نشریه روش های عددی در مهندسی
سال چهلم شماره 1 (تابستان 1400)

Accurate determination of the response of structures under dynamic loads such as earthquake loads plays an important role in the safe and economical design of structures. The purpose of this paper is to utilize a novel solution method based on the use of exponential basis functions for dynamic analysis of Bernoulli beam subjected to different types of base excitations. This method was firstly introduced for solving scalar wave propagation problems, named as stepwise time-weighted residual method. The proposed method considers the solution as a series of exponential basis functions with unknown constant coefficients; and the problem is solved in time without the need for spatial discretization of the beam and by using an appropriate recursive relation to correct the coefficients of the exponential bases. In order to apply the earthquake excitation, first by using the central finite difference relation, the earthquake acceleration history is converted to displacement history. Moreover, the displacement history is applied to the beam as a time-varying boundary condition. In this study, the capabilities of the proposed method in solving several sample problems of vibration of single and multi-span beams under various stimuli such as earthquake acceleration variations are compared with the results of other existing methods.

In this paper, a multi-mode resource constrained project selection and scheduling problem is investigated considering the reinvestment strategy in a flexible time horizon. Among a set of available projects, a number of projects are selected and scheduled regarding the constraints on renewable resources and precedence relations. The benefits of project portfolio selection and scheduling are compared in both fixed and flexible time horizons. For this purpose, upper and lower tolerance limits are considered for the predetermined time horizon. If the schedule exceeds the time horizon, a penalty cost will be charged. The objective is to determine the optimal time horizon. A mixed-integer linear programming model is proposed for this problem, and solved by GAMS software/CPLEX solver and also a combination of a proposed heuristic algorithm, Genetic Algorithm, and a local search method. Numerical results show that the proposed approach has an acceptable performance in terms of the quality of the solution and the running time. Also, dealing with the problem in a flexible time horizon is more profitable compared to a fixed time horizon.

In this paper, nonlinear bending analysis of functionally graded rectangular and sectorial micro/nano plates is investigated using the modified couple stress theory. For this purpose, a higher-order shear deformation theory and von Kármán geometrically nonlinear theory are employed. The equilibrium equations and the boundary conditions for rectangular and annular sector plates are derived from the principle of minimum total potential energy and solved using the Semi-Analytical Polynomial Method (SAPM). One of the advantages of the implemented shear deformation theory is removing the defects of higher order shear deformation theory, and obtaining the response of the first and the third-order shear deformation theories at the same time. Afterwards, beside investigating the benefits of this theory compared with other ones, the results are verified with those by other researches. At the end, the effects of length scale parameter, boundary conditions, power law index, and geometrical dimensions are investigated

In this paper, static analysis of in-plane heterogeneous laminated composite plates is numerically studied. The Mindlin’s theory which considers linear transverse shear deformation has been implemented. The governing partial differential equation is satisfied by a weighted residual integration. Chebyshev polynomials of the first kind are used as basis functions and exponential functions make up the weight functions of the integration. The emerging integrals may be composed of some pre-evaluated 1D normalized ones, which effectively paces up the solution progress. To verify the method, several examples of homogeneous as well as heterogeneous plates with various lamination schemes and boundary conditions have been solved. Results are compared with those from the literature or by commercial codes, which reveal excellent accuracy of the proposed method.

In order to simulate multiphase flow in the presence of dielectric current using the Lattice Boltzmann Method (LBM), three distribution functions are used, two of which for using the He-Chen-Zhang phase field model and one for solving the potential field. Initially, the ability of the code to apply surface tension was tested using the Laplace law and the drop release test. The results show that the present numerical program is capable of modeling well the regulated surface tension force. Then, the Rayleigh–Taylor instability simulation is used to evaluate the codechr('39')s ability in applying volume forces. The results by the developed numerical program are in good agreement with the numerical results in the references. In this study, for the first time, the effect of electric field on a droplet immersed in another fluid and the presence of droplet in a porous medium is investigated by LBM. For this purpose, first the droplet motion due to the potential difference in the porous and non-porous media is investigated. After modeling the droplet motion due to the potential difference, two electric fields areapplied to the droplet to reverse the droplet deformation. Through various tests, it is shown that at a given potential difference, the droplet breaks down after much deformation and is divided into smaller droplets. The decomposition of droplets in a pre-mixed emulsion is a common technique in the production of monodisperse droplets. The presence of monodisperse droplets in an emulsion improves the physical properties of polymer science experts.

Corrosive factors along with mechanical loads on the gas turbine compressor blades, cause phenomena such as pitting corrosion, stress corrosion cracking and corrosion fatigue. Due to erosion of particles in the presence of a corrosive environment, pitting happens on the blade surfaces, which is a source of subsequent cracks. Therefore, it is necessary to get knowledge of its mechanism in order to prevent the phenomena as much as possible. The main purpose of this paper is to investigate the growth of pitting corrosion in CUSTOM 450 stainless steel and to obtain strain values in the growing pits at the maximum bending region. In this regard, a two-point bending specimen was made and subjected to a potentio-static test under the potential of 350 mVSCE in the 3.5 wt% sodium chloride solution. Then the propagated pits were numerically examined. By the digital image correlation method, the local strain was calculated in the pits and a relation was presented to obtain the maximum strain time. Therefore, growth direction of pitting corrosion could be estimated by having maximum strain region. Finally, by simulating the pitting corrosion process of a stress-free sample under the potential of 350 mVSCE in 3.5 wt% sodium chloride solution in COMSOL Multiphysics software, variations in the concentration of ions, electric potential, and corrosion current density were shown in the existing pit. The potential was decreased by moving in-depth and the maximum current density was found at the depth of 18 μm. Thus, without the need of advanced laboratory facilities for surface scanning and analysis, useful information from surface corrosion conditions could be obtained

Complex nonlinear behaviors such as chaotic motion have devastating effects on dynamic systems. In this study, nonlinear behavior of simply supported rectangular viscoelastic plates was examined during supersonic aerodynamics and compared with the nonlinear elastic plate. Classical plate theory was used to obtain the plate equations, and Von- Kármán strain-displacement relations were used to consider the nonlinear geometric effects. The Kelvin Voigt  model was also used to describe the viscoelastic properties and the “first-order piston theory" was used for supersonic aerodynamic flow. The equations of motion of the rectangular plate were extracted using the Lagrangian method and then, discretized by the Rayleigh-Ritz method. Solution of the equations was performed using fourth order Runge Kutta method. To investigate the dynamic behavior of the plates, the eigenvalues of the system, time history curves, phase portraits, Poincaré maps, and bifurcation diagrams were studied and analyzed. The results show that in some aspect ratios, the threshold for the occurrence of the flutter in the viscoelastic plate will be lower than that in the elastic plate. On the other hand, when the control parameter increases, complex nonlinear behavior such as chaos in the elastic plate goes simpler in the viscoelastic plate, such as periodic motion.