the vibration mode excited by the internal resonance mechanism

In this paper, a finite element model is presented for the transient analysis of low velocity impact, and the impact induced damage in the composite plate subjected to low velocity impact is studied. The failure criteria suggested by Choi and Chang and the Tsai-Hill failure criteria are used for the prediction of the damage in the composite plate; then the effect of various parameters on the impact induced damage is investigated. The first order shear deformation plate theory and the Ritz finite element method are employed for modeling the behavior of plate, and the modified Hertz contact low is used for the prediction of the contact force through the impact. In the numerical results, the time history of indentation, contact force and stress during the impact and the impact induced damage is investigated. The matrix cracking and delamination in the plies of the laminated composite plate subjected to low velocity impact are studied and the effects of various parameters are investigated.

The purpose of this article is the numerical study of flow and heat transfer characteristics of Nanofluids inside a cylindrical microchannel with rectangular, triangular, and circular cross-sections. The size and shape of these sections have a significant impact on the thermal and hydraulic performance of the microchannel heat exchanger. The Nanofluids used in this work include water and De-Ethylene Glycol (DEG) as the base fluids and Al2O3, Cu, SiO2 and CuO as the nanoparticles. To solve the problem and extract the required data, a 3-D simulation was performed for the microchannel using ANSYS FLUENT 15.0 software and the effect of the cross-sectional shape of the fluid flow and the type of nanoparticles on the thermal transfer and fluid flow parameters was studied. From the obtained results, it can be observed that the addition of nanoparticles to the base fluid increases the heat transfer and pressure drop. The results also show that rectangular channels have the best performance among the three geometries examined as its heat transfer coefficient was 19.26% higher than the triangular cross section which had the worst performance.

In this paper, finite element analysis of thin viscoelastic plates is performed by proposing new plate elements using complex Fourier shape functions. New discrete Kirchhoff Fourier Theory (DKFT) plate elements are constructed by the enrichment of quadratic function fields in a six-noded triangular plate element with complex Fourier radial basis functions. In order to illustrate the validity and accuracy of the presented approach and robustness of the proposed elements in viscoelasticity, finite element analysis of square and elliptical viscoelastic thin plates is performed and the results are compared to those of analytical solutions and with those obtained by discrete Kirchhoff Theory (DKT) elements and the commercial software ABAQUS. The results show that FE solutions using DKFT elements have an  excellent agreement with the analytical solutions and ABAQUS solutions, even though noticeably fewer elements, in comparison to DKT and classic plate elements, are employed, which means that  the computational costs are reduced effectively.

Biot equations that consider fluid and soil interaction at the same time are the most applicable relationships in the soil dynamic analysis. However, in dynamic analysis, due to the sudden increase in the excess pore pressure caused by seismic excitation and the occurrence of high hydraulic gradients, the assumption of the Darcy flow used in these equations is questionable. In the present study, in the u-p form of Biot equations, non-Darcy flow is considered. Also, the nonlinear behavior of soil is modeled by the Pastor-Zienkiewicz -Chan model. For validation, the VELACS No.1 experiment is modeled and the effect of the nonlinear fluid flow assumption on the results is examined. The results indicate that in the low permeability coefficients, the obtained results of the non-Darcy and Darcy flow are in agreement; however, in high permeability coefficients, these two methods differ by time and depth.

Nowadays, electricity load forecasting, as one of the most important areas, plays a crucial role in the economic process. What separates electricity from other commodities is the impossibility of storing it on a large scale and cost-effective construction of new power generation and distribution plants. Also, the existence of seasonality, nonlinear complexity, and ambiguity pattern in electricity data set makes it more difficult to forecast by using the traditional methods. Therefore, new models, computational intelligence and soft computing tools and combining models are the most accurate and widely used methods for modeling the complexity and uncertainty in the data set. In this paper, a parallel optimal hybrid model using computational intelligence tools and soft computations is proposed to forecast the electricity load forecasting. The main idea of this model is the use of the advantages of the individual models in the modeling of complex systems in a structure and elimination of  the limitations of them, simultaneously. The experimental results indicate that the proposed hybrid model has a higher performance accuracy in comparison to iterative suboptimal hybrid models and its computational cost is lower than the other hybrid models; also, the proposed model can achieve more accurate results, as compared with its component and some other seasonal hybrid models.