نشریه روش های عددی در مهندسی
سال سی و چهارم شماره 2 (زمستان 1394)

The phase transformation phenomenon due to the crystallographic change of shape memory alloys subjected to mechanical or thermal loading is very complicated. Regarding the thermo-mechanical coupling effects in shape memory alloys, in case of high loading rates, heat generation/absorption during the forward/reverse transformation, will lead in temperaturedependent variation and consequently affects its mechanical behavior. In this paper, a numerical algorithm based on the finite element method is proposed to investigate complex mechanical, thermal, and coupled behavior of shape memory alloys, including both exclusive behaviours of these alloys, that are superelasticity and shape memory effect. Several key examples are simulated and discussed to assess the efficiency and accuracy of proposed algorithm .

The main objective of this paper is to provide an applied algorithm for analyzing propeller-shaft vibrations in marine vessels. Firstly an underwater marine vehicle has been analyzed at different speed in unsteady condition using the finite volume method. Based on the results of this analysis, flow field of marine vehicle (wake of stern) and velocity inlet to the marine propeller is extracted at different times. Propeller inlet flow field is applied in the boundary element code and using this code, marine propeller has been analyzed in unsteady state. In continue, main / lateral forces and moments over the propeller are extracted. Then the data obtained from the boundary element code alongwith exact geometry of the propeller and shaft have been studied, using finite element code. Natural and forced frequency of the propeller have been determined in various modes of vibration. According to obtained data from Finite Element Method (FEM) numerical analysis, maximum displacement of propeller is for displacement of the propeller tip in forced vibration state .

Grid dispersion is one of the criteria of validating the finite element method (FEM) in simulating acoustic or elastic wave propagation. The difficulty usually arisen when using this method for simulation of wave propagation problems, roots in the discontinuous field which causes the magnitude and the direction of the wave speed vector, to vary from one element to the adjacent one. To solve this problem and improve the response accuracy, two approaches are usually suggested: changing the integration method and changing shape functions. The Finite Element iso-geometric analysis (IGA) is used in this research. In the IGA, the B-spline or non-uniform rational B-spline (NURBS) functions are used which improve the response accuracy, especially in one-dimensional structural dynamics problems. At the boundary of two adjacent elements, the degree of continuity of the shape functions used in IGA can be higher than zero. In this research, for the first time, a two dimensional grid dispersion analysis has been used for wave propagation in plane strain problems using B-spline FEM is presented. Results indicate that, for the same degree of freedom, the grid dispersion of B-spline FEM is about half of the grid dispersion of the classic FEM.

This paper presents a macro model to predict unreinforced masonry structures in plane behavior. The model is based on the concept of multilaminate theory. In the past, the method has been used to model behavior of soil, disregarding the cohesion and the tensile strength. Regarding its mathematical base, and the possibility of applying in other cases, this method is used to predict the ultimate failur load in URM structures in present study. This model is intrinsically capable of spotting induced anisotropy of brittle material such as concrete, rocks and masonry, develponig as a result of cracking. Here, the yield surface applied, consists an generalized mohr-coulomb yield surface, along with a cap model and a cut-off tensile. Comparing numerical results predicted to be obtained in non-linear analysis of masonry structures unreinforced against lateral load, with the results of ther experimental data shows capability of the model in failure analysis of URM structures.

In the present paper thecompressibleflowoftheunderwaterexplosionhasbeensimulatedusing One-fluid method along with the Eulerian-Lagrangian ALE method. Besides, the exact Riemann solver and an appropriate equation of state which is consistent with the thermodynamic behavior of water in underwater explosion, is employed. The two dimensional underwater explosion problem near a flat plate is modeled. In order to increase the accuracy of the method for simulating the wave front, the adaptive grid is used. The simulated underwater explosion results agreed well with other similar numerical simulations. The numerical results indicate the capability of the present study in simulating the physics of underwater explosion and modeling the fluctuations of explosive bubble and also predicting the creation and collapse of the caviation zone.

Existence of singular points inside the solution domain or on its boundary deteriorates the accuracy and convergence rate of numerical methods. This phenomenon usually happens due to discontinuities in the boundary conditions or abrupt changes in the domain shape. This study has focused on the solution of singular plate problems using the exponential basis functions method. In this method, unknown functions are considered as a linear combination of exponential basis functions and the coefficients are calculated by approximate satisfaction of the boundary conditions. To increase the accuracy and convergence rate in problems with singular points, a series of singular, quasi-exponential functions are added to the method’s exponential basis functions. These functions have proper discontinuity in location of the singular points and satisfy the homogenous differential equation. The results obtained from the solution of three cracked plate problems show considerable increase in the accuracy and convergence rate of the proposed method compared with the exponential basis functions method without any noticeable increase in the computational cost.

The gear systems are widely used in industry to transmit the power or change the direction of the torque. Due to the extensive usage of the gears, the detailed designing and the subsequent maintenance of these systems are more and more evident. System recognition can be achieved through modeling the system, investigating the system behavior, and comparing the results obtained through the model with the actual system behavior. Up to now, the effect of dry friction has not been taken into account in nonlinear vibration analysis and modeling of a cracked one-stage gear power transmission system. In this paper, the nonlinear vibration of a pair of cracked spur-gear system in presence of dry friction, static transmission error, clearance and time-variant mesh stiffness is investigated. To this end, the time-variant mesh stiffness of an intact tooth is calculated analytically. Then, the tooth root crack is modeled as a cracked cantilever beam. The governing nonlinear equation of motion is extracted accordingly, and in order to consider the effect of dry friction, the governing equation solved by Rung- Kutta method in three separate time spans. Finally, the frequency response and bifurcation diagrams are used to study the effect of the friction and tooth root crack on the nonlinear vibration behavior of the system.

Having two stable configurations and no need to any permanent energy sources for remaining in each of these stable states, bi-stable composite plates have gained many applications. This paper has concentrated on control and dynamic response of cross ply bi-stable composite plates ( . ). To do this, using Hamilton principle , Rayleigh-Ritz method, and a MATLAB programme specifically designed for this study, have been applied in order to extract the governing equation of motions in plates. Then, in order to control the large vibration of the cross ply bi-stable plate, a fuzzy controller was proposed using a fuzzy logic and its prformance was simulated by Simulink in Matlab environment. In order to simulate the real conditions on the controller performance, the effect of disturbances and time delay on the responses of controller were also investigated.

Utilizing one of the mesh free methods, the present paper concerns static analysis of thin plates with various geometric shapes based on the mindlin classical plate theories. In this numerical method, the domain of issue is solely expressed through a set of nods and no gridding or element is required. To express the domain of issues with various geometric shapes, first a set of nodes are defined in a standard rectangular domain , then via a three-order map with, these nodes are transferred to the main domain of the original issue; therefore plates of various geometric shapes can be analyzed. Among meshfree numerical methods, Element Free Galerkin method (EFG) is utilized here. The method is one of the weak form integral methods that uses MLS shape functions for approximation. Regarding the absence of Delta feature in MLS functions, boundary conditions cannot be imposed directly; hence the Lagrangian method is utilized to impose boundary conditions. At the end, our outputs are compared with those of analytic and finite element methods for plates, in order to validate the exactness of our solution method, and then after reliability is established, a few new examples will be solved.

The present paper studies the effect of creating a fillet on fretting fatigue strength of an axle, using different multiaxial fatigue criteria and fretting fatigue damage parameter. Finite element method is applied to obtain stress and strain in the axle and the results obtained from modeling are compared with the experimental test data available in literature. The results show that fretting fatigue strength of the axle and fracture area depends on the ratio of diameter to fillet radius. Multiaxial fatigue criteria is almost capable of estimating the fatigue strength of the axle . However; the results obtained from investigating fretting fatigue damage parameter are almost in accordance with the results of experimental data and consequently fretting fatigue damage parameter can be appropriately used as a criterion for estimating fretting fatigue strength of the axles.