نشریه روش های عددی در مهندسی
سال چهل و دوم شماره 1 (تابستان 1402)

The problem of cooperative guidance of two pursuers against an evader equipped with higher maneuverability is investigated. The goal is that the distance between the evader and at least one of the pursuers becomes less than a predetermined threshold at the end of the flight time. To achieve this goal, firstly, the roles of pursuers are divided into two units, which include 1) pursuing the evader 2) Observing the evader’s scape space. Secondly, a novel cooperative guidance law based on the optimal separation of roles of the pursuers is proposed and formulated into a constrained nonlinear optimal control problem. Thirdly, the problem is solved using the Direct Collocation with Nonlinear Programming (DCNLP) method which is an optimization approach. Finally, several numerical simulations are presented to verify the effectiveness of the proposed cooperative guidance law.

Free vibration analysis of a rectangular thick sandwich plate consisting of outer homogeneous layers with saturated nonhomogeneous Functionally Graded Porous (FGP) core has been conducted. Material property in this porous core could vary along the plate thickness according to Biot’s stress theory and other related functions. Solution to this problem was based on Quasi-Three-Dimensional shear deformation theory, which results the governing differential equations and the boundary conditions of the plate model. The boundary conditions in the considered plate model were clamped-simple-simple-clamped supports, whereas in the previous studies generally Navier method is used in which simple supports is assumed for all sides of the plate. In the present study, in order to obtain our proposed numerical solution, the differential quadrature method is applied. Among advantages of this method are being simple and straightforward, having reduced computational effort compared to other numerical methods and being capable of accounting for plates with different boundary conditions. Convergence and validation of the results with respect to the grid points were first presented. The effect of different core properties such as porosity, thickness, Skempton’s coefficient, total plate thickness, and different boundary conditions on FGP sandwich plate frequencies were investigated. Application of the latest theory for free vibration analysis of FGP sandwich plates is another main advantage of the presented method compared to other recent studies.

Mixing is one of the first and necessary steps in the industrial process of rubber production. The main purpose of mixing involves combining materials, adding energy to break the molecular bonds, and combining materials with air. Executive operation is effective in the mixing quality. The present research is on the non-isothermal simulation of mixing in a Banbury mixer. Three-dimensional numerical studies, using computational fluid dynamics, have been carried out in order to use different operational parameters. The movement of the surfaces in the calculations has been considered through the sliding mesh technique, and the fluid volume method has been used in the Eulerian approach to track the interface between the rubber phase and air. The carreau-Yasuda non-Newtonian viscosity model, along with an Arrhenius formula, has been used to determine the temperature-dependent viscosity of rubber. The results of this research show that the high viscosity of rubber becomes viscous when heated. This phenomenon is especially in the narrow area between the tip of the rotor and the wall, where there is a higher shear, and this factor affects the viscosity and flow characteristics of the rubber.

Various types of dynamic instabilities in mechanical systems are one of the most important disruptive factors in such structures. Therefore, an accurate study of dynamic instability in beams, as one of the fundamental engineering structures, is of great importance. In this paper, dynamic instability problem of beams made of Functionally Graded Materials (FGM) is investigated. For this purpose, the first-order shear deformation (or the Timoshenko) beam theory with the effects of geometric nonlinearity is considered. Thus, the proposed model has the ability to determine mechanical behavior of thin and thick beams. By considering the energy functions of the system, and implementing the Hamilton’s principle, the governing equations are obtained along with different types of common boundary conditions. The Differential Quadrature Method (DQM), as one of the best-known numerical methods, is used. The nonlinear partial differential equations are written in the form of equivalent ordinary differential equations. Then, considering the harmonic responses for the system, the differential equations are converted to a set of nonlinear algebraic equations. Finally, in order to study the important parameters, various numerical examples are provided. The obtained numerical results are compared with the literature and thus, the validity of the presented formulation and solution methodology is revealed. Also, a comparative study between linear and nonlinear kinematic models shows that the importance of geometric nonlinearity of the model is quite significant.

In this article, a review of the evaluation methods of the domain integrals in the boundary element method will be presented. The emergence of domain integrals in the formulation of the boundary element method mainly originates from the inertia term in dynamic problems, body forces in static problems or the effects of material heterogeneity. There are several approaches to calculate boundary and domain integrals in boundary element methods. Choosing the type of integration method has a prominent effect on the accuracy of the numerical solution. In this research, a comprehensive review on the techniques of domain integrals computation will be presented based on two approaches, i.e. domain splitting, and converting the domain integrals to boundary ones. The review focuses primarily on the formulation of approaches without requiring domain splitting, because of their popularity. Among them, the dual reciprocity method and the radial integration method have been described as the most efficient. At the end, the details of the modified radial integration method for calculating the integrals within non-convex domains will be stated.

In this research, the free vibration of the joint of two hybrid cylindrical-conical shells have been studied, considering the continuity conditions in the joint of the two shells, based on the first order shear deformation shell theory. The equations of the joint of two shells have been extracted using the Hamilton’s principle, and solved by applying the generalized differential quadrature method under different boundary conditions. Also, hybrid shells are composed of composite layers in the core and two layers of aluminum metal at the top and bottom of the shells. In this study, the Carbon- Epoxy, Glass- Epoxy and Aramid-Epoxy composite materials are used. The results obtained in this research are compared with previous studies, and there is a very good agreement between the results. Also, the effects of cone angle of the conical shell, boundary conditions, volume fraction, circumferential mode, composite materials, variation of length to shell radius and variation of thickness to shell radius, on the natural frequency have been investigated. The results have shown that, with the increase of the cone angle of the conical shell, the dimensionless natural frequency of the joint of two cylindrical- conical shells increased. Also, with increase of the circumferential mode, the non-dimensional frequency of the structure of two joined hybrid shells, first decreased and then increased.

The Scaled Boundary Finite Element Method (SBFEM) discretizes only the boundary by using a technique for scaling the domain response onto its boundary. In this research, heat transfer problems in two-dimensional space are solved with a new approach based on combining the scaled boundary finite element method and the equilibrated basis functions. The SBFEM develops its relations in radial and circumferential coordinate systems, but only discretizes the boundary of the problem through development of a semi-analytical solution in radial direction. So the challenges of appropriate elemental grid for the solution domain, or the need for fundamental solutions of the equation, as usual in the finite element method or the boundary element method respectively, do not appear. In this research, after scaling the boundary in the scaled boundary finite element method and extracting the related equations, the equilibrated basis functions are used to approximate the semi-analytical solution in radial direction. After estimating the radial solution by the first kind Chebyshev polynomials, the weighted residual form of the governing equation is applied for approximately satisfaction. Finally, the unknown degrees of freedom of the boundary are derived, and there will be no need for the usual eigenvalue solution of the SBFEM. It will be shown that this approach benefits good accuracy and convergence rate.

The classical mechanics equations include displacement derivatives, which usually causes the inability to predict defects in damaged structures. Nowadays, in order to solve this challenge in the special conditions governing the crack tip and the discontinuities in the material, the theory of Peridynamics has been proposed to model progressive damage and rupture in cracked structures. Due to the inability of bond-based Peridynamics to predict failure in ductile materials, the main purpose of this paper is to present a new bond-based Peridynamics model with the ability to model elastoplastic materials using Variable Material Property method. For validation of the model, the results of the proposed Peridynamics model of two examples of a plate with a central hole and a plate with a central crack under tension are checked with those of ABAQUS software based on the assumptions of the continuum mechanics. The results related to von Mises stress, plastic zone size, equivalent plastic strain and displacements of the proposed model showed a good agreement as compared to the results by the finite element method, which indicates the good accuracy of the proposed model.