نشریه روش های عددی در مهندسی
سال چهل و سوم شماره 1 (بهار 1403)

Wavelet transform, as an advanced tool for frequency analysis of waves, has various applications in different fields of engineering. The main characteristic of the wavelet transform, compared to more traditional frequency analysis tools such as the Fourier transform, is its ability to be time-frequency. In other words, by using the wavelet transform, it is possible to obtain the occurrence time of different frequencies in stable and unstable waves. In the last two decades, the use of this tool in structural and earthquake engineering has also extensively expanded. It can be said that this tool is used in structural and earthquake engineering in three main categories of frequency analysis of earthquake waves, damage detection and de-noising. In this article, wavelet theory is first explained in a way related to structural engineering and earthquakes. Then, in the next step, the important studies conducted in each of the mentioned fields are presented separately

Since deterministic topology optimization (TO) does not consider the uncertainties in the structure, including materials, loading and geometric dimensions, it may provide the optimal designs with the lowest state of reliability and safety. To  solve this problem, reliability-based topology optimization (RBTO) is used, which is actually a combination of TO methods with reliability-based design methods (RBDO) based on a mathematical framework and process. In this article, by considering four TO methods including moving iso-surface threshold (MIST), SIMP, evolutionary structural optimization-extended finite element (XFEM-ESO) and level-set (LS), and considering a constraint or objective function, an optimal volume fraction (Vf) is obtained for TO by the bisection method. Then, with the aid of mean volume fraction, TO is performed and its optimized results are applied by an advanced reliability analysis method, i.e. accelerated dynamical mean value (ADMV), taking into account the uncertainties and their standard deviations to extract the most probable probability point (MPP). Having the MPP and the constraint, the bisection algorithm is used again and the optimized volume fraction for the RBTO model, and thereby the optimal layout for the RBTO solution, is achieved. Several examples are presented to validate and highlight the optimization capability of the RBTO method using a structural model and the mentioned TO methods, and the results are compared together. Based on the results, it is shown that the combination of RBDO and TO approach is able to result in powerful, stable, safe, and reliable structures completely different from the TO results.

Interpolation and approximation are the most important parts of partial differential equation solution procedures, which significantly affect the cost and the accuracy of the results. This paper is aimed to exhaustively investigate the interpolation algorithms and trace their chronologically developments. The interpolation methods are classified based on their mathematical representation, and then surveyed separately. An abridgement of calculation steps of methods are presented and for details, the reader is referred by the main references. The usage records in applied science and engineering are included and their numerical dominance, stability and convergence rate are discussed.

Thin aluminum films have various applications in different industries because of their special properties, including low density and high ductility. Due to the progress in the manufacturing process, it is now possible to produce ultra-thin aluminum films with very low thickness, even on the nanoscale. This paper aims to numerically investigate the mechanical behavior of ultra-thin aluminum films using the molecular dynamics (MD) method. Because of the high reactivity of aluminum in the vicinity of oxygen, the representative volume elements (RVEs) of the aluminum film are simulated based on the aluminum core-alumina shell model to study the effect of different thicknesses of the surface oxide layer. In order to stabilize the atomistic RVEs under environmental conditions, the relaxation process is applied, and the total energy of the system is minimized. Then, the relaxed configuration of RVEs is analyzed under different mechanical tests, and their different mechanical parameters such as Young's modulus, bulk modulus, shear modulus, and different material characteristics are calculated at different temperatures. The accuracy of the numerical simulations is validated by comparing the results with the experimental data. Based on the MD results, analytical relations are presented to determine the different mechanical parameters of thin aluminum films as a function of the oxide layer thickness and ambient temperature. Comparison of the proposed analytical relations with the experimental data, demonstrates their capability and generalizability for the micro- and macro-size aluminum sheets.

Sandwich plates as structural members, have received a lot of attention in industrial structures and large construction projects due to their low specific weight, resistance to fatigue and high bending strength. Since Industrial structures are commonly reposed to dynamic loads, plate vibration can result in injury to structures, especially when the excitation frequency is close to the natural frequency of the structure. Therefore, nonlinear vibration analysis of plates is one of the most attended topics in the dynamics of structures. In this article, the nonlinear free vibration of sandwich plates with a viscoelastic core is studied based on von Karman's assumptions and using the First-order shear deformation theory. The viscoelastic properties of the plate core follow Boltzmann's integral law. Also, the Laplace transform is used to convert equations from the time domain to the Laplace domain. For the discretization of the equations, the finite strip numerical method is used. Finally, by numerically solving an eigenvalue problem in the Laplace-Carson domain, the nonlinear frequencies of sandwich plates with a viscoelastic core with different vibration amplitudes are calculated. The results show that, with the increase of the vibration amplitude and the coefficients of the relaxation function of the viscoelastic core, the ratio of the nonlinear frequencies decreases in this type of plates.

TThe proposal and development of time integration algorithms in hyperelastic-based plasticity or hyperelastoplasticity, are consistently required due to complex issues such as objectivity. Through the multiplicative decomposition of the deformation gradient tensor, a local configuration known as the intermediate or plastic configuration is generated alongside the reference and the current configurations. Utilizing the intermediate configuration for time integrations eliminates the need to analyze the impact of rigid rotations in the current configuration. Moreover, as the Cauchy stress is derived from parameters in the intermediate configuration, there is no necessity to assess its objectivity. By employing the multiplicative decomposition of the gradient tensor of plastic deformation, equations for kinematic hardening can be derived, eliminating the need to verify objectivity. Therefore, in this article, the algorithm for the subloading surface model, based on the intermediate configuration, is derived by adapting the von Mises model. The rationale behind employing the von Mises model lies in its simplicity compared to the subloading surface model, along with its widespread usage. Additionally, in numerical implementation, the subloading surface model is more complex than the von Mises model. Building upon this, the problem of simple shear deformation with small and large elastic strains, incorporating isotropic, kinematic, and combined hardening in plasticity, has been investigated. The obtained results have been compared with the experimental data and findings from various references. The comparison between the results presented in this article and the available data indicates agreement, suggesting the viability of employing this model in practical applications.

In the current study, transportation of the microparticles deposition through a channel has been investigated where elliptical obstacle with constant cross sectional area but different shape factors was assumed in the channel. Numerical simulation was conducted using lattice Boltzmann method, and Lagrange method was used for particle tracking. A two-dimensional and nine-velocity model was used as the network model. A curved boundary condition was applied for the obstacle boundaries. In the designed model, particles at standard condition were injected at the inlet of the channel. Gravity force, drag force, Brownian force and Soffman lift force were applied in the motion equation of the particles. The effect of shape factor as a geometrical parameter, which was defined as the ratio of the diameters of elliptical obstacle, and the flow parameters such as Reynolds’ number was examined on the particle deposition and particle scattering. Results were examined at eight different shape factors and five different Reynolds numbers .Results revealed that the change in the shape factor varies the effect of the obstacle in the flowing stream, and also changes the flow regime. This variation was obtained at different Reynolds numbers. Furthermore, changes of the shape factor associated with variations in the flow regime and deposition mechanisms, changes the forces exerted on the particles. Generally, the effect of the mentioned parameters can be interpreted based on the number of the precipitated particles.